Blog Input © Saturday, March 21, 2026, by James Pate Williams, Jr., Three Model Universes

Blog Entry Saturday March 21 2026Download
#pragma once

class UniversalModels
{
public:
	static void deSitterUniverse(
		double epsilon, double lambda, double ct,
		double A, double B, double& K);
	static void RadiationUniverse(
		double A, double epsilon,
		double deltaT, double& K);
	static void FriedmannUniverse(
		int epsilon, double M,
		double cT, double& K);
};


#include "UniversalModels.h"
#include <math.h>

void UniversalModels::deSitterUniverse(
	double epsilon, double lambda,
	double ct, double A, double B, double& K)
{
	if (lambda > 0)
	{
		if (epsilon == +1)
		{
			K = cosh(B * ct) / B;
		}

		else if (epsilon == -1)
		{
			K = sinh(B * ct) / B;
		}

		else
		{
			K = A * exp(B * ct);
		}
	}

	else if (lambda < 0)
	{
		if (epsilon == -1)
		{
			lambda = -3.0 * B * B;
			K = cos(B * ct) / B;
		}
	}
}

void UniversalModels::RadiationUniverse(
	double A, double epsilon,
	double deltaT, double& K)
{
	double c = 1.0, kappa = 1.0;

	if (epsilon == 0)
	{
		K = sqrt(2.0 * c * sqrt(kappa * A / 3.0) * deltaT);
	}

	else if (epsilon == -1)
	{
		K = sqrt(c * c * pow(deltaT, 2.0) + 2 * c *
			sqrt(kappa * A / 3.0) * deltaT);
	}

	else if (epsilon == +1)
	{
		K = sqrt(-c * c * pow(deltaT, 2.0) + 2 * c *
			sqrt(kappa * A / 3.0) * deltaT);
	}
}

void UniversalModels::FriedmannUniverse(
	int epsilon, double M, double cT, double& K)
{
	if (epsilon == 0)
	{
		K = M * cT * cT / 12.0;
	}

	else if (epsilon == -1)
	{
		K = M * (cosh(cT) - 1.0) / 6.0;
	}

	else if (epsilon == +1)
	{
		K = M * (1.0 - cos(cT)) / 6.0;
	}
}


// ModelUniverses.cpp (c) Thursday, March 19, 2026
// by James Pate Williams, Jr., BA, BS, MSwE, PhD
// Reference: "General Relativity An Introduction
// to the theory of the gravitational field "
// (c) 1982 by Hans Stephani translated by Martin
// Pollack and John Stewart

#include "framework.h"
#include "ModelUniverses.h"
#include "UniversalModels.h"
#include <math.h>
#include <string>
#include <vector>

#define MAX_LOADSTRING 100

typedef struct tagPoint2dDeSitter
{
    double ct, K;
} Point2dDeSitter, * PPoint2dDeSitter;

typedef struct tagPoint2dRadiation
{
    double deltaT, K;
} Point2dRadiation, * PPoint2dRadiation;

typedef struct tagPoint2dFriedmann
{
    double cT, K;
} Point2dFriedmann, * PPoint2dFriedmann;


// Global Variables:
HINSTANCE hInst;                                // current instance
WCHAR szTitle[MAX_LOADSTRING];                  // The title bar text
WCHAR szWindowClass[MAX_LOADSTRING];            // the main window class name
bool deSitter, radiation, friedmann;            // universal model type
std::wstring fTitle, xTitle, yTitle;            // graph titles
std::vector<Point2dDeSitter> pointsDeSitter;    // graph points
std::vector<Point2dRadiation> pointsRadiation;  // graph points
std::vector<Point2dFriedmann> pointsFriedmann;  // graph points

// Forward declarations of functions included in this code module:
ATOM                MyRegisterClass(HINSTANCE hInstance);
BOOL                InitInstance(HINSTANCE, int);
LRESULT CALLBACK    WndProc(HWND, UINT, WPARAM, LPARAM);
INT_PTR CALLBACK    About(HWND, UINT, WPARAM, LPARAM);
INT_PTR CALLBACK    DataInputDialogDeSitter(HWND, UINT, WPARAM, LPARAM);
INT_PTR CALLBACK    DrawGraphDialogDeSitter(HWND, UINT, WPARAM, LPARAM);
INT_PTR CALLBACK    DataInputDialogRadiation(HWND, UINT, WPARAM, LPARAM);
INT_PTR CALLBACK    DrawGraphDialogRadiation(HWND, UINT, WPARAM, LPARAM);
INT_PTR CALLBACK    DataInputDialogFriedmann(HWND, UINT, WPARAM, LPARAM);
INT_PTR CALLBACK    DrawGraphDialogFriedmann(HWND, UINT, WPARAM, LPARAM);

int APIENTRY wWinMain(_In_ HINSTANCE hInstance,
                     _In_opt_ HINSTANCE hPrevInstance,
                     _In_ LPWSTR    lpCmdLine,
                     _In_ int       nCmdShow)
{
    UNREFERENCED_PARAMETER(hPrevInstance);
    UNREFERENCED_PARAMETER(lpCmdLine);

    // TODO: Place code here.

    // Initialize global strings
    LoadStringW(hInstance, IDS_APP_TITLE, szTitle, MAX_LOADSTRING);
    LoadStringW(hInstance, IDC_MODELUNIVERSES, szWindowClass, MAX_LOADSTRING);
    MyRegisterClass(hInstance);

    // Perform application initialization:
    if (!InitInstance (hInstance, nCmdShow))
    {
        return FALSE;
    }

    HACCEL hAccelTable = LoadAccelerators(hInstance, MAKEINTRESOURCE(IDC_MODELUNIVERSES));

    MSG msg;

    // Main message loop:
    while (GetMessage(&msg, nullptr, 0, 0))
    {
        if (!TranslateAccelerator(msg.hwnd, hAccelTable, &msg))
        {
            TranslateMessage(&msg);
            DispatchMessage(&msg);
        }
    }

    return (int) msg.wParam;
}

//
//  FUNCTION: MyRegisterClass()
//
//  PURPOSE: Registers the window class.
//
ATOM MyRegisterClass(HINSTANCE hInstance)
{
    WNDCLASSEXW wcex = { 0 };

    wcex.cbSize = sizeof(WNDCLASSEX);

    wcex.style          = CS_HREDRAW | CS_VREDRAW;
    wcex.lpfnWndProc    = WndProc;
    wcex.cbClsExtra     = 0;
    wcex.cbWndExtra     = 0;
    wcex.hInstance      = hInstance;
    wcex.hIcon          = LoadIcon(hInstance, MAKEINTRESOURCE(IDI_MODELUNIVERSES));
    wcex.hCursor        = LoadCursor(nullptr, IDC_ARROW);
    wcex.hbrBackground  = (HBRUSH)(COLOR_WINDOW+1);
    wcex.lpszMenuName   = MAKEINTRESOURCEW(IDC_MODELUNIVERSES);
    wcex.lpszClassName  = szWindowClass;
    wcex.hIconSm        = LoadIcon(wcex.hInstance, MAKEINTRESOURCE(IDI_SMALL));

    return RegisterClassExW(&wcex);
}

//
//   FUNCTION: InitInstance(HINSTANCE, int)
//
//   PURPOSE: Saves instance handle and creates main window
//
//   COMMENTS:
//
//        In this function, we save the instance handle in a global variable and
//        create and display the main program window.
//
BOOL InitInstance(HINSTANCE hInstance, int nCmdShow)
{
   hInst = hInstance; // Store instance handle in our global variable

   HWND hWnd = CreateWindowW(szWindowClass, szTitle, WS_OVERLAPPEDWINDOW,
      CW_USEDEFAULT, 0, CW_USEDEFAULT, 0, nullptr, nullptr, hInstance, nullptr);

   if (!hWnd)
   {
      return FALSE;
   }

   ShowWindow(hWnd, nCmdShow);
   UpdateWindow(hWnd);

   return TRUE;
}

//
//  FUNCTION: WndProc(HWND, UINT, WPARAM, LPARAM)
//
//  PURPOSE: Processes messages for the main window.
//
//  WM_COMMAND  - process the application menu
//  WM_PAINT    - Paint the main window
//  WM_DESTROY  - post a quit message and return
//
//
LRESULT CALLBACK WndProc(HWND hWnd, UINT message, WPARAM wParam, LPARAM lParam)
{
    switch (message)
    {
    case WM_COMMAND:
        {
            int wmId = LOWORD(wParam);
            // Parse the menu selections:
            switch (wmId)
            {
            case IDM_ABOUT:
                DialogBox(hInst, MAKEINTRESOURCE(IDD_ABOUTBOX), hWnd, About);
                break;
            case IDM_DE_SITTER:
                deSitter = true;
                fTitle = L"de Sitter Universe";
                xTitle = L"Bct";
                yTitle = L"K";
                DialogBox(hInst, MAKEINTRESOURCE(IDD_DATA_INPUT_DIALOG_DE_SITTER), 
                    hWnd, DataInputDialogDeSitter);
                break;
            case IDM_RADIATION:
                radiation = true;
                fTitle = L"Radiation Universe";
                xTitle = L"t - t0";
                yTitle = L"K";
                DialogBox(hInst, MAKEINTRESOURCE(IDD_DATA_INPUT_DIALOG_RADIATION), hWnd,
                    DataInputDialogRadiation);
                break;
            case IDM_FRIEDMANN:
                friedmann = true;
                fTitle = L"Friedmann Universe";
                xTitle = L"cT";
                yTitle = L"K";
                DialogBox(hInst, MAKEINTRESOURCE(IDD_DATA_INPUT_DIALOG_FRIEDMANN), hWnd,
                    DataInputDialogFriedmann);
                break;
            case IDM_EXIT:
                DestroyWindow(hWnd);
                break;
            default:
                return DefWindowProc(hWnd, message, wParam, lParam);
            }
        }
        break;
    case WM_PAINT:
        {
            PAINTSTRUCT ps;
            HDC hdc = BeginPaint(hWnd, &ps);
            // TODO: Add any drawing code that uses hdc here...
            EndPaint(hWnd, &ps);
        }
        break;
    case WM_DESTROY:
        PostQuitMessage(0);
        break;
    default:
        return DefWindowProc(hWnd, message, wParam, lParam);
    }
    return 0;
}

// Message handler for about box.
INT_PTR CALLBACK About(HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam)
{
    UNREFERENCED_PARAMETER(lParam);
    switch (message)
    {
    case WM_INITDIALOG:
        return (INT_PTR)TRUE;

    case WM_COMMAND:
        if (LOWORD(wParam) == IDOK || LOWORD(wParam) == IDCANCEL)
        {
            EndDialog(hDlg, LOWORD(wParam));
            return (INT_PTR)TRUE;
        }
        break;
    }
    return (INT_PTR)FALSE;
}

INT_PTR CALLBACK DataInputDialogDeSitter(
    HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam)
{
    UNREFERENCED_PARAMETER(lParam);
    static WCHAR data[128] = L"";
    static HWND hCombo_A = GetDlgItem(hDlg, IDC_COMBO_A_1);
    static HWND hCombo_B = GetDlgItem(hDlg, IDC_COMBO_B);
    static HWND hCombo_ct = GetDlgItem(hDlg, IDC_COMBO_CT);
    static HWND hCombo_epsilon = GetDlgItem(hDlg, IDC_COMBO_EPSILON_1);
    static HWND hCombo_lambda = GetDlgItem(hDlg, IDC_COMBO_LAMBDA);

    switch (message)
    {
    case WM_INITDIALOG:
        SendDlgItemMessage(hDlg, IDC_COMBO_A_1, CB_ADDSTRING, 0, (LPARAM)L"1");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_1, CB_ADDSTRING, 0, (LPARAM)L"2");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_1, CB_ADDSTRING, 0, (LPARAM)L"3");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_1, CB_ADDSTRING, 0, (LPARAM)L"4");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_1, CB_ADDSTRING, 0, (LPARAM)L"5");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_1, CB_ADDSTRING, 0, (LPARAM)L"6");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_1, CB_ADDSTRING, 0, (LPARAM)L"7");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_1, CB_ADDSTRING, 0, (LPARAM)L"8");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_1, CB_ADDSTRING, 0, (LPARAM)L"9");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_1, CB_ADDSTRING, 0, (LPARAM)L"10");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_1, CB_SETCURSEL, 0, 0);
        SendDlgItemMessage(hDlg, IDC_COMBO_B, CB_ADDSTRING, 0, (LPARAM)L"1");
        SendDlgItemMessage(hDlg, IDC_COMBO_B, CB_ADDSTRING, 0, (LPARAM)L"2");
        SendDlgItemMessage(hDlg, IDC_COMBO_B, CB_ADDSTRING, 0, (LPARAM)L"3");
        SendDlgItemMessage(hDlg, IDC_COMBO_B, CB_ADDSTRING, 0, (LPARAM)L"4");
        SendDlgItemMessage(hDlg, IDC_COMBO_B, CB_ADDSTRING, 0, (LPARAM)L"5");
        SendDlgItemMessage(hDlg, IDC_COMBO_B, CB_ADDSTRING, 0, (LPARAM)L"6");
        SendDlgItemMessage(hDlg, IDC_COMBO_B, CB_ADDSTRING, 0, (LPARAM)L"7");
        SendDlgItemMessage(hDlg, IDC_COMBO_B, CB_ADDSTRING, 0, (LPARAM)L"8");
        SendDlgItemMessage(hDlg, IDC_COMBO_B, CB_ADDSTRING, 0, (LPARAM)L"9");
        SendDlgItemMessage(hDlg, IDC_COMBO_B, CB_ADDSTRING, 0, (LPARAM)L"10");
        SendDlgItemMessage(hDlg, IDC_COMBO_B, CB_SETCURSEL, 0, 0);
        SendDlgItemMessage(hDlg, IDC_COMBO_CT, CB_ADDSTRING, 0, (LPARAM)L"1");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT, CB_ADDSTRING, 0, (LPARAM)L"2");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT, CB_ADDSTRING, 0, (LPARAM)L"3");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT, CB_ADDSTRING, 0, (LPARAM)L"4");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT, CB_ADDSTRING, 0, (LPARAM)L"5");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT, CB_ADDSTRING, 0, (LPARAM)L"6");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT, CB_ADDSTRING, 0, (LPARAM)L"7");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT, CB_ADDSTRING, 0, (LPARAM)L"8");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT, CB_ADDSTRING, 0, (LPARAM)L"9");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT, CB_ADDSTRING, 0, (LPARAM)L"10");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT, CB_SETCURSEL, 0, 0);
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_1, CB_ADDSTRING, 0, (LPARAM)L"-1");
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_1, CB_ADDSTRING, 0, (LPARAM)L"0");
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_1, CB_ADDSTRING, 0, (LPARAM)L"+1");
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_1, CB_SETCURSEL, 0, 0);
        SendDlgItemMessage(hDlg, IDC_COMBO_LAMBDA, CB_ADDSTRING, 0, (LPARAM)L"-5");
        SendDlgItemMessage(hDlg, IDC_COMBO_LAMBDA, CB_ADDSTRING, 0, (LPARAM)L"-4");
        SendDlgItemMessage(hDlg, IDC_COMBO_LAMBDA, CB_ADDSTRING, 0, (LPARAM)L"-3");
        SendDlgItemMessage(hDlg, IDC_COMBO_LAMBDA, CB_ADDSTRING, 0, (LPARAM)L"-2");
        SendDlgItemMessage(hDlg, IDC_COMBO_LAMBDA, CB_ADDSTRING, 0, (LPARAM)L"-1");
        SendDlgItemMessage(hDlg, IDC_COMBO_LAMBDA, CB_ADDSTRING, 0, (LPARAM)L"1");
        SendDlgItemMessage(hDlg, IDC_COMBO_LAMBDA, CB_ADDSTRING, 0, (LPARAM)L"2");
        SendDlgItemMessage(hDlg, IDC_COMBO_LAMBDA, CB_ADDSTRING, 0, (LPARAM)L"3");
        SendDlgItemMessage(hDlg, IDC_COMBO_LAMBDA, CB_ADDSTRING, 0, (LPARAM)L"4");
        SendDlgItemMessage(hDlg, IDC_COMBO_LAMBDA, CB_ADDSTRING, 0, (LPARAM)L"5");
        SendDlgItemMessage(hDlg, IDC_COMBO_LAMBDA, CB_SETCURSEL, 0, 0);
        return (INT_PTR)TRUE;
    case WM_COMMAND:
    {
        if (LOWORD(wParam) == IDC_BUTTON_DRAW_DE_SITTER)
        {
            char line[128] = "";
            GetDlgItemTextA(hDlg, IDC_COMBO_A_1, line, 128);
            double A = atof(line);
            GetDlgItemTextA(hDlg, IDC_COMBO_B, line, 128);
            double B = atof(line);
            GetDlgItemTextA(hDlg, IDC_COMBO_CT, line, 128);
            double CT = atof(line);
            int epsilon = GetDlgItemInt(hDlg, IDC_COMBO_EPSILON_1, FALSE, TRUE);
            GetDlgItemTextA(hDlg, IDC_COMBO_LAMBDA, line, 128);
            double lambda = atof(line);
			double ct = 0.0, K = 0.0;
			double delta_ct = CT / 256.0;
			int index = 0;

            pointsDeSitter.clear();

			while (ct <= CT)
			{
                UniversalModels::deSitterUniverse(
                    epsilon, lambda, ct, A, B, K);
				Point2dDeSitter pt = { 0 };
				pt.ct = ct;
				pt.K = K;
				ct += delta_ct;
                pointsDeSitter.push_back(pt);
			}

			DialogBox(hInst, MAKEINTRESOURCE(IDD_DRAW_GRAPH_DIALOG_DE_SITTER),
				hDlg, DrawGraphDialogDeSitter);
            return (INT_PTR)TRUE;
        }

        else if (LOWORD(wParam) == IDCANCEL)
        {
            EndDialog(hDlg, LOWORD(wParam));
            return (INT_PTR)TRUE;
        }
    }
    }

    return (INT_PTR)FALSE;
}

static void FindMinMaxDeSitter(
    double& xmin,
    double& xmax,
    double& ymin,
    double& ymax)
{
    xmin = pointsDeSitter[0].ct;
    xmax = pointsDeSitter[0].ct;
    ymin = pointsDeSitter[0].K;
    ymax = pointsDeSitter[0].K;

    for (int i = 1; i < pointsDeSitter.size(); i++)
    {
        Point2dDeSitter pt = pointsDeSitter[i];

        if (pt.ct < xmin)
            xmin = pt.ct;
        if (pt.ct > xmax)
            xmax = pt.ct;
        if (pt.K < ymin)
            ymin = pt.K;
        if (pt.K > ymax)
            ymax = pt.K;
    }
}

static void DrawTitles(
    HDC hdc, RECT clientRect,
    const std::wstring& fTitle,
    const std::wstring& xTitle,
    const std::wstring& yTitle,
    int sx0, int sx1, int sy0, int sy1)
{
    HFONT hCustomFont = CreateFont(
        -MulDiv(10, GetDeviceCaps(hdc, LOGPIXELSY), 72), // Height in logical units
        0,                      // Width (0 = default)
        0,                      // Escapement
        0,                      // Orientation
        FW_BOLD,                // Weight (700 = bold)
        FALSE,                  // Italic
        FALSE,                  // Underline
        FALSE,                  // StrikeOut
        DEFAULT_CHARSET,        // Charset
        OUT_DEFAULT_PRECIS,     // Output precision
        CLIP_DEFAULT_PRECIS,    // Clipping precision
        DEFAULT_QUALITY,        // Quality
        FIXED_PITCH | FF_MODERN,// Pitch and family
        L"Courier New"          // Typeface name
    );

    HFONT hOldFont = (HFONT)SelectObject(hdc, hCustomFont);

    SIZE sz;
    int width = clientRect.right - clientRect.left;

    // Title: fTitle
    GetTextExtentPoint32W(hdc, fTitle.c_str(), (int)fTitle.length(), &sz);
    int w = sz.cx;
    int h = sz.cy;
    TextOutW(hdc, (width - w) / 2, h, fTitle.c_str(), (int)fTitle.length());
    // draw x-axis title
    GetTextExtentPoint32W(hdc, xTitle.c_str(), (int)xTitle.length(), &sz);
    w = sz.cx;
    TextOutW(hdc, sx0 + (sx1 - sx0 - w) / 2, sy1 + 2 * h, 
        xTitle.c_str(), (int)xTitle.length());
    // draw y-axis title
    GetTextExtentPoint32W(hdc, yTitle.c_str(), (int)yTitle.length(), &sz);
    w = sz.cx;
    TextOutW(hdc, sx1 + w / 5, sy0 + (sy1 - sy0) / 2 - h / 2, 
        yTitle.c_str(), (int)yTitle.length());
    SelectObject(hdc, hOldFont); // Restore original font
}

static void DrawFormattedText(HDC hdc, char loctext[], RECT rect)
{
    // Draw the text with formatting options
    DrawTextA(hdc, loctext, (int)strlen(loctext), &rect, DT_SINGLELINE | DT_NOCLIP);
}

static INT_PTR CALLBACK DrawGraphDialogDeSitter(
    HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam)
{
    UNREFERENCED_PARAMETER(lParam);
    char line[256] = "";
    switch (message)
    {
    case WM_INITDIALOG:
        strcpy_s(line, 256, "Drawing Dialog deSitter Universe");
        SetWindowTextA(hDlg, line);
        return (INT_PTR)TRUE;
    case WM_COMMAND:
        if (LOWORD(wParam) == IDOK || LOWORD(wParam) == IDCANCEL)
        {
            EndDialog(hDlg, LOWORD(wParam));
            return (INT_PTR)TRUE;
        }
        break;
    case WM_PAINT:
        double xmax = 0, xmin = 0;
        double ymax = 0, ymin = 0;
        FindMinMaxDeSitter(xmin, xmax, ymin, ymax);
        double h = 0, pi = 0, plm = 0, theta = 0;
        float xSpan = (float)(xmax - xmin);
        float ySpan = (float)(ymax - ymin);
        RECT rect = { };
        GetClientRect(hDlg, &rect);
        float width = (float)(rect.right - rect.left + 1);
        float height = (float)(rect.bottom - rect.top - 32 + 1);
        float sx0 = 2.0f * width / 16.0f;
        float sx1 = 14.0f * width / 16.0f;
        float sy0 = 2.0f * height / 16.0f;
        float sy1 = 14.0f * height / 16.0f;
        float deltaX = xSpan / 8.0f;
        float deltaY = ySpan / 8.0f;
        float xSlope = (sx1 - sx0) / xSpan;
        float xInter = (float)(sx0 - xSlope * xmin);
        float ySlope = (sy0 - sy1) / ySpan;
        float yInter = (float)(sy0 - ySlope * ymax);
        float px = 0, py = 0, sx = 0, sy = 0;
        PAINTSTRUCT ps;
        POINT wPt = { };
        HDC hdc = BeginPaint(hDlg, &ps);
        int i = 0;
        float x = (float)xmin;
        float y = (float)ymax;
        DrawTitles(hdc, rect, fTitle, xTitle, yTitle,
            (int)sx0, (int)sx1, (int)sy0, (int)sy1);
        px = (float)pointsDeSitter[0].ct;
        py = (float)pointsDeSitter[0].K;
        sx = xSlope * px + xInter;
        sy = ySlope * py + yInter;
        MoveToEx(hdc, (int)sx, (int)sy0, &wPt);

        while (i <= 8)
        {
            sx = xSlope * x + xInter;
            wPt.x = wPt.y = 0;
            MoveToEx(hdc, (int)sx, (int)sy0, &wPt);
            LineTo(hdc, (int)sx, (int)sy1);
            char numberStr[128] = "";
            sprintf_s(numberStr, 128, "%5.4lf", x);
            SIZE size = { };
            GetTextExtentPoint32A(
                hdc,
                numberStr,
                (int)strlen(numberStr),
                &size);
            RECT textRect = { };
            textRect.left = (long)(sx - size.cx / 2.0f);
            textRect.right = (long)(sx + size.cx / 2.0f);
            textRect.top = (long)sy1;
            textRect.bottom = (long)(sy1 + size.cy / 2.0f);
            DrawFormattedText(hdc, numberStr, textRect);
            x += deltaX;
            i++;
        }

        i = 0;
        y = (float)ymin;

        while (i <= 8)
        {
            sy = ySlope * y + yInter;
            wPt.x = wPt.y = 0;
            MoveToEx(hdc, (int)sx0, (int)sy, &wPt);
            LineTo(hdc, (int)sx, (int)sy);

            if (i != 0)
            {
                char numberStr[128] = "";
                sprintf_s(numberStr, 128, "%+5.3lf", y);
                SIZE size = { };
                GetTextExtentPoint32A(
                    hdc,
                    numberStr,
                    (int)strlen(numberStr),
                    &size);
                RECT textRect = { 0 };
                textRect.left = (long)(sx0 - size.cx - size.cx / 2.0f);
                textRect.right = (long)(sx0 - size.cx / 2.0f);
                textRect.top = (long)(sy - size.cy / 2.0f);
                textRect.bottom = (long)(sy + size.cy / 2.0f);
                DrawFormattedText(hdc, numberStr, textRect);
            }

            y += deltaY;
            i++;
        }

        HGDIOBJ bPenNew = NULL;
        HGDIOBJ hPenOld = NULL;

        bPenNew = CreatePen(PS_SOLID, 2, RGB(0, 0, 255));
        hPenOld = SelectObject(hdc, bPenNew);

        HRGN clipRegion = CreateRectRgn(
            (int)sx0, (int)sy0,              // Left, Top
            (int)(sx1), (int)(sy1)           // Right, Bottom
        );

        // Apply clipping region

        SelectClipRgn(hdc, clipRegion);

        px = (float)pointsDeSitter[0].ct;
        py = (float)pointsDeSitter[0].K;
        sx = xSlope * px + xInter;
        sy = ySlope * py + yInter;
        wPt.x = wPt.y = 0;
        MoveToEx(hdc, (int)sx, (int)sy, &wPt);

        for (size_t j = 1; j < pointsDeSitter.size(); j++)
        {
            px = (float)pointsDeSitter[j].ct;
            py = (float)pointsDeSitter[j].K;
            sx = xSlope * px + xInter;
            sy = ySlope * py + yInter;
            LineTo(hdc, (int)sx, (int)sy);
        }

        DeleteObject(bPenNew);
        bPenNew = NULL;

        SelectObject(hdc, hPenOld);
        DeleteObject(clipRegion);
        EndPaint(hDlg, &ps);
        return (INT_PTR)TRUE;
    }

    return (INT_PTR)FALSE;
}

INT_PTR CALLBACK DataInputDialogRadiation(
    HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam)
{
    UNREFERENCED_PARAMETER(lParam);
    static WCHAR data[128] = L"";
    static HWND hCombo_B = GetDlgItem(hDlg, IDC_COMBO_B);
    static HWND hCombo_ct = GetDlgItem(hDlg, IDC_COMBO_DELTA_T);
    static HWND hCombo_epsilon = GetDlgItem(hDlg, IDC_COMBO_EPSILON_2);
    static HWND hCombo_lambda = GetDlgItem(hDlg, IDC_COMBO_LAMBDA);

    switch (message)
    {
    case WM_INITDIALOG:
        SendDlgItemMessage(hDlg, IDC_COMBO_A_2, CB_ADDSTRING, 0, (LPARAM)L"1e1");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_2, CB_ADDSTRING, 0, (LPARAM)L"1e2");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_2, CB_ADDSTRING, 0, (LPARAM)L"1e3");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_2, CB_ADDSTRING, 0, (LPARAM)L"1e4");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_2, CB_ADDSTRING, 0, (LPARAM)L"1e5");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_2, CB_ADDSTRING, 0, (LPARAM)L"6");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_2, CB_ADDSTRING, 0, (LPARAM)L"7");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_2, CB_ADDSTRING, 0, (LPARAM)L"8");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_2, CB_ADDSTRING, 0, (LPARAM)L"9");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_2, CB_ADDSTRING, 0, (LPARAM)L"10");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_2, CB_SETCURSEL, 0, 0);
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_ADDSTRING, 0, (LPARAM)L"1.0e-5");
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_ADDSTRING, 0, (LPARAM)L"1.0e-4");
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_ADDSTRING, 0, (LPARAM)L"1.0e-3");
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_ADDSTRING, 0, (LPARAM)L"1.0e-2");
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_ADDSTRING, 0, (LPARAM)L"1.0e-1");
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_ADDSTRING, 0, (LPARAM)L"1.0e+0");
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_ADDSTRING, 0, (LPARAM)L"1.0e+1");
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_ADDSTRING, 0, (LPARAM)L"1.0e+2");
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_ADDSTRING, 0, (LPARAM)L"1.0e+3");
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_ADDSTRING, 0, (LPARAM)L"1.0e+4");
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_ADDSTRING, 0, (LPARAM)L"1.0e+5");
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_SETCURSEL, 0, 0);
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_2, CB_ADDSTRING, 0, (LPARAM)L"-1");
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_2, CB_ADDSTRING, 0, (LPARAM)L"0");
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_2, CB_ADDSTRING, 0, (LPARAM)L"+1");
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_2, CB_SETCURSEL, 0, 0);
        return (INT_PTR)TRUE;
    case WM_COMMAND:
    {
        if (LOWORD(wParam) == IDC_BUTTON_DRAW_RADIATION)
        {
            char line[128] = "";
            GetDlgItemTextA(hDlg, IDC_COMBO_A_2, line, 128);
            double A = atof(line);
            GetDlgItemTextA(hDlg, IDC_COMBO_DELTA_T, line, 128);
            double deltaT = atof(line);
            int epsilon = GetDlgItemInt(hDlg, IDC_COMBO_EPSILON_2, FALSE, TRUE);
            double step = deltaT / 256.0, t = 0.0, K = 0.0;
            int index = 0;

            pointsRadiation.clear();

            while (t <= deltaT)
            {
                UniversalModels::RadiationUniverse(
                    A, epsilon, t, K);
                Point2dRadiation pt = { 0 };
                pt.deltaT = t;
                pt.K = K;
                t += step;
                pointsRadiation.push_back(pt);
            }

            DialogBox(hInst, MAKEINTRESOURCE(IDD_DRAW_GRAPH_DIALOG_RADIATION),
                hDlg, DrawGraphDialogRadiation);
            return (INT_PTR)TRUE;
        }

        else if (LOWORD(wParam) == IDCANCEL)
        {
            EndDialog(hDlg, LOWORD(wParam));
            return (INT_PTR)TRUE;
        }
    }
    }

    return (INT_PTR)FALSE;
}

static void FindMinMaxRadiation(
    double& xmin,
    double& xmax,
    double& ymin,
    double& ymax)
{
    xmin = pointsRadiation[0].deltaT;
    xmax = pointsRadiation[0].deltaT;
    ymin = pointsRadiation[0].K;
    ymax = pointsRadiation[0].K;

    for (int i = 1; i < pointsRadiation.size(); i++)
    {
        Point2dRadiation pt = pointsRadiation[i];

        if (pt.deltaT < xmin)
            xmin = pt.deltaT;
        if (pt.deltaT > xmax)
            xmax = pt.deltaT;
        if (pt.K < ymin)
            ymin = pt.K;
        if (pt.K > ymax)
            ymax = pt.K;
    }
}

static INT_PTR CALLBACK DrawGraphDialogRadiation(
    HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam)
{
    UNREFERENCED_PARAMETER(lParam);
    char line[256] = "";
    switch (message)
    {
    case WM_INITDIALOG:
        strcpy_s(line, 256, "Drawing Dialog Radiation Universe");
        SetWindowTextA(hDlg, line);
        return (INT_PTR)TRUE;
    case WM_COMMAND:
        if (LOWORD(wParam) == IDOK || LOWORD(wParam) == IDCANCEL)
        {
            EndDialog(hDlg, LOWORD(wParam));
            return (INT_PTR)TRUE;
        }
        break;
    case WM_PAINT:
        double xmax = 0, xmin = 0;
        double ymax = 0, ymin = 0;
        FindMinMaxRadiation(xmin, xmax, ymin, ymax);
        double h = 0, pi = 0, plm = 0, theta = 0;
        float xSpan = (float)(xmax - xmin);
        float ySpan = (float)(ymax - ymin);
        RECT rect = { };
        GetClientRect(hDlg, &rect);
        float width = (float)(rect.right - rect.left + 1);
        float height = (float)(rect.bottom - rect.top - 32 + 1);
        float sx0 = 2.0f * width / 16.0f;
        float sx1 = 14.0f * width / 16.0f;
        float sy0 = 2.0f * height / 16.0f;
        float sy1 = 14.0f * height / 16.0f;
        float deltaX = xSpan / 8.0f;
        float deltaY = ySpan / 8.0f;
        float xSlope = (sx1 - sx0) / xSpan;
        float xInter = (float)(sx0 - xSlope * xmin);
        float ySlope = (sy0 - sy1) / ySpan;
        float yInter = (float)(sy0 - ySlope * ymax);
        float px = 0, py = 0, sx = 0, sy = 0;
        PAINTSTRUCT ps;
        POINT wPt = { };
        HDC hdc = BeginPaint(hDlg, &ps);
        int i = 0;
        float x = (float)xmin;
        float y = (float)ymax;
        DrawTitles(hdc, rect, fTitle, xTitle, yTitle,
            (int)sx0, (int)sx1, (int)sy0, (int)sy1);
        px = (float)pointsRadiation[0].deltaT;
        py = (float)pointsRadiation[0].K;
        sx = xSlope * px + xInter;
        sy = ySlope * py + yInter;
        MoveToEx(hdc, (int)sx, (int)sy0, &wPt);

        while (i <= 8)
        {
            sx = xSlope * x + xInter;
            wPt.x = wPt.y = 0;
            MoveToEx(hdc, (int)sx, (int)sy0, &wPt);
            LineTo(hdc, (int)sx, (int)sy1);
            char numberStr[128] = "";
            sprintf_s(numberStr, 128, "%5.4lf", x);
            SIZE size = { };
            GetTextExtentPoint32A(
                hdc,
                numberStr,
                (int)strlen(numberStr),
                &size);
            RECT textRect = { };
            textRect.left = (long)(sx - size.cx / 2.0f);
            textRect.right = (long)(sx + size.cx / 2.0f);
            textRect.top = (long)sy1;
            textRect.bottom = (long)(sy1 + size.cy / 2.0f);
            DrawFormattedText(hdc, numberStr, textRect);
            x += deltaX;
            i++;
        }

        i = 0;
        y = (float)ymin;

        while (i <= 8)
        {
            sy = ySlope * y + yInter;
            wPt.x = wPt.y = 0;
            MoveToEx(hdc, (int)sx0, (int)sy, &wPt);
            LineTo(hdc, (int)sx, (int)sy);

            if (i != 0)
            {
                char numberStr[128] = "";
                sprintf_s(numberStr, 128, "%+5.3lf", y);
                SIZE size = { };
                GetTextExtentPoint32A(
                    hdc,
                    numberStr,
                    (int)strlen(numberStr),
                    &size);
                RECT textRect = { 0 };
                textRect.left = (long)(sx0 - size.cx - size.cx / 2.0f);
                textRect.right = (long)(sx0 - size.cx / 2.0f);
                textRect.top = (long)(sy - size.cy / 2.0f);
                textRect.bottom = (long)(sy + size.cy / 2.0f);
                DrawFormattedText(hdc, numberStr, textRect);
            }

            y += deltaY;
            i++;
        }

        HGDIOBJ bPenNew = NULL;
        HGDIOBJ hPenOld = NULL;

        bPenNew = CreatePen(PS_SOLID, 2, RGB(0, 0, 255));
        hPenOld = SelectObject(hdc, bPenNew);

        HRGN clipRegion = CreateRectRgn(
            (int)sx0, (int)sy0,              // Left, Top
            (int)(sx1), (int)(sy1)           // Right, Bottom
        );

        // Apply clipping region

        SelectClipRgn(hdc, clipRegion);

        px = (float)pointsRadiation[0].deltaT;
        py = (float)pointsRadiation[0].K;
        sx = xSlope * px + xInter;
        sy = ySlope * py + yInter;
        wPt.x = wPt.y = 0;
        MoveToEx(hdc, (int)sx, (int)sy, &wPt);

        for (size_t j = 1; j < pointsRadiation.size(); j++)
        {
            px = (float)pointsRadiation[j].deltaT;
            py = (float)pointsRadiation[j].K;
            sx = xSlope * px + xInter;
            sy = ySlope * py + yInter;
            LineTo(hdc, (int)sx, (int)sy);
        }

        DeleteObject(bPenNew);
        bPenNew = NULL;

        SelectObject(hdc, hPenOld);
        DeleteObject(clipRegion);
        EndPaint(hDlg, &ps);
        return (INT_PTR)TRUE;
    }

    return (INT_PTR)FALSE;
}

INT_PTR CALLBACK DataInputDialogFriedmann(
    HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam)
{
    UNREFERENCED_PARAMETER(lParam);
    static WCHAR data[128] = L"";
    static HWND hCombo_M = GetDlgItem(hDlg, IDC_COMBO_M);
    static HWND hCombo_CT1 = GetDlgItem(hDlg, IDC_COMBO_CT1);
    static HWND hCombo_epsilon = GetDlgItem(hDlg, IDC_COMBO_EPSILON_3);

    switch (message)
    {
    case WM_INITDIALOG:
        SendDlgItemMessage(hDlg, IDC_COMBO_M, CB_ADDSTRING, 0, (LPARAM)L"1");
        SendDlgItemMessage(hDlg, IDC_COMBO_M, CB_ADDSTRING, 0, (LPARAM)L"2");
        SendDlgItemMessage(hDlg, IDC_COMBO_M, CB_ADDSTRING, 0, (LPARAM)L"3");
        SendDlgItemMessage(hDlg, IDC_COMBO_M, CB_ADDSTRING, 0, (LPARAM)L"4");
        SendDlgItemMessage(hDlg, IDC_COMBO_M, CB_ADDSTRING, 0, (LPARAM)L"5");
        SendDlgItemMessage(hDlg, IDC_COMBO_M, CB_ADDSTRING, 0, (LPARAM)L"6");
        SendDlgItemMessage(hDlg, IDC_COMBO_M, CB_ADDSTRING, 0, (LPARAM)L"7");
        SendDlgItemMessage(hDlg, IDC_COMBO_M, CB_ADDSTRING, 0, (LPARAM)L"8");
        SendDlgItemMessage(hDlg, IDC_COMBO_M, CB_ADDSTRING, 0, (LPARAM)L"9");
        SendDlgItemMessage(hDlg, IDC_COMBO_M, CB_ADDSTRING, 0, (LPARAM)L"10");
        SendDlgItemMessage(hDlg, IDC_COMBO_M, CB_SETCURSEL, 0, 0);
        SendDlgItemMessage(hDlg, IDC_COMBO_CT1, CB_ADDSTRING, 0, (LPARAM)L"1");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT1, CB_ADDSTRING, 0, (LPARAM)L"2");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT1, CB_ADDSTRING, 0, (LPARAM)L"3");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT1, CB_ADDSTRING, 0, (LPARAM)L"4");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT1, CB_ADDSTRING, 0, (LPARAM)L"5");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT1, CB_ADDSTRING, 0, (LPARAM)L"6");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT1, CB_ADDSTRING, 0, (LPARAM)L"7");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT1, CB_ADDSTRING, 0, (LPARAM)L"8");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT1, CB_ADDSTRING, 0, (LPARAM)L"9");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT1, CB_ADDSTRING, 0, (LPARAM)L"10");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT1, CB_SETCURSEL, 0, 0);
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_3, CB_ADDSTRING, 0, (LPARAM)L"-1");
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_3, CB_ADDSTRING, 0, (LPARAM)L"0");
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_3, CB_ADDSTRING, 0, (LPARAM)L"+1");
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_3, CB_SETCURSEL, 0, 0);
        return (INT_PTR)TRUE;
    case WM_COMMAND:
    {
        if (LOWORD(wParam) == IDC_BUTTON_DRAW_FRIEDMANN)
        {
            char line[128] = "";
            GetDlgItemTextA(hDlg, IDC_COMBO_M, line, 128);
            double M = atof(line);
            GetDlgItemTextA(hDlg, IDC_COMBO_CT1, line, 128);
            double cT = atof(line);
            int epsilon = GetDlgItemInt(hDlg, IDC_COMBO_EPSILON_3, FALSE, TRUE);
            double step = cT / 256.0, t = 0.0, K = 0.0;
            int index = 0;

            pointsFriedmann.clear();

            while (t <= cT)
            {
                UniversalModels::FriedmannUniverse(
                    epsilon, M, t, K);
                Point2dFriedmann pt = { 0 };
                pt.cT = t;
                pt.K = K;
                t += step;
                pointsFriedmann.push_back(pt);
            }

            DialogBox(hInst, MAKEINTRESOURCE(IDD_DRAW_GRAPH_DIALOG_FRIEDMANN),
                hDlg, DrawGraphDialogFriedmann);
            return (INT_PTR)TRUE;
        }

        else if (LOWORD(wParam) == IDCANCEL)
        {
            EndDialog(hDlg, LOWORD(wParam));
            return (INT_PTR)TRUE;
        }
    }
    }

    return (INT_PTR)FALSE;
}

static void FindMinMaxFriedmann(
    double& xmin,
    double& xmax,
    double& ymin,
    double& ymax)
{
    xmin = pointsFriedmann[0].cT;
    xmax = pointsFriedmann[0].cT;
    ymin = pointsFriedmann[0].K;
    ymax = pointsFriedmann[0].K;

    for (int i = 1; i < pointsFriedmann.size(); i++)
    {
        Point2dFriedmann pt = pointsFriedmann[i];

        if (pt.cT < xmin)
            xmin = pt.cT;
        if (pt.cT > xmax)
            xmax = pt.cT;
        if (pt.K < ymin)
            ymin = pt.K;
        if (pt.K > ymax)
            ymax = pt.K;
    }
}

static INT_PTR CALLBACK DrawGraphDialogFriedmann(
    HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam)
{
    UNREFERENCED_PARAMETER(lParam);
    char line[256] = "";
    switch (message)
    {
    case WM_INITDIALOG:
        strcpy_s(line, 256, "Drawing Dialog Friedmann Universe");
        SetWindowTextA(hDlg, line);
        return (INT_PTR)TRUE;
    case WM_COMMAND:
        if (LOWORD(wParam) == IDOK || LOWORD(wParam) == IDCANCEL)
        {
            EndDialog(hDlg, LOWORD(wParam));
            return (INT_PTR)TRUE;
        }
        break;
    case WM_PAINT:
        double xmax = 0, xmin = 0;
        double ymax = 0, ymin = 0;
        FindMinMaxFriedmann(xmin, xmax, ymin, ymax);
        double h = 0, pi = 0, plm = 0, theta = 0;
        float xSpan = (float)(xmax - xmin);
        float ySpan = (float)(ymax - ymin);
        RECT rect = { };
        GetClientRect(hDlg, &rect);
        float width = (float)(rect.right - rect.left + 1);
        float height = (float)(rect.bottom - rect.top - 32 + 1);
        float sx0 = 2.0f * width / 16.0f;
        float sx1 = 14.0f * width / 16.0f;
        float sy0 = 2.0f * height / 16.0f;
        float sy1 = 14.0f * height / 16.0f;
        float deltaX = xSpan / 8.0f;
        float deltaY = ySpan / 8.0f;
        float xSlope = (sx1 - sx0) / xSpan;
        float xInter = (float)(sx0 - xSlope * xmin);
        float ySlope = (sy0 - sy1) / ySpan;
        float yInter = (float)(sy0 - ySlope * ymax);
        float px = 0, py = 0, sx = 0, sy = 0;
        PAINTSTRUCT ps;
        POINT wPt = { };
        HDC hdc = BeginPaint(hDlg, &ps);
        int i = 0;
        float x = (float)xmin;
        float y = (float)ymax;
        DrawTitles(hdc, rect, fTitle, xTitle, yTitle,
            (int)sx0, (int)sx1, (int)sy0, (int)sy1);
        px = (float)pointsFriedmann[0].cT;
        py = (float)pointsFriedmann[0].K;
        sx = xSlope * px + xInter;
        sy = ySlope * py + yInter;
        MoveToEx(hdc, (int)sx, (int)sy0, &wPt);

        while (i <= 8)
        {
            sx = xSlope * x + xInter;
            wPt.x = wPt.y = 0;
            MoveToEx(hdc, (int)sx, (int)sy0, &wPt);
            LineTo(hdc, (int)sx, (int)sy1);
            char numberStr[128] = "";
            sprintf_s(numberStr, 128, "%5.4lf", x);
            SIZE size = { };
            GetTextExtentPoint32A(
                hdc,
                numberStr,
                (int)strlen(numberStr),
                &size);
            RECT textRect = { };
            textRect.left = (long)(sx - size.cx / 2.0f);
            textRect.right = (long)(sx + size.cx / 2.0f);
            textRect.top = (long)sy1;
            textRect.bottom = (long)(sy1 + size.cy / 2.0f);
            DrawFormattedText(hdc, numberStr, textRect);
            x += deltaX;
            i++;
        }

        i = 0;
        y = (float)ymin;

        while (i <= 8)
        {
            sy = ySlope * y + yInter;
            wPt.x = wPt.y = 0;
            MoveToEx(hdc, (int)sx0, (int)sy, &wPt);
            LineTo(hdc, (int)sx, (int)sy);

            if (i != 0)
            {
                char numberStr[128] = "";
                sprintf_s(numberStr, 128, "%+5.3lf", y);
                SIZE size = { };
                GetTextExtentPoint32A(
                    hdc,
                    numberStr,
                    (int)strlen(numberStr),
                    &size);
                RECT textRect = { 0 };
                textRect.left = (long)(sx0 - size.cx - size.cx / 2.0f);
                textRect.right = (long)(sx0 - size.cx / 2.0f);
                textRect.top = (long)(sy - size.cy / 2.0f);
                textRect.bottom = (long)(sy + size.cy / 2.0f);
                DrawFormattedText(hdc, numberStr, textRect);
            }

            y += deltaY;
            i++;
        }

        HGDIOBJ bPenNew = NULL;
        HGDIOBJ hPenOld = NULL;

        bPenNew = CreatePen(PS_SOLID, 2, RGB(0, 0, 255));
        hPenOld = SelectObject(hdc, bPenNew);

        HRGN clipRegion = CreateRectRgn(
            (int)sx0, (int)sy0,              // Left, Top
            (int)(sx1), (int)(sy1)           // Right, Bottom
        );

        // Apply clipping region

        SelectClipRgn(hdc, clipRegion);

        px = (float)pointsFriedmann[0].cT;
        py = (float)pointsFriedmann[0].K;
        sx = xSlope * px + xInter;
        sy = ySlope * py + yInter;
        wPt.x = wPt.y = 0;
        MoveToEx(hdc, (int)sx, (int)sy, &wPt);

        for (size_t j = 1; j < pointsFriedmann.size(); j++)
        {
            px = (float)pointsFriedmann[j].cT;
            py = (float)pointsFriedmann[j].K;
            sx = xSlope * px + xInter;
            sy = ySlope * py + yInter;
            LineTo(hdc, (int)sx, (int)sy);
        }

        DeleteObject(bPenNew);
        bPenNew = NULL;

        SelectObject(hdc, hPenOld);
        DeleteObject(clipRegion);
        EndPaint(hDlg, &ps);
        return (INT_PTR)TRUE;
    }

    return (INT_PTR)FALSE;
}


//Microsoft Visual C++ generated resource script.
//
#include "resource.h"

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// Generated from the TEXTINCLUDE resource.
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#ifndef APSTUDIO_INVOKED
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LANGUAGE 9, 1

/////////////////////////////////////////////////////////////////////////////
//
// Icon
//

// Icon with lowest ID value placed first to ensure application icon
// remains consistent on all systems.

IDI_MODELUNIVERSES       ICON         "ModelUniverses.ico"
IDI_SMALL               ICON         "small.ico"

/////////////////////////////////////////////////////////////////////////////
//
// Menu
//

IDC_MODELUNIVERSES MENU
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        MENUITEM "&de Sitter Universe", IDM_DE_SITTER
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//
// Accelerator
//

IDC_MODELUNIVERSES ACCELERATORS
BEGIN
    "?",            IDM_ABOUT,              ASCII,  ALT
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IDD_ABOUTBOX DIALOGEX 0, 0, 170, 62
STYLE DS_SETFONT | DS_MODALFRAME | DS_FIXEDSYS | WS_POPUP | WS_CAPTION | WS_SYSMENU
CAPTION "About ModelUniverses"
FONT 8, "MS Shell Dlg"
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FONT 10, "Courier New", 700
BEGIN
LTEXT       "A:", IDC_STATIC, 10, 10, 100, 10
COMBOBOX    IDC_COMBO_A_1, 120, 10, 50, 60, CBS_DROPDOWNLIST
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LTEXT       "epsilon:",
IDC_STATIC, 10, 100, 50, 60
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| WS_VSCROLL | WS_TABSTOP
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IDC_STATIC, 10, 130, 50, 60
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PUSHBUTTON  "Draw", IDC_BUTTON_DRAW_RADIATION, 10, 100, 50, 16
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STYLE DS_SETFONT | WS_POPUP | WS_CAPTION | WS_SYSMENU
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BEGIN
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COMBOBOX    IDC_COMBO_M, 120, 10, 50, 60, CBS_DROPDOWNLIST
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LTEXT       "cT:", IDC_STATIC, 10, 40, 100, 10
COMBOBOX    IDC_COMBO_CT1, 120, 40, 50, 60, CBS_DROPDOWNLIST
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LTEXT       "epsilon:",
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STYLE DS_SETFONT | WS_POPUP | WS_VISIBLE | WS_CAPTION | WS_SYSMENU
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FONT 10, "Courier New", 700
BEGIN
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2 TEXTINCLUDE
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3 TEXTINCLUDE
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   IDS_APP_TITLE       "ModelUniverses"
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//{{NO_DEPENDENCIES}}
// Microsoft Visual C++ generated include file.
// Used by ModelUniverses.rc

#define IDS_APP_TITLE			103

#define IDR_MAINFRAME			128
#define IDD_MODELUNIVERSES_DIALOG	102
#define IDD_ABOUTBOX			103
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#ifndef APSTUDIO_READONLY_SYMBOLS

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#define _APS_NEXT_COMMAND_VALUE		32771
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#define IDD_DATA_INPUT_DIALOG_DE_SITTER	1000
#define IDC_COMBO_A_1				1010
#define IDC_COMBO_B					1020
#define IDC_COMBO_CT				1030
#define IDC_COMBO_EPSILON_1			1040
#define IDC_COMBO_LAMBDA			1050
#define IDC_BUTTON_DRAW_DE_SITTER	1060
#define IDD_DRAW_GRAPH_DIALOG_DE_SITTER	2000
#define IDD_DATA_INPUT_DIALOG_RADIATION	3000
#define IDC_COMBO_A_2				3010
#define IDC_COMBO_DELTA_T			3020
#define IDC_COMBO_EPSILON_2			3030
#define IDC_BUTTON_DRAW_RADIATION	3040
#define IDD_DRAW_GRAPH_DIALOG_RADIATION	4000
#define IDD_DATA_INPUT_DIALOG_FRIEDMANN 5000
#define IDC_COMBO_M					5010
#define IDC_COMBO_CT1				5020
#define IDC_COMBO_EPSILON_3			5030
#define IDC_BUTTON_DRAW_FRIEDMANN	5040
#define IDD_DRAW_GRAPH_DIALOG_FRIEDMANN	6000
#define IDM_DE_SITTER				32771
#define IDM_RADIATION				32772
#define IDM_FRIEDMANN				32773

Blog Entry © Thursday, March 19, 2026, by James Pate Williams, Jr. Solution of Laplace’s Two-Dimensional Equation on a Square Boundary

LaplaceFD2dDownload
#pragma once

class Laplace
{
private:
    static int N;

public:
    Laplace(int N);
    double** Solve(
        double L,
        double epsilon,
        int& iterations,
        double (*f)(double));
    void PrintSolution(
        double L,
        double epsilon,
        double** u,
        double** w,
        int& iterations);
};


#include "Laplace.h"
#include <float.h>
#include <math.h>
#include <iomanip>
#include <iostream>

int Laplace::N = 0;

static double fxy(double x, double y)
{
    return x * y * exp(-0.5 * (x * x + y * y));
}

static double gxy(double x, double y)
{
    return x * sin(y);
}

Laplace::Laplace(int N)
{
    this->N = N;
}

double** Laplace::Solve(
    double L, double epsilon, int& iterations,
    double (*f)(double))
{
    double h = L / (N + 1.0), uv = 0, max = 0;
    double** u = new double*[N + 2];

    if (u == nullptr)
        exit(-1);

    for (int i = 0; i < N + 2; i++)
    {
        u[i] = new double[N + 2];

        if (u[i] == nullptr)
            exit(-2);

        for (int j = 0; j < N + 2; j++)
            u[i][j] = 0.0;
    }

    double** v = new double* [N + 2];

    if (v == nullptr)
        exit(-3);

    for (int i = 0; i < N + 2; i++)
    {
        v[i] = new double[N + 2];

        if (v[i] == nullptr)
            exit(-4);

        for (int j = 0; j < N + 2; j++)
            v[i][j] = 0.0;
    }

    iterations = 0;

    for (int j = 0; j <= N + 1; j++)
        u[0][j] = 0.0;

    for (int j = 0; j <= N + 1; j++)
        u[N + 1][j] = 0.0;

    for (int i = 0; i <= N + 1; i++)
        u[i][0] = f(i * h);

    for (int i = 0; i <= N + 1; i++)
        u[i][N + 1] = 0.0;

    do
    {
        iterations++;

        for (int i = 1; i <= N; i++)
            for (int j = 1; j <= N; j++)
                u[i][j] = 0.25 * (u[i - 1][j] + u[i + 1][j] + u[i][j - 1] +
                    u[i][j + 1]);

        for (int i = 0; i <= N + 1; i++)
            for (int j = 0; j <= N + 1; j++)
                v[i][j] = u[i][j];

        for (int i = 1; i <= N; i++)
            for (int j = 1; j <= N; j++)
                v[i][j] = 0.25 * (v[i - 1][j] + v[i + 1][j] + v[i][j - 1] +
                    v[i][j + 1]);

        max = DBL_MIN;

        for (int i = 1; i <= N; i++)
        {
            for (int j = 1; j <= N; j++)
            {
                uv = fabs(v[i][j] - u[i][j]);
                max = fmax(uv, max);
            }
        }

        for (int i = 0; i <= N + 1; i++)
            for (int j = 0; j <= N + 1; j++)
                u[i][j] = v[i][j];

    } while (max > epsilon);

    for (int i = 0; i < N + 2; i++)
        delete v[i];

    return u;
}

void Laplace::PrintSolution(
    double L,
    double epsilon,
    double** u,
    double** w,
    int& iterations)
{
    double h = L / (N + 1.0);
    
    std::cout << std::endl;
    std::cout << "x\t\ty\t\tu(x, y)\t\tw(x, y)\t\tpercent error\r\n\r\n";

    for (int i = 0; i <= N + 1; i++)
    {
        double x = i * h;

        for (int j = 0; j <= N + 1; j++)
        {
            double y = j * h;
            std::cout << std::fixed << std::setprecision(5);
            std::cout << std::setw(8);
            std::cout << x << '\t';
            std::cout << std::fixed << std::setprecision(5);
            std::cout << std::setw(8);
            std::cout << y << '\t';
            std::cout << std::fixed << std::setprecision(5);
            std::cout << std::setw(8);
            std::cout << u[i][j] << '\t';
            std::cout << std::fixed << std::setprecision(5);
            std::cout << std::setw(8);
            std::cout << w[i][j] << '\t';
            double error = 0.0;
            if (w[i][j] != 0.0)
                error = 100.0 * fabs(u[i][j] - w[i][j]) /
                    fabs(w[i][j]);
            std::cout << std::fixed << std::setprecision(5);
            std::cout << std::setw(8);
            std::cout << error << std::endl;
        }
    }

    std::cout << std::endl;
    std::cout << "iterations = " << iterations;
    std::cout << std::endl;
}


// LaplaceEquationFD2d.cpp (c) Tuesday, March 17, 2026 
// by James Pate Williams, Jr., BA, BS, MSwE, PhD
// by James Pate Williams, Jr., BA, ,BS, MSwE, PhD
// Reference: Numerical Computation 2 Methods,
// Software And Analysis (c) 1995 by Chrisoph E. Ueberhuber
// Pages 392 - 393 Poisson Matrices
// https://math.libretexts.org/Bookshelves/Differential_Equations/Introduction_to_Partial_Differential_Equations_(Herman)/06%3A_Problems_in_Higher_Dimensions/6.03%3A_Laplaces_Equation_in_2D

#include <math.h>
#include <iostream>
#include "Laplace.h"

double** w;

double SimpsonsRule(double L, double a, double b,
    int Nsr, int n, double (*f)(double, double, int))
{
    double h = (b - a) / Nsr;
    double h2 = 2.0 * h;
    double s = 0.0;
    double t = 0.0;
    double x = a + h;

    for (int i = 1; i < Nsr; i += 2)
    {
        s += f(L, x, n);
        x += h2;
    }

    x = a + h2;

    for (int i = 2; i < Nsr; i += 2)
    {
        t += f(L, x, n);
        x += h2;
    }

    return
        h * (f(L, a, n) + 4 * s + 2 * t + f(L, b, n)) / 3.0;
}

double f(double x)
{
    return x * exp(-x) * cos(x);
}

double g(double L, double x, int n)
{
    double pi = 4.0 * atan(1.0);
    double fx = f(x);
    return fx * sin(n * pi * x / L);
}

double bn(double L, int Nsr, int n)
{
    double cs = 2.0 / L;
    double sr = SimpsonsRule(L, 0.0, L, Nsr, n, g);
    return cs * sr;
}

void ComputeW(double L, int N)
{
    double h = L / (N + 1.0);

    w = new double* [N + 2];

    if (w == nullptr)
        exit(-5);

    for (int i = 0; i < N + 2; i++)
    {
        w[i] = new double[N + 2];

        if (w[i] == nullptr)
            exit(-6);

        for (int j = 0; j < N + 2; j++)
            w[i][j] = 0.0;
    }

    for (int j = 0; j <= N; j++)
        w[0][j] = 0.0;

    for (int j = 0; j <= N; j++)
        w[N + 1][j] = 0.0;

    for (int i = 0; i <= N; i++)
        w[i][0] = f(i * h);

    for (int i = 0; i <= N; i++)
        w[i][N + 1] = 0.0;

    double pi = 4.0 * atan(1.0);
    double x = h, y = 0.0;

    for (int i = 1; i <= N; i++)
    {
        y = h;

        for (int j = 1; j <= N; j++)
        {
            double s = 0.0;

            for (int n = 1; n <= 64; n++)
            {
                double npi = n * pi;
                double an = bn(L, 512, n) / sinh(npi);
                s += an * sin(npi * x / L) * sinh(npi * (L - y) / L);
            }

            w[i][j] = s;
            y += h;
        }

        x += h;
    }
}

int main()
{
    while (true)
    {
        char line[128] = "";
        std::cout << "N = ";
        std::cin.getline(line, 128);
        int N = atoi(line);

        if (N < 4 || N > 128)
        {
            std::cout << "N < 4 || N > 128, try again";
            std::cout << std::endl;
        }

        std::cout << "epsilon = ";
        std::cin.getline(line, 128);

        double epsilon = atof(line);
        Laplace l(N);

        double L = 1.0;
        int iterations = 0;
        ComputeW(L, N);
        double** u = l.Solve(L, epsilon, iterations, f);
        l.PrintSolution(L, epsilon, u, w, iterations);

        for (int i = 0; i < N + 2; i++)
        {
            if (u[i] != nullptr)
                delete u[i];

            if (w[i] != nullptr)
                delete w[i];
        }

        break;
    }

    return 0;
}

Blog Entry © Tuesday, March 17, 2026, by James Pate Williams, Jr., Comparison of Power Series Arctangent and Arcsine Functions with the C++ Built-In Functions

Blog Entry Tuesday March 17 2026Download
#pragma once

//https://scipp-legacy.pbsci.ucsc.edu/~haber/ph116A/taylor11.pdf

class Functions
{
public:
	static void initialize();
	static double factorial(int n);
	static double arccosine(double x, int n);
	static double arccosecant(double x);
	static double arccotangent(double x);
	static double arcsecant(double x);
	static double arcsine(double x, int n);
	static double arctangent(double x, int n);
};


#include "Functions.h"
#include <math.h> 

double pi2 = 0.0;

double Functions::factorial(int n)
{
	double nfactorial = 1.0;

	for (int i = 2; i <= n; i++)
		nfactorial *= i;

	return nfactorial;
}

void Functions::initialize()
{
	pi2 = 2.0 * atan(1.0);
}

double Functions::arccosine(double x, int n)
{
	double sum = pi2 - arcsine(x, n);
	return sum;
}

double Functions::arccosecant(double x)
{
	double sum = 0;
	return sum;
}

double Functions::arccotangent(double x)
{
	double sum = 0;
	return sum;
}

double Functions::arcsecant(double x)
{
	double sum = 0;
	return sum;
}

double Functions::arcsine(double x, int n)
{
	double sum = 0.0;

	if (fabs(x) <= 1.0)
	{
		for (int i = n; i >= 0; i--)
		{
			double ifact = factorial(i);
			double i2 = 2.0 * i, i21 = 2 * i + 1;
			double coeff = factorial(i2) /
				(pow(2, i2) * ifact * ifact * (i21));
			sum += coeff * pow(x, i21);
		}
	}

	return sum;
}

double Functions::arctangent(double x, int n)
{
	double sum = 0.0;

	if (fabs(x) <= 1.0)
	{
		double one = 0.0;

		if (n % 2 == 0)
			one = 1.0;
		else
			one = -1.0;

		for (int i = 2 * n + 1; i >= 0; i--)
		{
			one = -one;
			double i21 = 2 * i + 1.0;
			sum += one * pow(x, i21) / i21;
		}
	}

	return sum;
}


// InvTrigConsoleCPP.cpp (c) Monday, March 16, 2026
// by James Pate Williams, Jr., BA, BS, MSwE, PhD

#include "Functions.h"
#include <math.h>
#include <iomanip>
#include <iostream>

static void CreateTable(
	char title[],
	double a, double b, int n, int nPts,
	double(*fx)(double, int), double(*gx)(double))
{
	double x = a;
	double deltaX = (b - a) / nPts;
	std::cout << title << std::endl;
	std::cout << "# Terms = " << (2 * n + 2) << std::endl;
	std::cout << "x" << '\t' << "fx" << "\t\t";
	std::cout << "sx" << "\t\t" << "error" << std::endl;

	for (int i = 0; i < nPts; i++)
	{
		double f = fx(x, n);
		double s = gx(x);
		double e = 0.0;

		if (fabs(s) != 0)
			e = 100.0 * fabs(f - s) / fabs(s);

		std::cout << std::fixed << std::setprecision(4);
		std::cout << std::setw(4);
		std::cout << x << '\t';
		std::cout << std::fixed << std::setprecision(11);
		std::cout << std::setw(12);
		std::cout << f << '\t';
		std::cout << std::fixed << std::setprecision(11);
		std::cout << std::setw(12);
		std::cout << s << '\t';
		std::cout << e << std::endl;
		x += deltaX;
	}
}

int main()
{
	Functions::initialize();

	while (true)
	{
		char line[128] = "";
		std::cout << "== Menu == " << std::endl;
		std::cout << "1 arcsine" << std::endl;
		std::cout << "2 arctangent" << std::endl;
		std::cout << "3 exit" << std::endl;
		std::cout << "option # : ";
		std::cin.getline(line, 128);
		char option = line[0];

		if (option == '3')
			break;

		if (option < '1' || option > '2')
		{
			std::cout << "invalid option" << std::endl;
			continue;
		}

		std::cout << "# points: ";
		std::cin.getline(line, 128);
		int nPts = atoi(line);

		std::cout << "# terms: ";
		std::cin.getline(line, 128);
		int n = atoi(line);

		if (option == '1')
		{
			char title[] = "Series arcsin Versus C++ asin";
			CreateTable(title, 0.0, 1.0, n, nPts,
				Functions::arcsine, asin);
		}
		else if (option == '2')
		{
			char title[] = "Series arctan Versus C++ atan";
			CreateTable(title, 0.0, 1.0, n, nPts,
				Functions::arctangent, atan);
		}
	}

	return 0;
}

Blog Entry © Sunday March 15, 2026, by James Pate Williams, Jr. Graphing Integer Order Bessel Functions of the First Kind and the real Gamma Function

Blog Entry Sunday March 15 2026Download

Blog Entry © Saturday, March 14, 2026, by James Pate Williams, Jr. Power Series Solution of a Second Order Linear Ordinary Differential Equation

Blog Entry Saturday March 14 2026Download
// SecondOrderLinearODE.cpp (c) Friday March 13, 2026
// by James Pate Williams, Jr., BA, BS, MSwE, PhD
// Solves the Bessel Equation of the First Kind for Order 0
// Using the power series found in the reference below - 
// References: https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/17%3A_Second-Order_Differential_Equations/17.04%3A_Series_Solutions_of_Differential_Equations
// https://mathworld.wolfram.com/BesselDifferentialEquation.html

#include "framework.h"
#include <Windows.h>
#include "SecondOrderLinearODE.h"
#include <string>
#include <vector>

#define MAX_LOADSTRING 100

// Global Variables:
HINSTANCE hInst;                                // current instance
WCHAR szTitle[MAX_LOADSTRING];                  // The title bar text
WCHAR szWindowClass[MAX_LOADSTRING];            // the main window class name
WCHAR fTitle[128];
double chi[1025], eta[1025], coeff[65];

// Forward declarations of functions included in this code module:
ATOM                MyRegisterClass(HINSTANCE hInstance);
BOOL                InitInstance(HINSTANCE, int);
LRESULT CALLBACK    WndProc(HWND, UINT, WPARAM, LPARAM);
INT_PTR CALLBACK    About(HWND, UINT, WPARAM, LPARAM);

int APIENTRY wWinMain(_In_ HINSTANCE hInstance,
                     _In_opt_ HINSTANCE hPrevInstance,
                     _In_ LPWSTR    lpCmdLine,
                     _In_ int       nCmdShow)
{
    UNREFERENCED_PARAMETER(hPrevInstance);
    UNREFERENCED_PARAMETER(lpCmdLine);

    // TODO: Place code here.

    // Initialize global strings
    LoadStringW(hInstance, IDS_APP_TITLE, szTitle, MAX_LOADSTRING);
    LoadStringW(hInstance, IDC_SECONDORDERLINEARODE, szWindowClass, MAX_LOADSTRING);
    MyRegisterClass(hInstance);

    // Perform application initialization:
    if (!InitInstance (hInstance, nCmdShow))
    {
        return FALSE;
    }

    HACCEL hAccelTable = LoadAccelerators(hInstance, MAKEINTRESOURCE(IDC_SECONDORDERLINEARODE));

    MSG msg;

    // Main message loop:
    while (GetMessage(&msg, nullptr, 0, 0))
    {
        if (!TranslateAccelerator(msg.hwnd, hAccelTable, &msg))
        {
            TranslateMessage(&msg);
            DispatchMessage(&msg);
        }
    }

    return (int) msg.wParam;
}

//
//  FUNCTION: MyRegisterClass()
//
//  PURPOSE: Registers the window class.
//
ATOM MyRegisterClass(HINSTANCE hInstance)
{
    WNDCLASSEXW wcex = { 0 };

    wcex.cbSize = sizeof(WNDCLASSEX);

    wcex.style          = CS_HREDRAW | CS_VREDRAW;
    wcex.lpfnWndProc    = WndProc;
    wcex.cbClsExtra     = 0;
    wcex.cbWndExtra     = 0;
    wcex.hInstance      = hInstance;
    wcex.hIcon          = LoadIcon(hInstance, MAKEINTRESOURCE(IDI_SECONDORDERLINEARODE));
    wcex.hCursor        = LoadCursor(nullptr, IDC_ARROW);
    wcex.hbrBackground  = (HBRUSH)(COLOR_WINDOW+1);
    wcex.lpszMenuName   = MAKEINTRESOURCEW(IDC_SECONDORDERLINEARODE);
    wcex.lpszClassName  = szWindowClass;
    wcex.hIconSm        = LoadIcon(wcex.hInstance, MAKEINTRESOURCE(IDI_SMALL));

    return RegisterClassExW(&wcex);
}

//
//   FUNCTION: InitInstance(HINSTANCE, int)
//
//   PURPOSE: Saves instance handle and creates main window
//
//   COMMENTS:
//
//        In this function, we save the instance handle in a global variable and
//        create and display the main program window.
//
BOOL InitInstance(HINSTANCE hInstance, int nCmdShow)
{
   hInst = hInstance; // Store instance handle in our global variable

   HWND hWnd = CreateWindowW(szWindowClass, szTitle, WS_OVERLAPPEDWINDOW,
      CW_USEDEFAULT, 0, CW_USEDEFAULT, 0, nullptr, nullptr, hInstance, nullptr);

   if (!hWnd)
   {
      return FALSE;
   }

   ShowWindow(hWnd, nCmdShow);
   UpdateWindow(hWnd);

   return TRUE;
}

static double Factorial(int n)
{
    double factorial = 1.0;

    for (int i = 2; i <= n; i++)
        factorial *= i;

    return factorial;
}

static void ComputeCoefficients()
{
    double a0 = 1.0;

    for (int k = 0; k <= 64; k++)
    {
        double kFactorial = Factorial(k);

        coeff[k] = a0 * pow(-1.0, k) /
            (pow(2.0, 2.0 * k) * pow(kFactorial, 2.0));
    }
}

static void ComputePoints()
{
    double chi0 = -15.0;
    double deltaChi = 30.0 / 1024;
 
    for (int i = 0; i <= 1024; i++)
    {
        double sum = 0.0;

        for (int k = 64; k >= 0; k--)
            sum += pow(chi0, 2 * k) * coeff[k];

        chi[i] = chi0;
        eta[i] = sum;

        chi0 += deltaChi;
    }
}

static void FindMinMax(
    double x[],
    double& min,
    double& max)
{
    min = x[0];
    max = x[0];

    for (int i = 1; i <= 1024; i++)
    {
        if (x[i] < min)
            min = x[i];
        if (x[i] > max)
            max = x[i];
    }
}

static void DrawTitles(HDC hdc, RECT clientRect, const std::wstring& fTitle,
    int sx0, int sx1, int sy0, int sy1)
{
    HFONT hCustomFont = CreateFont(
        -MulDiv(10, GetDeviceCaps(hdc, LOGPIXELSY), 72), // Height in logical units
        0,                      // Width (0 = default)
        0,                      // Escapement
        0,                      // Orientation
        FW_BOLD,                // Weight (700 = bold)
        FALSE,                  // Italic
        FALSE,                  // Underline
        FALSE,                  // StrikeOut
        DEFAULT_CHARSET,        // Charset
        OUT_DEFAULT_PRECIS,     // Output precision
        CLIP_DEFAULT_PRECIS,    // Clipping precision
        DEFAULT_QUALITY,        // Quality
        FIXED_PITCH | FF_MODERN,// Pitch and family
        L"Courier New"          // Typeface name
    );

    HFONT hOldFont = (HFONT)SelectObject(hdc, hCustomFont);

    SIZE sz;
    int width = clientRect.right - clientRect.left;

    // Title: fTitle
    GetTextExtentPoint32(hdc, fTitle.c_str(), (int)fTitle.length(), &sz);
    int w = sz.cx;
    int h = sz.cy;
    TextOut(hdc, (width - w) / 2, h, fTitle.c_str(), (int)fTitle.length());

    // x-axis title: "x"
    std::wstring xTitle = L"x";
    GetTextExtentPoint32W(hdc, xTitle.c_str(), (int)xTitle.length(), &sz);
    w = sz.cx;
    TextOutW(hdc, sx0 + (sx1 - sx0 - w) / 2, sy1 + 2 * h, xTitle.c_str(), (int)xTitle.length());

    // y-axis title: "p(x)"
    std::wstring yTitle = L"J0(x)";
    GetTextExtentPoint32W(hdc, yTitle.c_str(), (int)yTitle.length(), &sz);
    w = sz.cx;
    TextOutW(hdc, sx1 + w / 5, sy0 + (sy1 - sy0) / 2 - h / 2, yTitle.c_str(), (int)yTitle.length());

    SelectObject(hdc, hOldFont); // Restore original font
}

static void DrawFormattedText(HDC hdc, char loctext[], RECT rect)
{
    // Draw the text with formatting options
    DrawTextA(hdc, loctext, (int)strlen(loctext), &rect, DT_SINGLELINE | DT_NOCLIP);
}

//
//  FUNCTION: WndProc(HWND, UINT, WPARAM, LPARAM)
//
//  PURPOSE: Processes messages for the main window.
//
//  WM_COMMAND  - process the application menu
//  WM_PAINT    - Paint the main window
//  WM_DESTROY  - post a quit message and return
//
//
LRESULT CALLBACK WndProc(HWND hWnd, UINT message, WPARAM wParam, LPARAM lParam)
{
    switch (message)
    {
    case WM_CREATE:
        ComputeCoefficients();
        ComputePoints();
        break;
    case WM_COMMAND:
        {
            int wmId = LOWORD(wParam);
            // Parse the menu selections:
            switch (wmId)
            {
            case IDM_ABOUT:
                DialogBox(hInst, MAKEINTRESOURCE(IDD_ABOUTBOX), hWnd, About);
                break;
            case IDM_EXIT:
                DestroyWindow(hWnd);
                break;
            default:
                return DefWindowProc(hWnd, message, wParam, lParam);
            }
        }
        break;
    case WM_PAINT:
    {
        PAINTSTRUCT ps;
        HDC hdc = BeginPaint(hWnd, &ps);

        ComputePoints();
        double xMin = 0, yMin = 0;
        double xMax = 0, yMax = 0;
        FindMinMax(chi, xMin, xMax);
        FindMinMax(eta, yMin, yMax);

        double h = 0, pi = 0, plm = 0, theta = 0;
        float xSpan = (float)(xMax - xMin);
        float ySpan = (float)(yMax - yMin);
        RECT rect = { };
        GetClientRect(hWnd, &rect);
        float width = (float)(rect.right - rect.left + 1);
        float height = (float)(rect.bottom - rect.top - 32 + 1);
        float sx0 = 2.0f * width / 16.0f;
        float sx1 = 14.0f * width / 16.0f;
        float sy0 = 2.0f * height / 16.0f;
        float sy1 = 14.0f * height / 16.0f;
        float deltaX = xSpan / 8.0f;
        float deltaY = ySpan / 8.0f;
        float xSlope = (sx1 - sx0) / xSpan;
        float xInter = (float)(sx0 - xSlope * xMin);
        float ySlope = (sy0 - sy1) / ySpan;
        float yInter = (float)(sy0 - ySlope * yMax);
        float px = 0, py = 0, sx = 0, sy = 0;
        POINT wPt = { 0 };
        int i = 0;
        float x = (float)xMin;
        float y = (float)yMax;
        wcscpy_s(fTitle, 128, L"Bessel Function of the First Kind Order 0");
        DrawTitles(hdc, rect, fTitle, (int)sx0, (int)sx1, (int)sy0, (int)sy1);


        px = (float)chi[0];
        py = (float)eta[0];

        sx = xSlope * px + xInter;
        sy = ySlope * py + yInter;
        MoveToEx(hdc, (int)sx, (int)sy0, &wPt);

        while (i <= 8)
        {
            sx = xSlope * x + xInter;
            wPt.x = wPt.y = 0;
            MoveToEx(hdc, (int)sx, (int)sy0, &wPt);
            LineTo(hdc, (int)sx, (int)sy1);
            char numberStr[128] = "";
            sprintf_s(numberStr, 128, "%5.4lf", x);
            SIZE size = { };
            GetTextExtentPoint32A(
                hdc,
                numberStr,
                (int)strlen(numberStr),
                &size);
            RECT textRect = { 0 };
            textRect.left = (long)(sx - size.cx / 2.0f);
            textRect.right = (long)(sx + size.cx / 2.0f);
            textRect.top = (long)sy1;
            textRect.bottom = (long)(sy1 + size.cy / 2.0f);
            DrawFormattedText(hdc, numberStr, textRect);
            x += deltaX;
            i++;
        }

        i = 0;
        y = (float)yMin;

        while (i <= 8)
        {
            sy = ySlope * y + yInter;
            wPt.x = wPt.y = 0;
            MoveToEx(hdc, (int)sx0, (int)sy, &wPt);
            LineTo(hdc, (int)sx, (int)sy);

            if (i != 0)
            {
                char numberStr[128] = "";
                sprintf_s(numberStr, 128, "%+5.3lf", y);
                SIZE size = { };
                GetTextExtentPoint32A(
                    hdc,
                    numberStr,
                    (int)strlen(numberStr),
                    &size);
                RECT textRect = { 0 };
                textRect.left = (long)(sx0 - size.cx - size.cx / 2.0f);
                textRect.right = (long)(sx0 - size.cx / 2.0f);
                textRect.top = (long)(sy - size.cy / 2.0f);
                textRect.bottom = (long)(sy + size.cy / 2.0f);
                DrawFormattedText(hdc, numberStr, textRect);
            }

            y += deltaY;
            i++;
        }

        HGDIOBJ nPenNew = NULL;
        HGDIOBJ hPenOld = NULL;

        nPenNew = CreatePen(PS_SOLID, 2, RGB(0, 0, 255));
        hPenOld = SelectObject(hdc, nPenNew);

        HRGN clipRegion = CreateRectRgn(
            (int)sx0, (int)sy0,              // Left, Top
            (int)(sx1), (int)(sy1)           // Right, Bottom
        );

        // Apply clipping region

        SelectClipRgn(hdc, clipRegion);


        px = (float)chi[0];
        py = (float)eta[0];

        sx = xSlope * px + xInter;
        sy = ySlope * py + yInter;
        wPt.x = wPt.y = 0;
        MoveToEx(hdc, (int)sx, (int)sy, &wPt);

        for (size_t j = 1; j <= 1024; j++)
        {

            px = (float)chi[j];
            py = (float)eta[j];

            sx = xSlope * px + xInter;
            sy = ySlope * py + yInter;
            LineTo(hdc, (int)sx, (int)sy);
        }

        DeleteObject(nPenNew);
        nPenNew = NULL;

        SelectObject(hdc, hPenOld);
        DeleteObject(clipRegion);

        EndPaint(hWnd, &ps);
    }
    break;
    case WM_DESTROY:
        PostQuitMessage(0);
        break;
    default:
        return DefWindowProc(hWnd, message, wParam, lParam);
    }
    return 0;
}

// Message handler for about box.
INT_PTR CALLBACK About(HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam)
{
    UNREFERENCED_PARAMETER(lParam);
    switch (message)
    {
    case WM_INITDIALOG:
        return (INT_PTR)TRUE;

    case WM_COMMAND:
        if (LOWORD(wParam) == IDOK || LOWORD(wParam) == IDCANCEL)
        {
            EndDialog(hDlg, LOWORD(wParam));
            return (INT_PTR)TRUE;
        }
        break;
    }
    return (INT_PTR)FALSE;
}

Blog Entry © Thursday and Friday, March 12 – 13, 2026, Naive Power Series Computations of the Cosine and Sine Trigonometric Functions and Polynomial Fit to the Trig Functions Using Least Squares

Blog Entry Thursday March 12 2026Download
// TrigLSPolyFit.cpp (c) Thursday, March 12, 2026
// by James Pate Williams, Jr.
// Least Squares Curve Fitting to the Trigonometric
// functions Cosine and Sine

#include <iomanip>
#include <iostream>
#include <vector>
#include "PolyLSFit.h"

static const int HornerN = 50;
double even_factors[HornerN], odd_factors[HornerN + 1];

static double factorial(int n)
{
	double nfactorial = 1.0;

	for (int i = 2; i <= n; i++)
		nfactorial *= i;
	return nfactorial;
}

static void computeEvenFactors()
{
	int one = 1;

	for (int n = 0; n < 50; n += 2)
	{
		even_factors[n] = one / factorial(n);
		one = -one;
	}
}

static void computeOddFactors()
{
	int one = 1;

	for (int n = 1; n < 51; n += 2)
	{
		odd_factors[n] = one / factorial(n);
		one = -one;
	}
}

static double fx_cos(double x, int n)
{
	double sum = even_factors[n];

	for (int i = n - 1; i >= 0; i--)
	{
		sum = sum * x + even_factors[i];
	}

	return sum;
}

static double fx_sin(double x, int n)
{
	double sum = odd_factors[n];

	for (int i = n - 1; i >= 0; i--)
	{
		sum = sum * x + odd_factors[i];
	}

	return sum;
}

static const int M = 33, N = 100, N21 = N + N + 1;
std::vector<double> cosX(N21), cosY(N21), cosCoeff;
std::vector<double> sinX(N21), sinY(N21), sinCoeff;
std::vector<double> pX(M), pY(M);

static void LSPolyFit(int HornerN, int degree)
{
	double pi = 4.0 * atan(1.0);
	double deltaX = 2.0 * pi / N;
	double X = -pi;

	for (int i = 0; i < N21; i++)
	{
		cosX[i] = X;
		cosY[i] = fx_cos(X, HornerN);
		sinX[i] = X;
		sinY[i] = fx_sin(X, HornerN + 1);
		X += deltaX;
	}

	PolyLSFit::leastSquares(cosX, cosY, cosCoeff, degree, N21);
	PolyLSFit::leastSquares(sinX, sinY, sinCoeff, degree, N21);

	std::cout << std::setw(6) << "x";
	std::cout << std::setw(17) << "fit cos";
	std::cout << std::setw(17) << "C++ cos";
	std::cout << std::setw(17) << "% Error";
	std::cout << std::endl;

	deltaX = 2.0 * pi / (M - 1);
	X = -pi;

	for (int i = 0; i < M; i++)
	{
		double Y = cosCoeff[degree];

		for (int j = degree - 1; j >= 0; j--)
		{
			Y = Y * X + cosCoeff[j];
		}

		pX[i] = X;
		pY[i] = Y;

		std::cout << std::fixed << std::setprecision(3);
		std::cout << std::setw(6);
		std::cout << X << ' ';

		if (Y >= 0)
			std::cout << '+';
		else
			std::cout << '-';

		std::cout << std::fixed << std::setprecision(16);
		std::cout << std::setw(16);
		
		std::cout << fabs(Y) << ' ';
		double cx = cos(X);

		if (cx >= 0)
			std::cout << '+';
		else
			std::cout << '-';

		std::cout << std::fixed << std::setprecision(16);
		std::cout << std::setw(16);
		
		std::cout << fabs(cx) << ' ';
		double pcDifference = 0.0;

		if (fabs(cx) >= 1.0e-12)
			pcDifference = 100.0 * fabs(Y - cx) / fabs(cx);
		else
			pcDifference = -1.0;

		std::cout << std::fixed << std::setprecision(16);
		std::cout << std::setw(16);

		if (pcDifference != -1.0)
			std::cout << pcDifference << std::endl;
		else
			std::cout << "not a number" << std::endl;

		X += deltaX;
	}

	std::cout << std::endl;

	std::cout << std::setw(6) << "x";
	std::cout << std::setw(17) << "fit sin";
	std::cout << std::setw(17) << "C++ sin";
	std::cout << std::setw(17) << "% Error";
	std::cout << std::endl;

	deltaX = 2.0 * pi / (M - 1);
	X = -pi;

	for (int i = 0; i < M; i++)
	{
		double Y = sinCoeff[degree];

		for (int j = degree - 1; j >= 0; j--)
		{
			Y = Y * X + sinCoeff[j];
		}

		pX[i] = X;
		pY[i] = Y;

		std::cout << std::fixed << std::setprecision(3);
		std::cout << std::setw(6);
		std::cout << X << ' ';

		if (Y >= 0)
			std::cout << '+';
		else
			std::cout << '-';

		std::cout << std::fixed << std::setprecision(16);
		std::cout << std::setw(16);

		std::cout << fabs(Y) << ' ';
		double sx = sin(X);

		if (sx >= 0)
			std::cout << '+';
		else
			std::cout << '-';

		std::cout << std::fixed << std::setprecision(16);
		std::cout << std::setw(16);

		std::cout << fabs(sx) << ' ';
		double pcDifference = 0.0;

		if (fabs(sx) >= 1.0e-12)
			pcDifference = 100.0 * fabs(Y - sx) / fabs(sx);
		else
			pcDifference = -1.0;

		std::cout << std::fixed << std::setprecision(16);
		std::cout << std::setw(16);

		if (pcDifference != -1.0)
			std::cout << pcDifference << std::endl;
		else
			std::cout << "not a number" << std::endl;

		X += deltaX;
	}

	std::cout << std::endl;
}

int main()
{
	computeEvenFactors();
	computeOddFactors();
	std::cout << "# terms 16" << std::endl;
	LSPolyFit(HornerN, 16);
	std::cout << "# terms 20" << std::endl;
	LSPolyFit(HornerN, 20);
	std::cout << "# terms 24" << std::endl;
	LSPolyFit(HornerN, 24);
	return 0;
}

Blog Entry (c) Wednesday, March 11, 2026, More Advanced Encryption Standard Results

Reference: Cryptographic Standards and Guidelines | CSRC

== Menu ==
1 Detailed NIST FIPS 197 128-Bit Encryption
2 Detailed NIST FIPS 197 128-Bit Decryption
3 ECB Encryption 128-Bit Test Vectors
4 ECB Decryption 128-Bit Test Vectors
5 ECB Encryption 192-Bit Test Vectors
6 ECB Decryption 192-Bit Test Vectors
7 ECB Encryption 256-Bit Test Vectors
8 ECB Decryption 256-Bit Test Vectors
9 Exit
Enter option = 3
NIST Standard Test Data
128-Bit Cipher Key
2B7E1516 28AED2A6 ABF71588 09CF4F3C
Electronic Codebook (ECB) Mode
ECB-AES128 (Encryption)
NIST Standard Test Data
AES-128 (Nk = 4, Nr = 10)
Test Vectors
Round[0] Input to Cipher
6BC1BEE2 2E409F96 E93D7E11 7393172A
Round[0] After Add Round Key
40BFABF4 06EE4D30 42CA6B99 7A5C5816
Round[1] After Sub Bytes
090862BF 6F28E304 2C747FEE DA4A6A47
Round[1] After Shift Rows
09287F47 6F746ABF 2C4A6204 DA08E3EE
Round[1] After Mix Columns
529F16C2 978615CA E01AAE54 BA1A2659
Round[1] After Add Round Key
F265E8D5 1FD2397B C3B9976D 9076505C
Round[2] After Sub Bytes
894D9B03 C0B51221 2E56883C 6038534A
Round[2] After Shift Rows
89B5884A C0565303 2E389B21 604D123C
Round[2] After Mix Columns
0F31E929 319A3558 AEC95893 39F04D87
Round[2] After Add Round Key
FDF37CDB 4B0C8C1B F7FCD8E9 4AA9BBF8
Round[3] After Sub Bytes
540D10B9 B3FE64AF 68B0611E D6D3EA41
Round[3] After Shift Rows
54FE6141 B3B0EAB9 68D310AF D60D641E
Round[3] After Mix Columns
9151ABE1 E5541CFD 014A713E DA7E3134
Round[3] After Add Round Key
ACD1EC9C A242E2C3 1F690F7A B704B90F
Round[4] After Sub Bytes
913ECEDE 3A2C982E C0F976DA A9F25676
Round[4] After Shift Rows
912C7676 3AF956DE C0F2CE2E A93E98DA
Round[4] After Mix Columns
4D25CB1E ECF71646 7658C73B 49BCC9E9
Round[4] After Add Round Key
A2616E5F 44A54D39 C029E200 92B764E9
Round[5] After Sub Bytes
3AEF9FCF 1B06E312 BAA59863 4FA9431E
Round[5] After Shift Rows
3A06981E 1BA543CF BAA99F12 4FEFE363
Round[5] After Mix Columns
F89B35EC 4E40724E 025B00C7 34D7D81B
Round[5] After Add Round Key
2C4AF314 32C3EFC9 C8A9B87B 252ECDA7
Round[6] After Sub Bytes
71D60DFA 232EDFDD E8D36C21 3F31BD5C
Round[6] After Shift Rows
712E6C5C 23D3BDFA E8310DDD 3FD6DF21
Round[6] After Mix Columns
A0C56369 6FB884E4 4840BFBE E1D32F0A
Round[6] After Add Round Key
CD4DC013 7EB3BA19 93B939FF 2BD3BCF7
Round[7] After Sub Bytes
BDE3BA7D F36DF4D4 DC561216 F1666568
Round[7] After Shift Rows
BD6D1268 F356657D DC66BAD4 F1E3F416
Round[7] After Mix Columns
AC394C73 1F8DE8C7 6711B210 253DDB33
Round[7] After Add Round Key
E26DBB7D 40D22134 E3B7FDA2 6B9B077C
Round[8] After Sub Bytes
983CEAFF 09B5FD18 11A9543A 7F14C510
Round[8] After Shift Rows
98B55410 09A9C5FF 1114EA18 7F3CFD3A
Round[8] After Mix Columns
AB05B572 C8EB2B92 EC04E2FD 7D21EC34
Round[8] After Add Round Key
41D7C653 7D669140 DD2F179D 02ACC51B
Round[9] After Sub Bytes
830EB4ED FF338109 C115F05E 7791A6AF
Round[9] After Shift Rows
8333F0AF FF15A6ED C191B409 770E815E
Round[9] After Mix Columns
1741A118 91C99168 8C36386F 23AD82AA
Round[9] After Add Round Key
BB36C7EB 88334D49 A4E7112E 74F182C4
Round[10] After Sub Bytes
EA05C6E9 C4C3E33B 49948231 92A1131C
Round[10] After Shift Rows
EAC3821C C49413E9 49A1C63B 9205E331
Round[10] After Add Round Key
3AD77BB4 0D7A3660 A89ECAF3 2466EF97
Round[0] Input to Cipher
AE2D8A57 1E03AC9C 9EB76FAC 45AF8E51
Round[0] After Add Round Key
85539F41 36AD7E3A 35407A24 4C60C16D
Round[1] After Sub Bytes
97EDDB83 0595F380 9609DA36 29D0783C
Round[1] After Shift Rows
9795DA3C 05097883 96D0DB80 29EDF336
Round[1] After Mix Columns
77EFE995 EA1C6263 07DB70B1 BBD06309
Round[1] After Add Round Key
D7151782 62484ED2 24784988 91BC150C
Round[2] After Sub Bytes
0E59F013 AA522FB5 36BC3BC4 816559FE
Round[2] After Shift Rows
0E523BFE AABC5913 3665F0B5 81592FC4
Round[2] After Mix Columns
2F19339C DA319126 86426CBE 1986D17D
Round[2] After Add Round Key
DDDBA66E A0A72865 DF77ECC4 6ADF2702
Round[3] After Sub Bytes
C1B9249F E05C344D 9EF5CE1C 029ECC77
Round[3] After Shift Rows
C15CCE77 E0F5CC9F 9E9E244D 02B9341C
Round[3] After Mix Columns
C4478324 8CC12C27 F7989F99 FC2BF7B3
Round[3] After Add Round Key
F9C7C459 CBD7D219 E9BBE1DD 91517F88
Round[4] After Sub Bytes
99C61CCB 1F0EB5D4 1EEAF8C1 81D1D2C4
Round[4] After Shift Rows
990EF8C4 1FEAD2CB 1ED11CD4 81C6B5C1
Round[4] After Mix Columns
07522BD5 02760C94 9C57905C 3C136E72
Round[4] After Add Round Key
E8168E94 AA2457EB 2A26B567 E718C372
Round[5] After Sub Bytes
9B471922 AC365BE9 E5F7D585 94AD2E40
Round[5] After Shift Rows
9B36D540 ACF72E22 E5AD19E9 94475B85
Round[5] After Mix Columns
E2D3DCD5 4D096172 CD665A49 2472F1AA
Round[5] After Add Round Key
36021A2D 318AFCF5 0794E2F5 358BE416
Round[6] After Sub Bytes
0577A2D8 C77EB0E6 C52298E6 963D6947
Round[6] After Shift Rows
057E9847 C72269D8 C53DA2E6 9677B0E6
Round[6] After Mix Columns
570D9967 42E044B2 92A4961C F855ABB1
Round[6] After Add Round Key
3A853A1D 53EB7A4F 495D105D 3255384C
Round[7] After Sub Bytes
809780A4 EDE9DA84 3B4CCA4C 23FC0729
Round[7] After Shift Rows
80E9CA29 ED4C07A4 3BFC8084 2397DA4C
Round[7] After Mix Columns
D8259DEA B6D85834 6DC74B22 722FCFB0
Round[7] After Add Round Key
96716AE4 E98791C7 E9610490 3C8913FF
Round[8] After Sub Bytes
90A30269 1E1781C6 1EEFF260 EBA77D16
Round[8] After Shift Rows
9017F216 1EEF7D69 1EA702C6 EBA38160
Round[8] After Mix Columns
E6A54262 0235B062 0A8BEC10 D24EF1C4
Round[8] After Add Round Key
0C773143 B7B80AB0 3BA01970 ADC3D8EB
Round[9] After Sub Bytes
FEF5C71A A96C67E7 E2E0D451 952E61E9
Round[9] After Shift Rows
FE6CD4E9 A9E0611A E22EC7E7 95F56751
Round[9] After Mix Columns
6EA80168 09CBA555 8D0B6B01 039C5D94
Round[9] After Add Round Key
C2DF679B 10317974 A5DA4240 54C05DFA
Round[10] After Sub Bytes
259E8514 CAC7B692 06572C09 20BA4C2D
Round[10] After Shift Rows
25C72C2D CA574C14 06BA8592 209EB609
Round[10] After Add Round Key
F5D3D585 03B9699D E785895A 96FDBAAF
Round[0] Input to Cipher
30C81C46 A35CE411 E5FBC119 1A0A52EF
Round[0] After Add Round Key
1BB60950 8BF236B7 4E0CD491 13C51DD3
Round[1] After Sub Bytes
AF4E0153 3D8905A9 2FFE4881 7DA6A466
Round[1] After Shift Rows
AF894866 3DFEA453 2FA601A9 7D4E0581
Round[1] After Mix Columns
EB181CE7 947E65BB 07D26B9F AC6FA1D5
Round[1] After Add Round Key
4BE2E2F0 1C2A490A 247152A6 8603D7D0
Round[2] After Sub Bytes
B398988C 9CE53B67 36A30024 447B0E70
Round[2] After Shift Rows
B3E50070 9CA30E8C 367B9867 44983B24
Round[2] After Mix Columns
3912C6CB 5F5FAC11 1E14CF77 2406C627
Round[2] After Add Round Key
CBD05339 25C91552 47214F0D 575F3058
Round[3] After Sub Bytes
1F70ED12 3FDD5900 A0FD84D7 5BCF046A
Round[3] After Shift Rows
1FDD846A 3FFD0412 A0CFED00 5B7059D7
Round[3] After Mix Columns
AC436FAC 74C0FC9C FC09AED9 A887FB71
Round[3] After Add Round Key
91C328D1 33D602A2 E22AD09D C5FD734A
Round[4] After Sub Bytes
812E343E C3F6773A 98E5705E A6548FD6
Round[4] After Shift Rows
81F670D6 C3E58F3E 9854343A A62E775E
Round[4] After Mix Columns
BE30F6A9 18A66148 D956EAA7 0C3D8414
Round[4] After Add Round Key
517453E8 B0F43A37 6F27CF9C D7362914
Round[5] After Sub Bytes
D192ED9B E7BF809A A8CC8ADE 0E05A5FA
Round[5] After Shift Rows
D1BF8AFA E7CCA59B A805ED9A 0E9280DE
Round[5] After Mix Columns
13CB74B2 A40BCC76 3314D924 EF74FEA7
Round[5] After Add Round Key
C71AB24A D88851F1 F9E66198 FE8DEB1B
Round[6] After Sub Bytes
C6A237D6 61C4D1A1 998EEF46 BB5DE9AF
Round[6] After Shift Rows
C6C4EFAF 618EE9D6 995D37A1 BBA2D146
Round[6] After Mix Columns
80D02D3F 74904773 58DB5283 07CA6A29
Round[6] After Add Round Key
ED588E45 659B798E 8322D4C2 CDCAF9D4
Round[7] After Sub Bytes
556A196E 4D14B619 EC934825 BD749948
Round[7] After Shift Rows
55144848 4D93996E EC741919 BD6AB625
Round[7] After Mix Columns
96ED0933 C3AE4501 5F368170 4C8DCF4A
Round[7] After Add Round Key
D8B9FE3D 9CF18CF2 DB90CEC2 022B1305
Round[8] After Sub Bytes
6156BB27 DEA16489 B9608B25 77F17D6B
Round[8] After Shift Rows
61A18B6B DE607D27 B9F1BB89 77566425
Round[8] After Mix Columns
DAD5705F 5DBE2D2A 531FA593 555286E1
Round[8] After Add Round Key
3007037E E83397F8 623450F3 2ADFAFCE
Round[9] After Sub Bytes
04C57BF3 9BC38841 AA18530D E59E798B
Round[9] After Shift Rows
04C3538B 9B1879F3 AA9E7B41 E5C5880D
Round[9] After Mix Columns
8EE7E791 8FD37F2A CC410182 00FA3C63
Round[9] After Add Round Key
22908162 9629A30B E49028C3 57A63C0D
Round[10] After Sub Bytes
93600CAA 90A50A2B 6960342E 5B24EBD7
Round[10] After Shift Rows
93A534D7 9060EBAA 69240C2B 5B600A2E
Round[10] After Add Round Key
43B1CD7F 598ECE23 881B00E3 ED030688
Round[0] Input to Cipher
F69F2445 DF4F9B17 AD2B417B E66C3710
Round[0] After Add Round Key
DDE13153 F7E149B1 06DC54F3 EFA3782C
Round[1] After Sub Bytes
C1F8C7ED 68F83BC8 6F86200D DF0ABC71
Round[1] After Shift Rows
C1F82071 6886BCED 6F0AC7C8 DFF83B0D
Round[1] After Mix Columns
DB3BEA62 104DA143 CFE1B3F7 807446A3
Round[1] After Add Round Key
7BC11475 98198DF2 EC428ACE AA1830A6
Round[2] After Sub Bytes
2178FA9D 46D45D89 CE2C7E8B ACAD0424
Round[2] After Shift Rows
21D47E24 462C049D CEADFA89 AC785D8B
Round[2] After Mix Columns
7F346581 618FDEC3 18130C17 1D30E8C7
Round[2] After Add Round Key
8DF6F073 1B196780 41268C6D 6E691EB8
Round[3] After Sub Bytes
5D428C8F AFD485CD 83F7643C 9FF9726C
Round[3] After Shift Rows
5DD4646C AFF7728F 83F98CCD 9F42853C
Round[3] After Mix Columns
D52EF58F BA43366A 4C28356A 5AB38805
Round[3] After Add Round Key
E8AEB2F2 FD55C854 520B4B2E 37C9003E
Round[4] After Sub Bytes
9BE43789 54FCE820 002BB331 9ADD63B2
Round[4] After Shift Rows
9BFCB3B2 542B6389 00DD3720 9AE4E831
Round[4] After Mix Columns
3304D786 3F2E39BD 6BD8D3AA C15BE6DB
Round[4] After Add Round Key
DC4072C7 977C62C2 DDA9F691 1A504BDB
Round[5] After Sub Bytes
860940C6 8810AA25 C1D34281 A253B3B9
Round[5] After Shift Rows
861042B9 88D3B3C6 C1534025 A209AA81
Round[5] After Mix Columns
DCD9C2AA 103D7774 09827D01 6FD47C47
Round[5] After Add Round Key
08080452 6CBEEAF3 C370C5BD 7E2D69FB
Round[6] After Sub Bytes
3030F200 50AE870D 2E51A67A F3D8F90F
Round[6] After Shift Rows
30AEA60F 5051F900 2ED8F20D F330877A
Round[6] After Mix Columns
2089D846 AAE2E858 D0851E42 507B584D
Round[6] After Add Round Key
4D017B3C BBE9D6A5 0B7C9803 9A7BCBB0
Round[7] After Sub Bytes
E37C21EB EA1EF606 2B10467B B8211FE7
Round[7] After Shift Rows
E31E46E7 EA101FEB 2B212106 B87CF67B
Round[7] After Mix Columns
5EF243B3 0B00E2E7 120C4271 623ABEAF
Round[7] After Add Round Key
10A6B4BD 545F2B14 96AA0DC3 2C9C62E0
Round[8] After Sub Bytes
CA248D7A 20CFF1FA 90ACD72E 71DEAAE1
Round[8] After Shift Rows
CACFD7E1 20ACAA7A 90DE8DFA 7124F12E
Round[8] After Mix Columns
F3CC8884 7FFC4D92 35415A17 511FDE1A
Round[8] After Add Round Key
191EFBA5 CA71F740 046AAF77 2E92F735
Round[9] After Sub Bytes
D4720F06 74A36809 F20279F5 314F6896
Round[9] After Shift Rows
D4A37996 74026806 F24F0F09 317268F5
Round[9] After Mix Columns
A294248A 80CEACFA 2874B85F 699897B8
Round[9] After Add Round Key
0EE34279 993470DB 00A5911E 3EC497D6
Round[10] After Sub Bytes
AB112CB6 EE1851B9 63068172 B21C88F6
Round[10] After Shift Rows
AB1881F6 EE0688B6 631C2CB9 B2115172
Round[10] After Add Round Key
7B0C785E 27E8AD3F 82232071 04725DD4
== Menu ==
1 Detailed NIST FIPS 197 128-Bit Encryption
2 Detailed NIST FIPS 197 128-Bit Decryption
3 ECB Encryption 128-Bit Test Vectors
4 ECB Decryption 128-Bit Test Vectors
5 ECB Encryption 192-Bit Test Vectors
6 ECB Decryption 192-Bit Test Vectors
7 ECB Encryption 256-Bit Test Vectors
8 ECB Decryption 256-Bit Test Vectors
9 Exit
Enter option = 4
NIST Standard Test Data
128-Bit Cipher Key
2B7E1516 28AED2A6 ABF71588 09CF4F3C
Electronic Codebook (ECB) Mode
ECB-AES128 (Decryption)
NIST Standard Test Data
AES-128 (Nk = 4, Nr = 10)
Test Vectors
Round[10] Input to Inverse Cipher
3AD77BB4 0D7A3660 A89ECAF3 2466EF97
Round[10] After Add Round Key
EAC3821C C49413E9 49A1C63B 9205E331
Round[10] After Inverse Sub Bytes
BB3311C4 88E782EB A4F1C749 74364D2E
Round[10] After Inverse Shift Rows
BB36C7EB 88334D49 A4E7112E 74F182C4
Round[9] After Add RoundKey
1741A118 91C99168 8C36386F 23AD82AA
Round[9] After Mix Columns
8333F0AF FF15A6ED C191B409 770E815E
Round[9] After Inverse Sub Bytes
4166171B 7D2FC553 DDACC640 02D7919D
Round[9] After Inverse Shift Rows
41D7C653 7D669140 DD2F179D 02ACC51B
Round[8] After Add RoundKey
AB05B572 C8EB2B92 EC04E2FD 7D21EC34
Round[8] After Mix Columns
98B55410 09A9C5FF 1114EA18 7F3CFD3A
Round[8] After Inverse Sub Bytes
E2D2FD7C 40B7077D E39BBB34 6B6D21A2
Round[8] After Inverse Shift Rows
E26DBB7D 40D22134 E3B7FDA2 6B9B077C
Round[7] After Add RoundKey
AC394C73 1F8DE8C7 6711B210 253DDB33
Round[7] After Mix Columns
BD6D1268 F356657D DC66BAD4 F1E3F416
Round[7] After Inverse Sub Bytes
CDB339F7 7EB9BC13 93D3C019 2B4DBAFF
Round[7] After Inverse Shift Rows
CD4DC013 7EB3BA19 93B939FF 2BD3BCF7
Round[6] After Add RoundKey
A0C56369 6FB884E4 4840BFBE E1D32F0A
Round[6] After Mix Columns
712E6C5C 23D3BDFA E8310DDD 3FD6DF21
Round[6] After Inverse Sub Bytes
2CC3B8A7 32A9CD14 C82EF3C9 254AEF7B
Round[6] After Inverse Shift Rows
2C4AF314 32C3EFC9 C8A9B87B 252ECDA7
Round[5] After Add RoundKey
F89B35EC 4E40724E 025B00C7 34D7D81B
Round[5] After Mix Columns
3A06981E 1BA543CF BAA99F12 4FEFE363
Round[5] After Inverse Sub Bytes
A2A5E2E9 4429645F C0B76E39 92614D00
Round[5] After Inverse Shift Rows
A2616E5F 44A54D39 C029E200 92B764E9
Round[4] After Add RoundKey
4D25CB1E ECF71646 7658C73B 49BCC9E9
Round[4] After Mix Columns
912C7676 3AF956DE C0F2CE2E A93E98DA
Round[4] After Inverse Sub Bytes
AC420F0F A269B99C 1F04ECC3 B7D1E27A
Round[4] After Inverse Shift Rows
ACD1EC9C A242E2C3 1F690F7A B704B90F
Round[3] After Add RoundKey
9151ABE1 E5541CFD 014A713E DA7E3134
Round[3] After Mix Columns
54FE6141 B3B0EAB9 68D310AF D60D641E
Round[3] After Inverse Sub Bytes
FD0CD8F8 4BFCBBDB F7A97C1B 4AF38CE9
Round[3] After Inverse Shift Rows
FDF37CDB 4B0C8C1B F7FCD8E9 4AA9BBF8
Round[2] After Add RoundKey
0F31E929 319A3558 AEC95893 39F04D87
Round[2] After Mix Columns
89B5884A C0565303 2E389B21 604D123C
Round[2] After Inverse Sub Bytes
F2D2975C 1FB950D5 C376E87B 9065396D
Round[2] After Inverse Shift Rows
F265E8D5 1FD2397B C3B9976D 9076505C
Round[1] After Add RoundKey
529F16C2 978615CA E01AAE54 BA1A2659
Round[1] After Mix Columns
09287F47 6F746ABF 2C4A6204 DA08E3EE
Round[1] After Inverse Sub Bytes
40EE6B16 06CA58F4 425CAB30 7ABF4D99
Round[1] After Inverse Shift Rows
40BFABF4 06EE4D30 42CA6B99 7A5C5816
Round[0] After Add Round Key
6BC1BEE2 2E409F96 E93D7E11 7393172A
Round[10] Input to Inverse Cipher
F5D3D585 03B9699D E785895A 96FDBAAF
Round[10] After Add Round Key
25C72C2D CA574C14 06BA8592 209EB609
Round[10] After Inverse Sub Bytes
C23142FA 10DA5D9B A5C06774 54DF7940
Round[10] After Inverse Shift Rows
C2DF679B 10317974 A5DA4240 54C05DFA
Round[9] After Add RoundKey
6EA80168 09CBA555 8D0B6B01 039C5D94
Round[9] After Mix Columns
FE6CD4E9 A9E0611A E22EC7E7 95F56751
Round[9] After Inverse Sub Bytes
0CB819EB B7A0D843 3BC331B0 AD770A70
Round[9] After Inverse Shift Rows
0C773143 B7B80AB0 3BA01970 ADC3D8EB
Round[8] After Add RoundKey
E6A54262 0235B062 0A8BEC10 D24EF1C4
Round[8] After Mix Columns
9017F216 1EEF7D69 1EA702C6 EBA38160
Round[8] After Inverse Sub Bytes
968704FF E96113E4 E9896AC7 3C719190
Round[8] After Inverse Shift Rows
96716AE4 E98791C7 E9610490 3C8913FF
Round[7] After Add RoundKey
D8259DEA B6D85834 6DC74B22 722FCFB0
Round[7] After Mix Columns
80E9CA29 ED4C07A4 3BFC8084 2397DA4C
Round[7] After Inverse Sub Bytes
3AEB104C 535D381D 49553A4F 32857A5D
Round[7] After Inverse Shift Rows
3A853A1D 53EB7A4F 495D105D 3255384C
Round[6] After Add RoundKey
570D9967 42E044B2 92A4961C F855ABB1
Round[6] After Mix Columns
057E9847 C72269D8 C53DA2E6 9677B0E6
Round[6] After Inverse Sub Bytes
368AE216 3194E42D 078B1AF5 3502FCF5
Round[6] After Inverse Shift Rows
36021A2D 318AFCF5 0794E2F5 358BE416
Round[5] After Add RoundKey
E2D3DCD5 4D096172 CD665A49 2472F1AA
Round[5] After Mix Columns
9B36D540 ACF72E22 E5AD19E9 94475B85
Round[5] After Inverse Sub Bytes
E824B572 AA26C394 2A188EEB E7165767
Round[5] After Inverse Shift Rows
E8168E94 AA2457EB 2A26B567 E718C372
Round[4] After Add RoundKey
07522BD5 02760C94 9C57905C 3C136E72
Round[4] After Mix Columns
990EF8C4 1FEAD2CB 1ED11CD4 81C6B5C1
Round[4] After Inverse Sub Bytes
F9D7E188 CBBB7F59 E951C419 91C7D2DD
Round[4] After Inverse Shift Rows
F9C7C459 CBD7D219 E9BBE1DD 91517F88
Round[3] After Add RoundKey
C4478324 8CC12C27 F7989F99 FC2BF7B3
Round[3] After Mix Columns
C15CCE77 E0F5CC9F 9E9E244D 02B9341C
Round[3] After Inverse Sub Bytes
DDA7EC02 A077276E DFDFA665 6ADB28C4
Round[3] After Inverse Shift Rows
DDDBA66E A0A72865 DF77ECC4 6ADF2702
Round[2] After Add RoundKey
2F19339C DA319126 86426CBE 1986D17D
Round[2] After Mix Columns
0E523BFE AABC5913 3665F0B5 81592FC4
Round[2] After Inverse Sub Bytes
D748490C 62781582 24BC17D2 91154E88
Round[2] After Inverse Shift Rows
D7151782 62484ED2 24784988 91BC150C
Round[1] After Add RoundKey
77EFE995 EA1C6263 07DB70B1 BBD06309
Round[1] After Mix Columns
9795DA3C 05097883 96D0DB80 29EDF336
Round[1] After Inverse Sub Bytes
85AD7A6D 3640C141 35609F3A 4C537E24
Round[1] After Inverse Shift Rows
85539F41 36AD7E3A 35407A24 4C60C16D
Round[0] After Add Round Key
AE2D8A57 1E03AC9C 9EB76FAC 45AF8E51
Round[10] Input to Inverse Cipher
43B1CD7F 598ECE23 881B00E3 ED030688
Round[10] After Add Round Key
93A534D7 9060EBAA 69240C2B 5B600A2E
Round[10] After Inverse Sub Bytes
2229280D 96903C62 E4A6810B 5790A3C3
Round[10] After Inverse Shift Rows
22908162 9629A30B E49028C3 57A63C0D
Round[9] After Add RoundKey
8EE7E791 8FD37F2A CC410182 00FA3C63
Round[9] After Mix Columns
04C3538B 9B1879F3 AA9E7B41 E5C5880D
Round[9] After Inverse Sub Bytes
303350CE E834AF7E 62DF03F8 2A0797F3
Round[9] After Inverse Shift Rows
3007037E E83397F8 623450F3 2ADFAFCE
Round[8] After Add RoundKey
DAD5705F 5DBE2D2A 531FA593 555286E1
Round[8] After Mix Columns
61A18B6B DE607D27 B9F1BB89 77566425
Round[8] After Inverse Sub Bytes
D8F1CE05 9C90133D DB2BFEF2 02B98CC2
Round[8] After Inverse Shift Rows
D8B9FE3D 9CF18CF2 DB90CEC2 022B1305
Round[7] After Add RoundKey
96ED0933 C3AE4501 5F368170 4C8DCF4A
Round[7] After Mix Columns
55144848 4D93996E EC741919 BD6AB625
Round[7] After Inverse Sub Bytes
ED9BD4D4 6522F945 83CA8E8E CD5879C2
Round[7] After Inverse Shift Rows
ED588E45 659B798E 8322D4C2 CDCAF9D4
Round[6] After Add RoundKey
80D02D3F 74904773 58DB5283 07CA6A29
Round[6] After Mix Columns
C6C4EFAF 618EE9D6 995D37A1 BBA2D146
Round[6] After Inverse Sub Bytes
C788611B D8E6EB4A F98DB2F1 FE1A5198
Round[6] After Inverse Shift Rows
C71AB24A D88851F1 F9E66198 FE8DEB1B
Round[5] After Add RoundKey
13CB74B2 A40BCC76 3314D924 EF74FEA7
Round[5] After Mix Columns
D1BF8AFA E7CCA59B A805ED9A 0E9280DE
Round[5] After Inverse Sub Bytes
51F4CF14 B02729E8 6F365337 D7743A9C
Round[5] After Inverse Shift Rows
517453E8 B0F43A37 6F27CF9C D7362914
Round[4] After Add RoundKey
BE30F6A9 18A66148 D956EAA7 0C3D8414
Round[4] After Mix Columns
81F670D6 C3E58F3E 9854343A A62E775E
Round[4] After Inverse Sub Bytes
91D6D04A 332A73D1 E2FD28A2 C5C3029D
Round[4] After Inverse Shift Rows
91C328D1 33D602A2 E22AD09D C5FD734A
Round[3] After Add RoundKey
AC436FAC 74C0FC9C FC09AED9 A887FB71
Round[3] After Mix Columns
1FDD846A 3FFD0412 A0CFED00 5B7059D7
Round[3] After Inverse Sub Bytes
CBC94F58 25213039 475F5352 57D0150D
Round[3] After Inverse Shift Rows
CBD05339 25C91552 47214F0D 575F3058
Round[2] After Add RoundKey
3912C6CB 5F5FAC11 1E14CF77 2406C627
Round[2] After Mix Columns
B3E50070 9CA30E8C 367B9867 44983B24
Round[2] After Inverse Sub Bytes
4B2A52D0 1C71D7F0 2403E20A 86E249A6
Round[2] After Inverse Shift Rows
4BE2E2F0 1C2A490A 247152A6 8603D7D0
Round[1] After Add RoundKey
EB181CE7 947E65BB 07D26B9F AC6FA1D5
Round[1] After Mix Columns
AF894866 3DFEA453 2FA601A9 7D4E0581
Round[1] After Inverse Sub Bytes
1BF2D4D3 8B0C1D50 4EC509B7 13B63691
Round[1] After Inverse Shift Rows
1BB60950 8BF236B7 4E0CD491 13C51DD3
Round[0] After Add Round Key
30C81C46 A35CE411 E5FBC119 1A0A52EF
Round[10] Input to Inverse Cipher
7B0C785E 27E8AD3F 82232071 04725DD4
Round[10] After Add Round Key
AB1881F6 EE0688B6 631C2CB9 B2115172
Round[10] After Inverse Sub Bytes
0E3491D6 99A59779 00C442DB 3EE3701E
Round[10] After Inverse Shift Rows
0EE34279 993470DB 00A5911E 3EC497D6
Round[9] After Add RoundKey
A294248A 80CEACFA 2874B85F 699897B8
Round[9] After Mix Columns
D4A37996 74026806 F24F0F09 317268F5
Round[9] After Inverse Sub Bytes
1971AF35 CA6AF7A5 0492FB40 2E1EF777
Round[9] After Inverse Shift Rows
191EFBA5 CA71F740 046AAF77 2E92F735
Round[8] After Add RoundKey
F3CC8884 7FFC4D92 35415A17 511FDE1A
Round[8] After Mix Columns
CACFD7E1 20ACAA7A 90DE8DFA 7124F12E
Round[8] After Inverse Sub Bytes
105F0DE0 54AA62BD 969CB414 2CA62BC3
Round[8] After Inverse Shift Rows
10A6B4BD 545F2B14 96AA0DC3 2C9C62E0
Round[7] After Add RoundKey
5EF243B3 0B00E2E7 120C4271 623ABEAF
Round[7] After Mix Columns
E31E46E7 EA101FEB 2B212106 B87CF67B
Round[7] After Inverse Sub Bytes
4DE998B0 BB7CCB3C 0B7B7BA5 9A01D603
Round[7] After Inverse Shift Rows
4D017B3C BBE9D6A5 0B7C9803 9A7BCBB0
Round[6] After Add RoundKey
2089D846 AAE2E858 D0851E42 507B584D
Round[6] After Mix Columns
30AEA60F 5051F900 2ED8F20D F330877A
Round[6] After Inverse Sub Bytes
08BEC5FB 6C706952 C32D04F3 7E08EABD
Round[6] After Inverse Shift Rows
08080452 6CBEEAF3 C370C5BD 7E2D69FB
Round[5] After Add RoundKey
DCD9C2AA 103D7774 09827D01 6FD47C47
Round[5] After Mix Columns
861042B9 88D3B3C6 C1534025 A209AA81
Round[5] After Inverse Sub Bytes
DC7CF6DB 97A94BC7 DD5072C2 1A406291
Round[5] After Inverse Shift Rows
DC4072C7 977C62C2 DDA9F691 1A504BDB
Round[4] After Add RoundKey
3304D786 3F2E39BD 6BD8D3AA C15BE6DB
Round[4] After Mix Columns
9BFCB3B2 542B6389 00DD3720 9AE4E831
Round[4] After Inverse Sub Bytes
E8554B3E FD0B00F2 52C9B254 37AEC82E
Round[4] After Inverse Shift Rows
E8AEB2F2 FD55C854 520B4B2E 37C9003E
Round[3] After Add RoundKey
D52EF58F BA43366A 4C28356A 5AB38805
Round[3] After Mix Columns
5DD4646C AFF7728F 83F98CCD 9F42853C
Round[3] After Inverse Sub Bytes
8D198CB8 1B261E73 4169F080 6EF6676D
Round[3] After Inverse Shift Rows
8DF6F073 1B196780 41268C6D 6E691EB8
Round[2] After Add RoundKey
7F346581 618FDEC3 18130C17 1D30E8C7
Round[2] After Mix Columns
21D47E24 462C049D CEADFA89 AC785D8B
Round[2] After Inverse Sub Bytes
7B198AA6 98423075 EC1814F2 AAC18DCE
Round[2] After Inverse Shift Rows
7BC11475 98198DF2 EC428ACE AA1830A6
Round[1] After Add RoundKey
DB3BEA62 104DA143 CFE1B3F7 807446A3
Round[1] After Mix Columns
C1F82071 6886BCED 6F0AC7C8 DFF83B0D
Round[1] After Inverse Sub Bytes
DDE1542C F7DC7853 06A331B1 EFE149F3
Round[1] After Inverse Shift Rows
DDE13153 F7E149B1 06DC54F3 EFA3782C
Round[0] After Add Round Key
F69F2445 DF4F9B17 AD2B417B E66C3710
== Menu ==
1 Detailed NIST FIPS 197 128-Bit Encryption
2 Detailed NIST FIPS 197 128-Bit Decryption
3 ECB Encryption 128-Bit Test Vectors
4 ECB Decryption 128-Bit Test Vectors
5 ECB Encryption 192-Bit Test Vectors
6 ECB Decryption 192-Bit Test Vectors
7 ECB Encryption 256-Bit Test Vectors
8 ECB Decryption 256-Bit Test Vectors
9 Exit
Enter option = 5
NIST Standard Test Data
192-Bit Cipher Key
8E73B0F7 DA0E6452 C810F32B 809079E5 62F8EAD2 522C6B7B
Electronic Codebook (ECB) Mode
ECB-AES192 (Encryption)
NIST Standard Test Data
AES-192 (Nk = 6, Nr = 12)
Test Vectors
Round[0] Input to Cipher
6BC1BEE2 2E409F96 E93D7E11 7393172A
Round[0] After Add Round Key
E5B20E15 F44EFBC4 212D8D3A F3036ECF
Round[1] After Sub Bytes
D937AB59 BF2F0F1C FDD85D80 0D7B9F8A
Round[1] After Shift Rows
D92F5D8A BFD89F59 FD7BAB1C 0D370F80
Round[1] After Mix Columns
0FEAC90D D0F7A92F DBF1EFF4 CCF2BF34
Round[1] After Add Round Key
6D1223DF 82DBC254 25FD7E03 E8F04A91
Round[2] After Sub Bytes
3CC9269E 13B92520 3F54F37B 9B8CD681
Round[2] After Shift Rows
3CB9F381 1354D69E 3F8C2620 9BC9257B
Round[2] After Mix Columns
DADAE017 92444990 F7769FAB 330695AC
Round[2] After Add Round Key
36C8E699 FEC636FB F90C0A12 6F506B6E
Round[3] After Sub Bytes
05E88EEE BBB4050F 99FE67C9 A8537F9F
Round[3] After Shift Rows
05B4679F BBFE7FEE 99538E0F A8E805C9
Round[3] After Mix Columns
3540C5F9 E5339290 5DB9DC73 A4A50A87
Round[3] After Add Round Key
78F77144 8C86D388 D81E9BE5 4D80327A
Round[4] After Sub Bytes
BC68A31B 644466C4 617214D9 E3CD23DA
Round[4] After Shift Rows
BC4414DA 6472231B 61CDA3C4 E36866D9
Round[4] After Mix Columns
61D2A520 66FE7DCB E9DAA65E DA403799
Round[4] After Add Round Key
868D0864 DDF72E4D A1805609 FBAF86D6
Round[5] After Sub Bytes
445D3043 C16831E3 32CDB101 0F7944F6
Round[5] After Shift Rows
4468B1F6 C1CD4443 327930E3 0F5D3101
Round[5] After Mix Columns
77AA54E2 D2CF4157 3C7315C2 C9E7337F
Round[5] After Add Round Key
D3E2A23B 9FA28F73 964176A2 D8DC0399
Round[6] After Sub Bytes
66983AE2 DB3A738F 9083383A 61867BEE
Round[6] After Shift Rows
663A38EE DB837BE2 90863A8F 6198733A
Round[6] After Mix Columns
54B4056F AAA99351 1F46E812 38E5513C
Round[6] After Add Round Key
F6EA7BBA 29185CCB 38BFD151 5271A65B
Round[7] After Sub Bytes
428721F4 A5AD4A1F 07083ED1 00A32439
Round[7] After Shift Rows
42AD3E39 A50824F4 07A3211F 00874AD1
Round[7] After Mix Columns
6F78D827 992DE22B CE26C7B5 091A7B74
Round[7] After Add Round Key
AFDE4C20 48B046CA 2231415E 66BC3205
Round[8] After Sub Bytes
791D29B7 52E75A74 93C78358 3365236B
Round[8] After Shift Rows
79E7836B 52C723B7 93652974 331D5A58
Round[8] After Mix Columns
28593E39 62151167 CF56380A 43BF72A2
Round[8] After Add Round Key
60064E0B 40DE9632 2D3B2B58 704FC511
Round[9] After Sub Bytes
D06F2F2B 091D9023 D8E2F16A 5184A682
Round[9] After Shift Rows
D01DF182 09E2A62B D8842F23 516F906A
Round[9] After Mix Columns
EF60A998 A20CC109 3099679E E94EBBD8
Round[9] After Add Round Key
AFDE42B0 8D146350 57DEB5F5 ACC2EEE6
Round[10] After Sub Bytes
791D2CE7 5DFAFB53 5B1DD5E6 9125288E
Round[10] After Shift Rows
79FAD58E 5D1D28E7 5B252C53 911DFBE6
Round[10] After Mix Columns
BC7CBBA3 52F82207 A636D342 035B5099
Round[10] After Add Round Key
1B9DFDCF C6E9D3D8 2429A648 AE5C87CA
Round[11] After Sub Bytes
AF5E548A B41E6661 36A52452 E44A1774
Round[11] After Shift Rows
AF1E2474 B4A5178A 364A5461 E45E6652
Round[11] After Mix Columns
378B6538 1A56BA7A 873F7786 05A080AB
Round[11] After Add Round Key
FDCB6000 959AEA7C AF1261EC B99C671E
Round[12] After Sub Bytes
541FD063 2AB88710 79C9EFCE 56DE8572
Round[12] After Shift Rows
54B8EF72 2AC98563 79DED010 561F87CE
Round[12] After Add Round Key
BD334F1D 6E45F25F F712A214 571FA5CC
Round[0] Input to Cipher
AE2D8A57 1E03AC9C 9EB76FAC 45AF8E51
Round[0] After Add Round Key
205E3AA0 C40DC8CE 56A79C87 C53FF7B4
Round[1] After Sub Bytes
B75880E0 1CD7E88B B15CDE17 A675688D
Round[1] After Shift Rows
B7D7DE8D 1C5C68E0 B175808B A658E817
Round[1] After Mix Columns
44F64BCA 54FCABCB ED4B5930 40220C6F
Round[1] After Add Round Key
260EA118 06D0C0B0 1347C8C7 6420F9CA
Round[2] After Sub Bytes
F7AB32AD 6F70BAE7 7DA0E8C6 43B79974
Round[2] After Shift Rows
F770E874 6FA099AD 7DB732E7 43ABBAC6
Round[2] After Mix Columns
F940D072 11290AC9 EDB99CD7 1C1DD643
Round[2] After Add Round Key
1552D6FC 7DAB75A2 E3C3096E 404B2881
Round[3] After Sub Bytes
5900F6B0 FF629D3A 112E019F 09B3340C
Round[3] After Shift Rows
5962010C FF2E34B0 11B3F63A 09009D9F
Round[3] After Mix Columns
19922D90 134F727B 20571B02 102A92A3
Round[3] After Add Round Key
5425992D 7AFA3363 A5F05C94 F90FAA5E
Round[4] After Sub Bytes
203FEED8 DA2DC3FB 068C4A22 9976AC58
Round[4] After Shift Rows
202D4A58 DA8CACD8 0676EEFB 993FC322
Round[4] After Mix Columns
25FC71B7 54EE66FE 8338A17F 899B5D08
Round[4] After Add Round Key
C2A3DCF3 EFE73578 CB625128 A874EC47
Round[5] After Sub Bytes
250A860D DF9496BC 1FAAD134 C292CEA0
Round[5] After Shift Rows
2594D1A0 DFAACE0D 1F9286BC C20A9634
Round[5] After Mix Columns
9CDEF371 83D4E504 A90D4556 2343A3A9
Round[5] After Add Round Key
389605A8 CEB92B20 033F2636 3278934F
Round[6] After Sub Bytes
07906BC2 8B56F1B7 7B75F705 23BCDC84
Round[6] After Shift Rows
0756F784 8B75DCC2 7BBC6BB7 2390F105
Round[6] After Mix Columns
872D33BB 8CDC00B0 F512D32F 1915450E
Round[6] After Add Round Key
25734D6E 0F6DCF2A D2EBEA6C 7381B269
Round[7] After Sub Bytes
3F8FE39F 763C8AE5 B5E98750 8F0C37F9
Round[7] After Shift Rows
3F3C87F9 76E9379F B50CE3E5 8F8F8A50
Round[7] After Mix Columns
442C0613 64794B61 637650FA 555FFF2F
Round[7] After Add Round Key
848A9214 B5E4EF80 8F61D611 3AF9B65E
Round[8] After Sub Bytes
5F7E4FFA D569DFCD 73EFF682 80994E58
Round[8] After Shift Rows
5F69F658 D5EF4EFA 73994FCD 807EDF82
Round[8] After Mix Columns
ABD429CE 2F38B32A D44638C2 C484C625
Round[8] After Add Round Key
E38B59FC 0DF3347F 362B2B90 F7747196
Round[9] After Sub Bytes
113DCBB0 D70D18D2 05F1F160 6892A390
Round[9] After Shift Rows
110DF190 D7F1A3B0 0592CBD2 683D1860
Round[9] After Mix Columns
54934EF4 AE60B04B BEAE77E9 EF5AC55D
Round[9] After Add Round Key
142DA5DC 81781212 D9E9A582 AAD69063
Round[10] After Sub Bytes
FAD80686 0CBCC9C9 351E0613 ACF660FB
Round[10] After Shift Rows
FABC06FB 0C1E6086 35F606C9 ACD8C913
Round[10] After Mix Columns
CD685C42 DC16437D A4018F26 EA54C8D8
Round[10] After Add Round Key
6A891A2E 4807B2A2 261EFA2C 47531F8B
Round[11] After Sub Bytes
02A7A231 52C5373A F7722D71 A0EDC03D
Round[11] After Shift Rows
02C52D3D 5272C031 F7EDA23A A0A73771
Round[11] After Mix Columns
40D9DA94 C3DCE826 41F10B39 EFDDFA89
Round[11] After Add Round Key
8A99DFAC 4C10B820 69DC1D53 53E11D3C
Round[12] After Sub Bytes
7EEE9E91 29CA6CB7 F986A4ED EDF8A4EB
Round[12] After Shift Rows
7ECAA4EB 2986A491 F9F89EB7 EDEE6CED
Round[12] After Add Round Key
97410484 6D0AD3AD 7734ECB3 ECEE4EEF
Round[0] Input to Cipher
30C81C46 A35CE411 E5FBC119 1A0A52EF
Round[0] After Add Round Key
BEBBACB1 79528043 2DEB3232 9A9A2B0A
Round[1] After Sub Bytes
AEEA91C8 B600CD1A D8E92323 B8B8F167
Round[1] After Shift Rows
AE002367 B6E9F1C8 D8B8911A B8EACD23
Round[1] After Mix Columns
03AC4104 6EBFE552 F301776E A018B6B2
Round[1] After Add Round Key
6154ABD6 3C938E29 0D0DE699 841A4317
Round[2] After Sub Bytes
EF2062F6 EBDC19A5 D7D78EEE 5FA21AF0
Round[2] After Shift Rows
EFDC8EF0 EBD71AF6 D7A262A5 5F2019EE
Round[2] After Mix Columns
C4353F83 4386091C 8F8B45F3 29DA641F
Round[2] After Add Round Key
2827390D 2F047677 81F1D04A 758C9ADD
Round[3] After Sub Bytes
34CC12D7 15F238F5 0CA170D6 9D64B8C1
Round[3] After Shift Rows
34F270C1 15A1B8D7 0C6412F5 9DCC38D6
Round[3] After Mix Columns
D49A7E47 BD48BD93 53074893 808040FF
Round[3] After Add Round Key
992DCAFA D4FDFC8B D6A00F05 69A57802
Round[4] After Sub Bytes
EED8742D 4854B03D F6E0766B F906BC77
Round[4] After Shift Rows
EE547677 48E0BC2D F606743D F9D8B06B
Round[4] After Mix Columns
3AABCFE5 3A61BCDE B45B5F09 41F2E7AE
Round[4] After Add Round Key
DDF462A1 8168EF58 FC01AF5E 601D56E1
Round[5] After Sub Bytes
C1BFAA32 0C45DF6A B07C7958 D0A4B1F8
Round[5] After Shift Rows
C14579F8 0C7CB132 B0A4AA6A D0BFDF58
Round[5] After Mix Columns
D738658F 1F0E5FBD 4C6CE511 E69722BB
Round[5] After Add Round Key
73709356 52639199 E65E8671 F7AC125D
Round[6] After Sub Bytes
8F51DCB1 00FB81EE 8E5844A3 6891C94C
Round[6] After Shift Rows
8FFB444C 0058C9B1 8E91DCEE 685181A3
Round[6] After Mix Columns
1BE228AD 904119E8 9D269503 01F1DE35
Round[6] After Add Round Key
B9BC5678 13F0D672 BADFAC40 6B652952
Round[7] After Sub Bytes
5665B1BC 7D8CF640 F49E9109 7F4DA500
Round[7] After Shift Rows
568C9100 7D9EA5BC F44DB140 7F65F609
Round[7] After Mix Columns
B2FDE3E7 5A126DDF D5E6007B AEBDF600
Round[7] After Add Round Key
725B77E0 8B8FC93E 39F18690 C11BBF71
Round[8] After Sub Bytes
4039F5E1 3D73DDB2 12A14460 78AF08A3
Round[8] After Shift Rows
407344A3 3DA108E1 12AFF5B2 7839DD60
Round[8] After Mix Columns
F2C945AA 6B9DB437 89E18113 061640AC
Round[8] After Add Round Key
BA963598 49563362 6B8C9241 35E6F71F
Round[9] After Sub Bytes
F4909646 3BB1C3AA 7F644F83 968E68C0
Round[9] After Shift Rows
F4B14FC0 3B646846 7F8E96AA 9690C383
Round[9] After Mix Columns
B49C8062 F40D45CD 4B7323D6 DC7005EF
Round[9] After Add Round Key
F4226B4A DB15E794 2C34F1BD 99FC50D1
Round[10] After Sub Bytes
BF937FD6 B9599422 7118A17A EEB0533E
Round[10] After Shift Rows
BF59A13E B91853D6 71B07F22 EE93947A
Round[10] After Mix Columns
11CBFD5E C4AA662C 74A95918 870EC0DA
Round[10] After Add Round Key
B62ABB32 50BB97F3 F6B62C12 2A091789
Round[11] After Sub Bytes
4EE5EA23 53EA880D 424E71C9 E501F0A7
Round[11] After Shift Rows
4EEA71A7 534EF023 4201EA0D E5E588C9
Round[11] After Mix Columns
6FB5B41C A7E7830D 60689B37 A47E4BD0
Round[11] After Add Round Key
A5F5B124 282BD30B 48458D5D 1842AC65
Round[12] After Sub Bytes
06E6C836 34F1662B 526E5D4C AD2C914D
Round[12] After Shift Rows
06F15D4D 346E9136 522CC82B ADE6664C
Round[12] After Add Round Key
EF7AFD22 70E2E60A DCE0BA2F ACE6444E
Round[0] Input to Cipher
F69F2445 DF4F9B17 AD2B417B E66C3710
Round[0] After Add Round Key
78EC94B2 0541FF45 653BB250 66FC4EF5
Round[1] After Sub Bytes
BCCE2237 6B83166E 4DE23753 33B02FE6
Round[1] After Shift Rows
BC8337E6 6BE22F37 4DB0226E 33CE1653
Round[1] After Mix Columns
2C1E60BC F3F28E1E 1D3E0B99 6ADD242B
Round[1] After Add Round Key
4EE68A6E A1DEE565 E3329A6E 4EDFD18E
Round[2] After Sub Bytes
2F8E7E9F 321DD94D 1123B89F 2F9E3E19
Round[2] After Shift Rows
2F1DB819 32233E9F 119E7E4D 2F8ED99F
Round[2] After Mix Columns
D8DF72E6 A0A9D76E A8F9A449 91C7B203
Round[2] After Add Round Key
34CD7468 CC2BA805 A68331F0 CD914CC1
Round[3] After Sub Bytes
18BD9245 4BF1C26B 24ECC78C BD812978
Round[3] After Shift Rows
18F1C778 4BEC2945 2481926B BDBDC28C
Round[3] After Mix Columns
87CBF4EE D5B63A92 29FB27A9 F30D10A0
Round[3] After Add Round Key
CA7C4053 BC037B8A AC5C603F 1A28285D
Round[4] After Sub Bytes
741009ED 657B217E 914AD075 A234344C
Round[4] After Shift Rows
747BD04C 654A34ED 9134097E A2102175
Round[4] After Mix Columns
F9A560AF CD406B10 129C3569 3B946F26
Round[4] After Add Round Key
1EFACDEB 76493896 5AC6C53E 1A7BDE69
Round[5] After Sub Bytes
722DBDE9 383B0790 BEB4A6B2 A2211DF9
Round[5] After Shift Rows
723BA6F9 38B41DE9 BE21BD90 A22D07B2
Round[5] After Mix Columns
F60C0EE2 43859628 29B0557E 9D434CA8
Round[5] After Add Round Key
5244F83B 0EE8580C 8382361E 8C787C4E
Round[6] After Sub Bytes
001B41E2 AB9B6AFE EC130572 64BC102F
Round[6] After Shift Rows
009B052F AB1310E2 ECBC41FE 641B6A72
Round[6] After Mix Columns
9C0DE0C0 8A5FA53A A3B2CB35 FD9E3D39
Round[6] After Add Round Key
3E539E15 09EE6AA0 844BF276 970ACA5E
Round[7] After Sub Bytes
B2ED0B59 012802E0 5FB38938 88677458
Round[7] After Shift Rows
B2288958 01B37459 5F670BE0 88ED0238
Round[7] After Mix Columns
D63A7BDC E1B9B176 FC6C1556 1D77291C
Round[7] After Add Round Key
169CEFDB 30241597 107B93BD 72D1606D
Round[8] After Sub Bytes
47DEDFB9 04365988 CA21DC7A 403ED03C
Round[8] After Shift Rows
4736DC3C 0421D0B9 CA3EDF88 40DE597A
Round[8] After Mix Columns
3468965B 02944E94 9A44D2AF DA76A2B3
Round[8] After Add Round Key
7C37E669 205FC9C1 7829C1FD E9861500
Round[9] After Sub Bytes
109A8EF9 B7CFDD78 BCA57854 1E445963
Round[9] After Shift Rows
10CF7863 B7A559F9 BC448E78 1E9ADD54
Round[9] After Mix Columns
717E8A41 21F4B0D7 59C577E5 0019D9CD
Round[9] After Add Round Key
31C06169 0EEC128E 3E82A58E 45958CF3
Round[10] After Sub Bytes
C7BAEFF9 ABCEC919 B2130619 6E2A640D
Round[10] After Shift Rows
C7CE060D AB1364F9 B22AEF19 6EBAC919
Round[10] After Mix Columns
D7471280 E5D86078 F7D5763A D95876F3
Round[10] After Add Round Key
70A654EC 71C991A7 75CA0330 745FA1A0
Round[11] After Sub Bytes
512420CE A3DD815C 9D747B04 92CF32E0
Round[11] After Shift Rows
51DD7BE0 A37432CE 9DCF205C 92248104
Round[11] After Mix Columns
459D418E 3DD3FA3F 1724F6EB D646A300
Round[11] After Add Round Key
8FDD44B6 B21FAA39 3F09E081 6A7A44B5
Round[12] After Sub Bytes
73C11B4E 37C0AC12 7501E10C 02DA1BD5
Round[12] After Shift Rows
73C0E1D5 37011B4E 75DA1B12 02C1AC0C
Round[12] After Add Round Key
9A4B41BA 738D6C72 FB166916 03C18E0E
== Menu ==
1 Detailed NIST FIPS 197 128-Bit Encryption
2 Detailed NIST FIPS 197 128-Bit Decryption
3 ECB Encryption 128-Bit Test Vectors
4 ECB Decryption 128-Bit Test Vectors
5 ECB Encryption 192-Bit Test Vectors
6 ECB Decryption 192-Bit Test Vectors
7 ECB Encryption 256-Bit Test Vectors
8 ECB Decryption 256-Bit Test Vectors
9 Exit
Enter option = 6
NIST Standard Test Data
192-Bit Cipher Key
8E73B0F7 DA0E6452 C810F32B 809079E5 62F8EAD2 522C6B7B
Electronic Codebook (ECB) Mode
ECB-AES192 (Decryption)
NIST Standard Test Data
AES-192 (Nk = 6, Nr = 12)
Test Vectors
Round[12] Input to Inverse Cipher
BD334F1D 6E45F25F F712A214 571FA5CC
Round[12] After Add Round Key
54B8EF72 2AC98563 79DED010 561F87CE
Round[12] After Inverse Sub Bytes
FD9A611E 95126700 AF9C607C B9CBEAEC
Round[12] After Inverse Shift Rows
FDCB6000 959AEA7C AF1261EC B99C671E
Round[11] After Add RoundKey
378B6538 1A56BA7A 873F7786 05A080AB
Round[11] After Mix Columns
AF1E2474 B4A5178A 364A5461 E45E6652
Round[11] After Inverse Sub Bytes
1BE9A6CA C62987CF 245CFDD8 AE9DD348
Round[11] After Inverse Shift Rows
1B9DFDCF C6E9D3D8 2429A648 AE5C87CA
Round[10] After Add RoundKey
BC7CBBA3 52F82207 A636D342 035B5099
Round[10] After Mix Columns
79FAD58E 5D1D28E7 5B252C53 911DFBE6
Round[10] After Inverse Sub Bytes
AF14B5E6 8DDEEEB0 57C24250 ACDE63F5
Round[10] After Inverse Shift Rows
AFDE42B0 8D146350 57DEB5F5 ACC2EEE6
Round[9] After Add RoundKey
EF60A998 A20CC109 3099679E E94EBBD8
Round[9] After Mix Columns
D01DF182 09E2A62B D8842F23 516F906A
Round[9] After Inverse Sub Bytes
60DE2B11 403BC50B 2D4F4E32 70069658
Round[9] After Inverse Shift Rows
60064E0B 40DE9632 2D3B2B58 704FC511
Round[8] After Add RoundKey
28593E39 62151167 CF56380A 43BF72A2
Round[8] After Mix Columns
79E7836B 52C723B7 93652974 331D5A58
Round[8] After Inverse Sub Bytes
AFB04105 48313220 22BC4CCA 66DE465E
Round[8] After Inverse Shift Rows
AFDE4C20 48B046CA 2231415E 66BC3205
Round[7] After Add RoundKey
6F78D827 992DE22B CE26C7B5 091A7B74
Round[7] After Mix Columns
42AD3E39 A50824F4 07A3211F 00874AD1
Round[7] After Inverse Sub Bytes
F618D15B 29BFA6BA 38717BCB 52EA5C51
Round[7] After Inverse Shift Rows
F6EA7BBA 29185CCB 38BFD151 5271A65B
Round[6] After Add RoundKey
54B4056F AAA99351 1F46E812 38E5513C
Round[6] After Mix Columns
663A38EE DB837BE2 90863A8F 6198733A
Round[6] After Inverse Sub Bytes
D3A27699 9F41033B 96DCA273 D8E28FA2
Round[6] After Inverse Shift Rows
D3E2A23B 9FA28F73 964176A2 D8DC0399
Round[5] After Add RoundKey
77AA54E2 D2CF4157 3C7315C2 C9E7337F
Round[5] After Mix Columns
4468B1F6 C1CD4443 327930E3 0F5D3101
Round[5] After Inverse Sub Bytes
86F756D6 DD808664 A1AF084D FB8D2E09
Round[5] After Inverse Shift Rows
868D0864 DDF72E4D A1805609 FBAF86D6
Round[4] After Add RoundKey
61D2A520 66FE7DCB E9DAA65E DA403799
Round[4] After Mix Columns
BC4414DA 6472231B 61CDA3C4 E36866D9
Round[4] After Inverse Sub Bytes
78869B7A 8C1E3244 D8807188 4DF7D3E5
Round[4] After Inverse Shift Rows
78F77144 8C86D388 D81E9BE5 4D80327A
Round[3] After Add RoundKey
3540C5F9 E5339290 5DB9DC73 A4A50A87
Round[3] After Mix Columns
05B4679F BBFE7FEE 99538E0F A8E805C9
Round[3] After Inverse Sub Bytes
36C60A6E FE0C6B99 F950E6FB 6FC83612
Round[3] After Inverse Shift Rows
36C8E699 FEC636FB F90C0A12 6F506B6E
Round[2] After Add RoundKey
DADAE017 92444990 F7769FAB 330695AC
Round[2] After Mix Columns
3CB9F381 1354D69E 3F8C2620 9BC9257B
Round[2] After Inverse Sub Bytes
6DDB7E91 82FD4ADF 25F02354 E812C203
Round[2] After Inverse Shift Rows
6D1223DF 82DBC254 25FD7E03 E8F04A91
Round[1] After Add RoundKey
0FEAC90D D0F7A92F DBF1EFF4 CCF2BF34
Round[1] After Mix Columns
D92F5D8A BFD89F59 FD7BAB1C 0D370F80
Round[1] After Inverse Sub Bytes
E54E8DCF F42D6E15 21030EC4 F3B2FB3A
Round[1] After Inverse Shift Rows
E5B20E15 F44EFBC4 212D8D3A F3036ECF
Round[0] After Add Round Key
6BC1BEE2 2E409F96 E93D7E11 7393172A
Round[12] Input to Inverse Cipher
97410484 6D0AD3AD 7734ECB3 ECEE4EEF
Round[12] After Add Round Key
7ECAA4EB 2986A491 F9F89EB7 EDEE6CED
Round[12] After Inverse Sub Bytes
8A101D3C 4CDC1DAC 69E1DF20 5399B853
Round[12] After Inverse Shift Rows
8A99DFAC 4C10B820 69DC1D53 53E11D3C
Round[11] After Add RoundKey
40D9DA94 C3DCE826 41F10B39 EFDDFA89
Round[11] After Mix Columns
02C52D3D 5272C031 F7EDA23A A0A73771
Round[11] After Inverse Sub Bytes
6A07FA8B 481E1F2E 26531AA2 4789B22C
Round[11] After Inverse Shift Rows
6A891A2E 4807B2A2 261EFA2C 47531F8B
Round[10] After Add RoundKey
CD685C42 DC16437D A4018F26 EA54C8D8
Round[10] After Mix Columns
FABC06FB 0C1E6086 35F606C9 ACD8C913
Round[10] After Inverse Sub Bytes
1478A563 81E990DC D9D6A512 AA2D1282
Round[10] After Inverse Shift Rows
142DA5DC 81781212 D9E9A582 AAD69063
Round[9] After Add RoundKey
54934EF4 AE60B04B BEAE77E9 EF5AC55D
Round[9] After Mix Columns
110DF190 D7F1A3B0 0592CBD2 683D1860
Round[9] After Inverse Sub Bytes
E3F32B96 0D2B71FC 3674597F F78B3490
Round[9] After Inverse Shift Rows
E38B59FC 0DF3347F 362B2B90 F7747196
Round[8] After Add RoundKey
ABD429CE 2F38B32A D44638C2 C484C625
Round[8] After Mix Columns
5F69F658 D5EF4EFA 73994FCD 807EDF82
Round[8] After Inverse Sub Bytes
84E4D65E B561B614 8FF99280 3A8AEF11
Round[8] After Inverse Shift Rows
848A9214 B5E4EF80 8F61D611 3AF9B65E
Round[7] After Add RoundKey
442C0613 64794B61 637650FA 555FFF2F
Round[7] After Mix Columns
3F3C87F9 76E9379F B50CE3E5 8F8F8A50
Round[7] After Inverse Sub Bytes
256DEA69 0FEBB26E D2814D2A 7373CF6C
Round[7] After Inverse Shift Rows
25734D6E 0F6DCF2A D2EBEA6C 7381B269
Round[6] After Add RoundKey
872D33BB 8CDC00B0 F512D32F 1915450E
Round[6] After Mix Columns
0756F784 8B75DCC2 7BBC6BB7 2390F105
Round[6] After Inverse Sub Bytes
38B9264F CE3F93A8 03780520 32962B36
Round[6] After Inverse Shift Rows
389605A8 CEB92B20 033F2636 3278934F
Round[5] After Add RoundKey
9CDEF371 83D4E504 A90D4556 2343A3A9
Round[5] After Mix Columns
2594D1A0 DFAACE0D 1F9286BC C20A9634
Round[5] After Inverse Sub Bytes
C2E75147 EF62ECF3 CB74DC78 A8A33528
Round[5] After Inverse Shift Rows
C2A3DCF3 EFE73578 CB625128 A874EC47
Round[4] After Add RoundKey
25FC71B7 54EE66FE 8338A17F 899B5D08
Round[4] After Mix Columns
202D4A58 DA8CACD8 0676EEFB 993FC322
Round[4] After Inverse Sub Bytes
54FA5C5E 7AF0AA2D A50F9963 F9253394
Round[4] After Inverse Shift Rows
5425992D 7AFA3363 A5F05C94 F90FAA5E
Round[3] After Add RoundKey
19922D90 134F727B 20571B02 102A92A3
Round[3] After Mix Columns
5962010C FF2E34B0 11B3F63A 09009D9F
Round[3] After Inverse Sub Bytes
15AB0981 7DC328FC E34BD6A2 4052756E
Round[3] After Inverse Shift Rows
1552D6FC 7DAB75A2 E3C3096E 404B2881
Round[2] After Add RoundKey
F940D072 11290AC9 EDB99CD7 1C1DD643
Round[2] After Mix Columns
F770E874 6FA099AD 7DB732E7 43ABBAC6
Round[2] After Inverse Sub Bytes
26D0C8CA 0647F918 1320A1B0 640EC0C7
Round[2] After Inverse Shift Rows
260EA118 06D0C0B0 1347C8C7 6420F9CA
Round[1] After Add RoundKey
44F64BCA 54FCABCB ED4B5930 40220C6F
Round[1] After Mix Columns
B7D7DE8D 1C5C68E0 B175808B A658E817
Round[1] After Inverse Sub Bytes
200D9CB4 C4A7F7A0 563F3ACE C55EC887
Round[1] After Inverse Shift Rows
205E3AA0 C40DC8CE 56A79C87 C53FF7B4
Round[0] After Add Round Key
AE2D8A57 1E03AC9C 9EB76FAC 45AF8E51
Round[12] Input to Inverse Cipher
EF7AFD22 70E2E60A DCE0BA2F ACE6444E
Round[12] After Add Round Key
06F15D4D 346E9136 522CC82B ADE6664C
Round[12] After Inverse Sub Bytes
A52B8D65 2845AC24 4842B10B 18F5D35D
Round[12] After Inverse Shift Rows
A5F5B124 282BD30B 48458D5D 1842AC65
Round[11] After Add RoundKey
6FB5B41C A7E7830D 60689B37 A47E4BD0
Round[11] After Mix Columns
4EEA71A7 534EF023 4201EA0D E5E588C9
Round[11] After Inverse Sub Bytes
B6BB2C89 50B61732 F609BBF3 2A2A9712
Round[11] After Inverse Shift Rows
B62ABB32 50BB97F3 F6B62C12 2A091789
Round[10] After Add RoundKey
11CBFD5E C4AA662C 74A95918 870EC0DA
Round[10] After Mix Columns
BF59A13E B91853D6 71B07F22 EE93947A
Round[10] After Inverse Sub Bytes
F415F1D1 DB34504A 2CFC6B94 9922E7BD
Round[10] After Inverse Shift Rows
F4226B4A DB15E794 2C34F1BD 99FC50D1
Round[9] After Add RoundKey
B49C8062 F40D45CD 4B7323D6 DC7005EF
Round[9] After Mix Columns
F4B14FC0 3B646846 7F8E96AA 9690C383
Round[9] After Inverse Sub Bytes
BA56921F 498CF798 6BE63562 35963341
Round[9] After Inverse Shift Rows
BA963598 49563362 6B8C9241 35E6F71F
Round[8] After Add RoundKey
F2C945AA 6B9DB437 89E18113 061640AC
Round[8] After Mix Columns
407344A3 3DA108E1 12AFF5B2 7839DD60
Round[8] After Inverse Sub Bytes
728F8671 8BF1BFE0 391B773E C15BC990
Round[8] After Inverse Shift Rows
725B77E0 8B8FC93E 39F18690 C11BBF71
Round[7] After Add RoundKey
B2FDE3E7 5A126DDF D5E6007B AEBDF600
Round[7] After Mix Columns
568C9100 7D9EA5BC F44DB140 7F65F609
Round[7] After Inverse Sub Bytes
B9F0AC52 13DF2978 BA655672 6BBCD640
Round[7] After Inverse Shift Rows
B9BC5678 13F0D672 BADFAC40 6B652952
Round[6] After Add RoundKey
1BE228AD 904119E8 9D269503 01F1DE35
Round[6] After Mix Columns
8FFB444C 0058C9B1 8E91DCEE 685181A3
Round[6] After Inverse Sub Bytes
7363865D 525E1256 E6AC9399 F7709171
Round[6] After Inverse Shift Rows
73709356 52639199 E65E8671 F7AC125D
Round[5] After Add RoundKey
D738658F 1F0E5FBD 4C6CE511 E69722BB
Round[5] After Mix Columns
C14579F8 0C7CB132 B0A4AA6A D0BFDF58
Round[5] After Inverse Sub Bytes
DD68AFE1 810156A1 FC1D6258 60F4EF5E
Round[5] After Inverse Shift Rows
DDF462A1 8168EF58 FC01AF5E 601D56E1
Round[4] After Add RoundKey
3AABCFE5 3A61BCDE B45B5F09 41F2E7AE
Round[4] After Mix Columns
EE547677 48E0BC2D F606743D F9D8B06B
Round[4] After Inverse Sub Bytes
99FD0F02 D4A078FA D6A5CA8B 692DFC05
Round[4] After Inverse Shift Rows
992DCAFA D4FDFC8B D6A00F05 69A57802
Round[3] After Add RoundKey
D49A7E47 BD48BD93 53074893 808040FF
Round[3] After Mix Columns
34F270C1 15A1B8D7 0C6412F5 9DCC38D6
Round[3] After Inverse Sub Bytes
2804D0DD 2FF19A0D 818C3977 7527764A
Round[3] After Inverse Shift Rows
2827390D 2F047677 81F1D04A 758C9ADD
Round[2] After Add RoundKey
C4353F83 4386091C 8F8B45F3 29DA641F
Round[2] After Mix Columns
EFDC8EF0 EBD71AF6 D7A262A5 5F2019EE
Round[2] After Inverse Sub Bytes
6193E617 3C0D43D6 0D1AAB29 84548E99
Round[2] After Inverse Shift Rows
6154ABD6 3C938E29 0D0DE699 841A4317
Round[1] After Add RoundKey
03AC4104 6EBFE552 F301776E A018B6B2
Round[1] After Mix Columns
AE002367 B6E9F1C8 D8B8911A B8EACD23
Round[1] After Inverse Sub Bytes
BE52320A 79EB2BB1 2D9AAC43 9ABB8032
Round[1] After Inverse Shift Rows
BEBBACB1 79528043 2DEB3232 9A9A2B0A
Round[0] After Add Round Key
30C81C46 A35CE411 E5FBC119 1A0A52EF
Round[12] Input to Inverse Cipher
9A4B41BA 738D6C72 FB166916 03C18E0E
Round[12] After Add Round Key
73C0E1D5 37011B4E 75DA1B12 02C1AC0C
Round[12] After Inverse Sub Bytes
8F1FE0B5 B20944B6 3F7A4439 6ADDAA81
Round[12] After Inverse Shift Rows
8FDD44B6 B21FAA39 3F09E081 6A7A44B5
Round[11] After Add RoundKey
459D418E 3DD3FA3F 1724F6EB D646A300
Round[11] After Mix Columns
51DD7BE0 A37432CE 9DCF205C 92248104
Round[11] After Inverse Sub Bytes
70C903A0 71CAA1EC 755F54A7 74A69130
Round[11] After Inverse Shift Rows
70A654EC 71C991A7 75CA0330 745FA1A0
Round[10] After Add RoundKey
D7471280 E5D86078 F7D5763A D95876F3
Round[10] After Mix Columns
C7CE060D AB1364F9 B22AEF19 6EBAC919
Round[10] After Inverse Sub Bytes
31ECA5F3 0E828C69 3E95618E 45C0128E
Round[10] After Inverse Shift Rows
31C06169 0EEC128E 3E82A58E 45958CF3
Round[9] After Add RoundKey
717E8A41 21F4B0D7 59C577E5 0019D9CD
Round[9] After Mix Columns
10CF7863 B7A559F9 BC448E78 1E9ADD54
Round[9] After Inverse Sub Bytes
7C5FC100 20291569 7886E6C1 E937C9FD
Round[9] After Inverse Shift Rows
7C37E669 205FC9C1 7829C1FD E9861500
Round[8] After Add RoundKey
3468965B 02944E94 9A44D2AF DA76A2B3
Round[8] After Mix Columns
4736DC3C 0421D0B9 CA3EDF88 40DE597A
Round[8] After Inverse Sub Bytes
1624936D 307B60DB 10D1EF97 729C15BD
Round[8] After Inverse Shift Rows
169CEFDB 30241597 107B93BD 72D1606D
Round[7] After Add RoundKey
D63A7BDC E1B9B176 FC6C1556 1D77291C
Round[7] After Mix Columns
B2288958 01B37459 5F670BE0 88ED0238
Round[7] After Inverse Sub Bytes
3EEEF25E 094BCA15 840A9EA0 97536A76
Round[7] After Inverse Shift Rows
3E539E15 09EE6AA0 844BF276 970ACA5E
Round[6] After Add RoundKey
9C0DE0C0 8A5FA53A A3B2CB35 FD9E3D39
Round[6] After Mix Columns
009B052F AB1310E2 ECBC41FE 641B6A72
Round[6] After Inverse Sub Bytes
52E8364E 0E827C3B 8378F80C 8C44581E
Round[6] After Inverse Shift Rows
5244F83B 0EE8580C 8382361E 8C787C4E
Round[5] After Add RoundKey
F60C0EE2 43859628 29B0557E 9D434CA8
Round[5] After Mix Columns
723BA6F9 38B41DE9 BE21BD90 A22D07B2
Round[5] After Inverse Sub Bytes
1E49C569 76C6DEEB 5A7BCD96 1AFA383E
Round[5] After Inverse Shift Rows
1EFACDEB 76493896 5AC6C53E 1A7BDE69
Round[4] After Add RoundKey
F9A560AF CD406B10 129C3569 3B946F26
Round[4] After Mix Columns
747BD04C 654A34ED 9134097E A2102175
Round[4] After Inverse Sub Bytes
CA03605D BC5C2853 AC28408A 1A7C7B3F
Round[4] After Inverse Shift Rows
CA7C4053 BC037B8A AC5C603F 1A28285D
Round[3] After Add RoundKey
87CBF4EE D5B63A92 29FB27A9 F30D10A0
Round[3] After Mix Columns
18F1C778 4BEC2945 2481926B BDBDC28C
Round[3] After Inverse Sub Bytes
342B31C1 CC834C68 A6917405 CDCDA8F0
Round[3] After Inverse Shift Rows
34CD7468 CC2BA805 A68331F0 CD914CC1
Round[2] After Add RoundKey
D8DF72E6 A0A9D76E A8F9A449 91C7B203
Round[2] After Mix Columns
2F1DB819 32233E9F 119E7E4D 2F8ED99F
Round[2] After Inverse Sub Bytes
4EDE9A8E A132D16E E3DF8A65 4EE6E56E
Round[2] After Inverse Shift Rows
4EE68A6E A1DEE565 E3329A6E 4EDFD18E
Round[1] After Add RoundKey
2C1E60BC F3F28E1E 1D3E0B99 6ADD242B
Round[1] After Mix Columns
BC8337E6 6BE22F37 4DB0226E 33CE1653
Round[1] After Inverse Sub Bytes
7841B2F5 053B4EB2 65FC9445 66ECFF50
Round[1] After Inverse Shift Rows
78EC94B2 0541FF45 653BB250 66FC4EF5
Round[0] After Add Round Key
F69F2445 DF4F9B17 AD2B417B E66C3710
== Menu ==
1 Detailed NIST FIPS 197 128-Bit Encryption
2 Detailed NIST FIPS 197 128-Bit Decryption
3 ECB Encryption 128-Bit Test Vectors
4 ECB Decryption 128-Bit Test Vectors
5 ECB Encryption 192-Bit Test Vectors
6 ECB Decryption 192-Bit Test Vectors
7 ECB Encryption 256-Bit Test Vectors
8 ECB Decryption 256-Bit Test Vectors
9 Exit
Enter option = 7
NIST Standard Test Data
256-Bit Cipher Key
603DEB10 15CA71BE 2B73AEF0 857D7781 1F352C07 3B6108D7 2D9810A3 0914DFF4
Electronic Codebook (ECB) Mode
ECB-AES256 (Encryption)
NIST Standard Test Data
AES-256 (Nk = 8, Nr = 14)
Test Vectors
Round[0] Input to Cipher
6BC1BEE2 2E409F96 E93D7E11 7393172A
Round[0] After Add Round Key
0BFC55F2 3B8AEE28 C24ED0E1 F6EE60AB
Round[1] After Sub Bytes
2BB0FC89 E27E2834 252F70F8 4228D062
Round[1] After Shift Rows
2B7E7062 E22FD089 2528FC34 42B028F8
Round[1] After Mix Columns
C62513B7 F75EF6CB FA5EB2D3 9FB9B1B5
Round[1] After Add Round Key
D9103FB0 CC3FFE1C D7C6A270 96AD6E41
Round[2] After Sub Bytes
35CA75E7 4B75BB9C 0EB43A51 90959F83
Round[2] After Shift Rows
35753A83 4BB49FE7 0E95759C 90CABB51
Round[2] After Mix Columns
4C12AA0D 2965E823 513CCED1 9498C478
Round[2] After Add Round Key
D7B1FE1C A70CCD8C F426458E B4FF38A6
Round[3] After Sub Bytes
0EC8BB9C 5CFEBD64 BFF76E19 8D160724
Round[3] After Shift Rows
0EFE6E24 5CF7079C BF16BB64 8DC8BD19
Round[3] After Mix Columns
4F7F40CA 213C1A37 802168BF E6C30FCB
Round[3] After Add Round Key
E7CFDCD0 B2ED8EFA 3E68ECD1 519E5451
Round[4] After Sub Bytes
948A8670 3755192D B245CE3E D10B20D1
Round[4] After Shift Rows
9455CED1 37452070 B20B862D D18A193E
Round[4] After Mix Columns
D3A62E85 F1ADA2DC C918D91A 1BCB2B87
Round[4] After Add Round Key
063CC23D AA5E6BCB 37F19B52 C5459511
Round[5] After Sub Bytes
6FEB2527 AC587F1F 9AA11400 A66E2A82
Round[5] After Shift Rows
6F581482 ACA12A27 9A6E251F A6EB7F00
Round[5] After Mix Columns
A06182E2 B6AC302A A7369FC0 0EEAB365
Round[5] After Add Round Key
15C8B068 90D4966D 3F07BDE9 2186CAD6
Round[6] After Sub Bytes
59E8E745 6048903C 75C57A1E FD4474F6
Round[6] After Shift Rows
59487AF6 60C57445 7544E73C FDE8901E
Round[6] After Mix Columns
E6B1E42E A528829B FDF3A044 4C830C58
Round[6] After Add Round Key
679D6583 7FF7CA21 D9C5AAB6 B63BB83C
Round[7] After Sub Bytes
855E4DEC D26874FD 35A6AC4E 4EE26CEB
Round[7] After Shift Rows
8568ACEB D2A66CEC 35E24DFD 4E5E744E
Round[7] After Mix Columns
EE51889D CEDD8364 E7C05111 44202A64
Round[7] After Add Round Key
76943754 70609AEA C14C6AB6 4DC06870
Round[8] After Sub Bytes
38229A20 51D0B887 7829024E E3BA4551
Round[8] After Shift Rows
38D00251 51294520 78BA9A87 E322B84E
Round[8] After Mix Columns
48D41F38 BCEC92DF 38257FBD 4D3A7838
Round[8] After Add Round Key
20D46494 0E33A1C9 AECC4659 216BF5B8
Round[9] After Sub Bytes
B7484322 ABC332DD E44B5ACB FD7FE66C
Round[9] After Shift Rows
B7C35A6C AB4BE622 E47F43DD FD4832CB
Round[9] After Mix Columns
1DA87483 542E510F CC0261AA C0F097EB
Round[9] After Add Round Key
D5BC9687 2287AA85 9C27A187 993515D2
Round[10] After Sub Bytes
03659017 9317AC97 DECC3217 EE9659B5
Round[10] After Shift Rows
031732B5 93CC5917 DE969097 EE65AC17
Round[10] After Mix Columns
B8CEB451 3CECD415 01D5D14A D3DCF1CE
Round[10] After Add Round Key
66DDDD36 50208E64 FBF0B2DF 45A81FDB
Round[11] After Sub Bytes
33C1C105 53B71943 0F8C379E 6EC2C0B9
Round[11] After Shift Rows
33B737B9 538CC005 0FC2C143 6EC1199E
Round[11] After Mix Columns
2AA63ABC EC0E4BB3 C18B9194 0342244D
Round[11] After Add Round Key
7220F0E1 C2217A64 BF81606E 248D578E
Round[12] After Sub Bytes
40B78CF8 25FDDA43 080CD09F 365D5B19
Round[12] After Shift Rows
40FDD019 250C5BF8 085D8C43 36B7DA9F
Round[12] After Mix Columns
55D32DDF FD288CD3 387E934F EBA99412
Round[12] After Add Round Key
214F6A74 E5789109 DA0BED00 9FA80448
Round[13] After Sub Bytes
FD840292 D9BC8101 572B5563 DBC2F252
Round[13] After Shift Rows
FDBC5552 D92BF292 57C20201 DB848163
Round[13] After Mix Columns
39331D51 B410A096 F0CF923B D833E3B5
Round[13] After Add Round Key
F3C9B7B2 50C53BA2 6A10F8F5 6523FAB8
Round[14] After Sub Bytes
0DDDA937 53A6E23A 02CA41E6 4D262D6C
Round[14] After Shift Rows
0DA6416C 53CA2D37 0226A93A 4DDDE2E6
Round[14] After Add Round Key
F3EED1BD B5D2A03C 064B5A7E 3DB181F8
Round[0] Input to Cipher
AE2D8A57 1E03AC9C 9EB76FAC 45AF8E51
Round[0] After Add Round Key
CE106147 0BC9DD22 B5C4C15C C0D2F9D0
Round[1] After Sub Bytes
8BCAEFA0 2BDDC193 D51C784A BAB59970
Round[1] After Shift Rows
8BDD7870 2B1C99A0 D5B5EF93 BACAC14A
Round[1] After Mix Columns
79D236C3 4B03E5A3 091D0B03 A127374A
Round[1] After Add Round Key
66E71AC4 7062ED74 24851BA0 A833E8BE
Round[2] After Sub Bytes
3394A21C 51AA5592 3697AFE0 C2C39BAE
Round[2] After Shift Rows
33AAAFAE 51979B1C 36C3A292 C29455E0
Round[2] After Mix Columns
82383517 87CECFC7 02C40704 8DEEC747
Round[2] After Add Round Key
199B6106 09A7EA68 A7DE8C5B AD893B99
Round[3] After Sub Bytes
D414EF6F 015C8745 5C1D6439 95A7E2EE
Round[3] After Shift Rows
D45C64EE 011DE26F 5CA7EF45 95148739
Round[3] After Mix Columns
DD2E6998 A8697222 E066F126 B316DF45
Round[3] After Add Round Key
759EF582 3BB8E6EF 5E2F7548 044B84DF
Round[4] After Sub Bytes
9D0BE613 E26C8EDF 58159D52 F2B35F9E
Round[4] After Shift Rows
9D6C9D9E E2155F13 58B3E6DF F20B8E52
Round[4] After Mix Columns
9667696A AC3A7C51 47CB4618 3E3F082C
Round[4] After Add Round Key
43FD85D2 F7C9B546 B9220450 E0B1B6BA
Round[5] After Sub Bytes
1A5497B5 68DDD55A 5693F253 E1C84EF4
Round[5] After Shift Rows
1ADDF2F4 68934EB5 56C8975A E154D553
Round[5] After Mix Columns
4E423FF2 8532A314 22254511 A37EF11F
Round[5] After Add Round Key
FBEB0D78 A34A0553 BA146738 8C1288AC
Round[6] After Sub Bytes
0FE9D7BC 0AD66BED F4FA8507 64C9C491
Round[6] After Shift Rows
0FD68591 0AFAC4BC F4C9D7ED 64E96B07
Round[6] After Mix Columns
6BBD607B 790EBC43 89F2A4D8 84175220
Round[6] After Add Round Key
EA91E1D6 A3D1F4F9 ADC4AE2A 7EAFE644
Round[7] After Sub Bytes
8781F8F6 0A3EBF99 951CE4E5 F3798E1B
Round[7] After Shift Rows
873EE41B 0A1C8EF6 9579F899 F381BFE5
Round[7] After Mix Columns
A8D7477E 484D107B DBEDB70C 3FD523E1
Round[7] After Add Round Key
3012F8B7 F6F009F5 FD618CAB 363561F5
Round[8] After Sub Bytes
04C941A9 428C01E6 54EF6462 0596EFE6
Round[8] After Shift Rows
048C64E6 42EFEFA9 549641E6 05C90162
Round[8] After Mix Columns
054D7133 E804888F AE4671FC 29ED6803
Round[8] After Add Round Key
6D4D0A9F 5ADBBB99 38AF4818 45BCE583
Round[9] After Sub Bytes
3CE367DB BEB9EAEE 077952AD 6E65D9EC
Round[9] After Shift Rows
3CB952EC BE79D9DB 076567EE 6EE3EAAD
Round[9] After Mix Columns
164F0E6C EEE718D4 288A85CC A53BAEFA
Round[9] After Add Round Key
DE5BEC68 984EE35E 78AF45E1 FCFE2CC3
Round[10] After Sub Bytes
1D39CE45 462F1158 BC796EF8 B0BB712E
Round[10] After Shift Rows
1D2F6E2E 46797145 BCBBCE58 B03911F8
Round[10] After Mix Columns
0BDF9C3A 33621248 23C0681A D909B808
Round[10] After Add Round Key
D5CCF55D 5FAE4839 D9E50B8F 4F7D561D
Round[11] After Sub Bytes
034BE64C CFE45212 35D92B73 84FFB1A4
Round[11] After Shift Rows
03E42BA4 CFD9B14C 35FFE612 844B5273
Round[11] After Mix Columns
BE094699 08E2BBBA 84F32B62 EF97FE68
Round[11] After Add Round Key
E68F8CC4 26CD8A6D FAF9DA98 C8588DAB
Round[12] After Sub Bytes
8E73641C F7BD7E3C 2D995746 E86A5D62
Round[12] After Shift Rows
8EBD5762 F7995D1C 2D6A643C E8737E46
Round[12] After Mix Columns
EE743BA7 0425F0FE BC69CB01 66CAADA2
Round[12] After Add Round Key
9AE87C0C 1C75ED24 5E1CB54E 12CB3DF8
Round[13] After Sub Bytes
B89B10FE 9C9D5536 589CD52F C91F2741
Round[13] After Shift Rows
B89DD541 9C9C27FE 581F1036 C99B552F
Round[13] After Mix Columns
43BC5719 452857E3 B7603D8B 453489D0
Round[13] After Add Round Key
8946FDFA A1FDCCD7 2DBF5745 F82490DD
Round[14] After Sub Bytes
A75A542D 32544B0E D8085B6E 413660C1
Round[14] After Shift Rows
A7545BC1 3208602D D836540E 415A4B6E
Round[14] After Add Round Key
591CCB10 D410ED26 DC5BA74A 31362870
Round[0] Input to Cipher
30C81C46 A35CE411 E5FBC119 1A0A52EF
Round[0] After Add Round Key
50F5F756 B69695AF CE886FE9 9F77256E
Round[1] After Sub Bytes
53E668B1 4E902A79 8BC4A81E DBF53F9F
Round[1] After Shift Rows
5390A89F 4EC43FB1 8BF56879 DBE62A1E
Round[1] After Mix Columns
3A1432E8 452D3C50 18BB25E9 A86C4B86
Round[1] After Add Round Key
25211EEF 7E4C3487 3523354A A1789472
Round[2] After Sub Bytes
3FFD72DF F3291817 962696D6 32BC2240
Round[2] After Shift Rows
3F299640 F32622DF 96BC7217 32FD18D6
Round[2] After Mix Columns
D38CE17E 6A06EBAF 8D74F741 B62D9E04
Round[2] After Add Round Key
482FB56F E46FCE00 286E7C1E 964A62DA
Round[3] After Sub Bytes
5215D5A8 69A88B63 349F1072 90D6AA57
Round[3] After Shift Rows
52A81057 699FAAA8 34D6D563 90158B72
Round[3] After Mix Columns
007E23E0 6A015AC5 BF84F699 FD4E1ED1
Round[3] After Add Round Key
A8CEBFFA F9D0CE08 01CD72F7 4A13454B
Round[4] After Sub Bytes
C28B082D 99708B30 7CBD4068 D67D6EB3
Round[4] After Shift Rows
C27040B3 99BD6E2D 7C7D0830 D68B8B68
Round[4] After Mix Columns
FC51FC10 B6678F39 47AE4191 D235E8B1
Round[4] After Add Round Key
29CB10A8 ED94462E B94703D9 0CBB5627
Round[5] After Sub Bytes
A51FCAC2 55225A31 56A07B35 FEEAB1CC
Round[5] After Shift Rows
A5227BCC 55A0B1C2 56EACA31 FE1F5A35
Round[5] After Mix Columns
80A03E2E 2204D171 72ED60B8 A91B0A36
Round[5] After Add Round Key
35090CA4 047C7736 EADC4291 86777385
Round[6] After Sub Bytes
9601FE49 F210F505 87862C81 44F58F97
Round[6] After Shift Rows
96102C97 F2868F49 87F5FE05 4401F581
Round[6] After Mix Columns
BC557CA8 A826AA96 EA6A9A93 FFC32C21
Round[6] After Add Round Key
3D79FD05 72F9E22C CE5C9061 057B9845
Round[7] After Sub Bytes
27B6546B 40999871 8B4A60EF 6B21466E
Round[7] After Shift Rows
2799606E 404A466B 8B215471 6BB698EF
Round[7] After Mix Columns
F0C0CC4C 73753B1A 4B449111 6040DC56
Round[7] After Add Round Key
68057385 CDC82294 6DC8AAB6 69A09E42
Round[8] After Sub Bytes
456B8F97 BDE89322 3CE8AC4E F9E00B2C
Round[8] After Shift Rows
45E8AC2C BDE80B97 3CE08F22 F96B934E
Round[8] After Mix Columns
294D9AD3 DEFCE10A EE4FBF6F 89CF7D74
Round[8] After Add Round Key
414DE17F 6C23D21C 78A6868B E59EF0F4
Round[9] After Sub Bytes
83E3F8D2 5026B59C BC24443D D90B8CBF
Round[9] After Shift Rows
832644BF 50248CD2 BC0BF89C D9E3B53D
Round[9] After Mix Columns
8CBCF799 92451AE7 1A25E30F 1FFD0C5C
Round[9] After Add Round Key
44A8159D E4ECE16D 4A002322 46388E65
Round[10] After Sub Bytes
1BC2595E 69CEF83C D6632693 5A07194D
Round[10] After Shift Rows
1BCE264D 6963195E D607593C 5AC2F893
Round[10] After Mix Columns
14BB4E5F 30DADA7D DB0F2747 8245DDE9
Round[10] After Add Round Key
CAA82738 5C16800C 212A44D2 143133FC
Round[11] After Sub Bytes
74C2CC07 4A47CDFE FDE51BB5 FAC7C3B0
Round[11] After Shift Rows
74471BB0 4AE5C307 FDC7CCFE FAC2CDB5
Round[11] After Mix Columns
8A67CEBB 64C23BF6 81D9A0F0 CA9C7D6B
Round[11] After Add Round Key
D2E104E6 4AED0A21 FFD3510A ED530EA8
Round[12] After Sub Bytes
B5F8F28E D65567FD 1666D167 55EDABC2
Round[12] After Shift Rows
B555D1C2 D666AB8E 16EDF2FD 55F86767
Round[12] After Mix Columns
9DB504DF 387274AB 0F2718C4 B970CAAE
Round[12] After Add Round Key
E9294374 20226971 ED52668B CD715AF4
Round[13] After Sub Bytes
1EA51A92 B793F9A3 5500333D BDA3BEBF
Round[13] After Shift Rows
1E9333BF B700BE92 55A31AA3 BDA5F93D
Round[13] After Mix Columns
1EC931E7 59FC7D43 ED853C1B 51C1B6FA
Round[13] After Add Round Key
D4339B04 BD29E677 775A56D5 ECD1AFF7
Round[14] After Sub Bytes
48C314F2 7AA58EF5 F5BEB103 CE3E7968
Round[14] After Shift Rows
48A5B168 7ABE79F2 F53E14F5 CEC38E03
Round[14] After Add Round Key
B6ED21B9 9CA6F4F9 F153E7B1 BEAFED1D
Round[0] Input to Cipher
F69F2445 DF4F9B17 AD2B417B E66C3710
Round[0] After Add Round Key
96A2CF55 CA85EAA9 8658EF8B 63114091
Round[1] After Sub Bytes
903A8AFC 749787D3 446ADF3D FB820981
Round[1] After Shift Rows
9097DF81 746A09FC 44828AD3 FB3A873D
Round[1] After Mix Columns
C75E3AFA A347131C 4C0DA779 192093D1
Round[1] After Add Round Key
D86B16FD 98261BCB 6195B7DA 10344C25
Round[2] After Sub Bytes
617F4754 46F7AF1F EF2AA957 CA18293F
Round[2] After Shift Rows
61F7A93F 462A2954 EF18471F CA7FAF57
Round[2] After Mix Columns
564B9E83 8F3DC261 B509584B F689093B
Round[2] After Add Round Key
CDE8CA92 0154E7CE 1013D314 D6EEF5E5
Round[3] After Sub Bytes
BD9B744F 7C20948B CA7D66FA F628E6D9
Round[3] After Shift Rows
BD2066D9 7C7DE64F CA28748B F69B94FA
Round[3] After Mix Columns
BE8E2133 D6F80781 088D8C14 2F864BE1
Round[3] After Add Round Key
163EBD29 4529934C B6C4087A 98DB107B
Round[4] After Sub Bytes
47B27AA5 6EA5DC29 4E1C30DA 46B9CA21
Round[4] After Shift Rows
47A53021 6E1CCAA5 4EB97A29 46B2DCDA
Round[4] After Mix Columns
6B67E11E 97B60935 1F807843 479C220B
Round[4] After Add Round Key
BEFD0DA6 CC45C022 E1693A0B 99129C9D
Round[5] After Sub Bytes
AE54D724 4B6EBA93 F8F9802B EEC9DE5E
Round[5] After Shift Rows
AE6E805E 4BF9DE24 F8C9D793 EE54BA2B
Round[5] After Mix Columns
2BB739BB 7CFF79B2 EF802A30 AAB8A891
Round[5] After Add Round Key
9E1E0B31 5A87DFF5 77B10819 85D4D122
Round[6] After Sub Bytes
0B722BC7 BE179EE6 F5C830D4 97483E93
Round[6] After Shift Rows
0B173093 BEC83EC7 F5482BE6 97729ED4
Round[6] After Mix Columns
8CE6D207 DDB058BA E4FEDAB0 E91EA5FD
Round[6] After Add Round Key
0DCA53AA 076F1000 C0C8D042 13A61199
Round[7] After Sub Bytes
D774EDAC C5A8CA63 BAE8702C 7D2482EE
Round[7] After Shift Rows
D7A870EE C5E882AC BA24ED63 7D74CA2C
Round[7] After Mix Columns
C8E2B67D 9C3FDD7D 8DBDFADA 80FCF261
Round[7] After Add Round Key
502709B4 2282C4F3 AB31C17D 891CB075
Round[8] After Sub Bytes
53CC018D 93131C0D 62C778FF A79CE79D
Round[8] After Shift Rows
5313789D 93C7E78D 629C010D A7CC1CFF
Round[8] After Mix Columns
76600CBF 05B90D8F 774FEB21 F9FF49C7
Round[8] After Add Round Key
1E607713 B7663E99 E1A6D2C5 95AEC447
Round[9] After Sub Bytes
72D0F57D A933B2EE F824B5A6 2AE41CA0
Round[9] After Shift Rows
7233B5A0 A9241C7D F8E4F5EE 2AD0B2A6
Round[9] After Mix Columns
A470CB4B 44B83222 C7C1C4C5 2BFA744B
Round[9] After Add Round Key
6C64294F 3211C9A8 97E404E8 723FF672
Round[10] After Sub Bytes
5043A584 2382DDC2 8869F29B 40754240
Round[10] After Shift Rows
5082F240 23694284 8875A5C2 4043DD9B
Round[10] After Mix Columns
8F02ED00 3BB3595D F354F1CC 03211473
Round[10] After Add Round Key
51118467 577F032C 09719259 9555FA66
Round[11] After Sub Bytes
D1825F85 5BD27B71 01A34FCB 2AFC2D33
Round[11] After Shift Rows
D1D24F33 5BA32D85 01FC5F71 2A827BCB
Round[11] After Mix Columns
A88CC893 E0F43672 3372D042 7973180A
Round[11] After Add Round Key
F00A02CE CEDB07A5 4D7821B8 5EBC6BC9
Round[12] After Sub Bytes
8C67778B 8BB9C506 E3BCFD6C 58657FDD
Round[12] After Shift Rows
8CB9FDDD 8BBC7F8B E3657706 5867C56C
Round[12] After Mix Columns
F324A86A 26E24F48 03B66220 B0AE1A92
Round[12] After Add Round Key
87B8EFC1 3EB25292 E1C31C6F C4AF8AC8
Round[13] After Sub Bytes
176CDF78 B237004F F82E9CA8 1C797EE8
Round[13] After Shift Rows
17379CE8 B22E7E78 F879DF4F 1C6C00A8
Round[13] After Mix Columns
032E2059 0B14E86D F03FF52B 246C9303
Round[13] After Add Round Key
C9D48ABA EFC17359 6AE09FE5 997C8A0E
Round[14] After Sub Bytes
DD487EF4 DF788FCB 02E1DBD9 EE107EAB
Round[14] After Shift Rows
DD78DBAB DFE17EF4 02107ECB EE488FD9
Round[14] After Add Round Key
23304B7A 39F9F3FF 067D8D8F 9E24ECC7
== Menu ==
1 Detailed NIST FIPS 197 128-Bit Encryption
2 Detailed NIST FIPS 197 128-Bit Decryption
3 ECB Encryption 128-Bit Test Vectors
4 ECB Decryption 128-Bit Test Vectors
5 ECB Encryption 192-Bit Test Vectors
6 ECB Decryption 192-Bit Test Vectors
7 ECB Encryption 256-Bit Test Vectors
8 ECB Decryption 256-Bit Test Vectors
9 Exit
Enter option = 8
NIST Standard Test Data
256-Bit Cipher Key
603DEB10 15CA71BE 2B73AEF0 857D7781 1F352C07 3B6108D7 2D9810A3 0914DFF4
Electronic Codebook (ECB) Mode
ECB-AES256 (Decryption)
NIST Standard Test Data
AES-256 (Nk = 8, Nr = 14)
Test Vectors
Round[14] Input to Inverse Cipher
F3EED1BD B5D2A03C 064B5A7E 3DB181F8
Round[14] After Add Round Key
0DA6416C 53CA2D37 0226A93A 4DDDE2E6
Round[14] After Inverse Sub Bytes
F3C5F8B8 5010FAB2 6A23B7A2 65C93BF5
Round[14] After Inverse Shift Rows
F3C9B7B2 50C53BA2 6A10F8F5 6523FAB8
Round[13] After Add RoundKey
39331D51 B410A096 F0CF923B D833E3B5
Round[13] After Mix Columns
FDBC5552 D92BF292 57C20201 DB848163
Round[13] After Inverse Sub Bytes
2178ED48 E50B0474 DAA86A09 9F4F9100
Round[13] After Inverse Shift Rows
214F6A74 E5789109 DA0BED00 9FA80448
Round[12] After Add RoundKey
55D32DDF FD288CD3 387E934F EBA99412
Round[12] After Mix Columns
40FDD019 250C5BF8 085D8C43 36B7DA9F
Round[12] After Inverse Sub Bytes
7221608E C28157E1 BF8DF064 24207A6E
Round[12] After Inverse Shift Rows
7220F0E1 C2217A64 BF81606E 248D578E
Round[11] After Add RoundKey
2AA63ABC EC0E4BB3 C18B9194 0342244D
Round[11] After Mix Columns
33B737B9 538CC005 0FC2C143 6EC1199E
Round[11] After Inverse Sub Bytes
6620B2DB 50F01F36 FBA8DD64 45DD8EDF
Round[11] After Inverse Shift Rows
66DDDD36 50208E64 FBF0B2DF 45A81FDB
Round[10] After Add RoundKey
B8CEB451 3CECD415 01D5D14A D3DCF1CE
Round[10] After Mix Columns
031732B5 93CC5917 DE969097 EE65AC17
Round[10] After Inverse Sub Bytes
D587A1D2 22271587 9C359685 99BCAA87
Round[10] After Inverse Shift Rows
D5BC9687 2287AA85 9C27A187 993515D2
Round[9] After Add RoundKey
1DA87483 542E510F CC0261AA C0F097EB
Round[9] After Mix Columns
B7C35A6C AB4BE622 E47F43DD FD4832CB
Round[9] After Inverse Sub Bytes
203346B8 0ECCF594 AE6B64C9 21D4A159
Round[9] After Inverse Shift Rows
20D46494 0E33A1C9 AECC4659 216BF5B8
Round[8] After Add RoundKey
48D41F38 BCEC92DF 38257FBD 4D3A7838
Round[8] After Mix Columns
38D00251 51294520 78BA9A87 E322B84E
Round[8] After Inverse Sub Bytes
76606A70 704C6854 C1C037EA 4D949AB6
Round[8] After Inverse Shift Rows
76943754 70609AEA C14C6AB6 4DC06870
Round[7] After Add RoundKey
EE51889D CEDD8364 E7C05111 44202A64
Round[7] After Mix Columns
8568ACEB D2A66CEC 35E24DFD 4E5E744E
Round[7] After Inverse Sub Bytes
67F7AA3C 7FC5B883 D93B6521 B69DCAB6
Round[7] After Inverse Shift Rows
679D6583 7FF7CA21 D9C5AAB6 B63BB83C
Round[6] After Add RoundKey
E6B1E42E A528829B FDF3A044 4C830C58
Round[6] After Mix Columns
59487AF6 60C57445 7544E73C FDE8901E
Round[6] After Inverse Sub Bytes
15D4BDD6 9007CA68 3F86B06D 21C896E9
Round[6] After Inverse Shift Rows
15C8B068 90D4966D 3F07BDE9 2186CAD6
Round[5] After Add RoundKey
A06182E2 B6AC302A A7369FC0 0EEAB365
Round[5] After Mix Columns
6F581482 ACA12A27 9A6E251F A6EB7F00
Round[5] After Inverse Sub Bytes
065E9B11 AAF1953D 3745C2CB C53C6B52
Round[5] After Inverse Shift Rows
063CC23D AA5E6BCB 37F19B52 C5459511
Round[4] After Add RoundKey
D3A62E85 F1ADA2DC C918D91A 1BCB2B87
Round[4] After Mix Columns
9455CED1 37452070 B20B862D D18A193E
Round[4] After Inverse Sub Bytes
E7EDEC51 B26854D0 3E9EDCFA 51CF8ED1
Round[4] After Inverse Shift Rows
E7CFDCD0 B2ED8EFA 3E68ECD1 519E5451
Round[3] After Add RoundKey
4F7F40CA 213C1A37 802168BF E6C30FCB
Round[3] After Mix Columns
0EFE6E24 5CF7079C BF16BB64 8DC8BD19
Round[3] After Inverse Sub Bytes
D70C45A6 A726381C F4FFFE8C B4B1CD8E
Round[3] After Inverse Shift Rows
D7B1FE1C A70CCD8C F426458E B4FF38A6
Round[2] After Add RoundKey
4C12AA0D 2965E823 513CCED1 9498C478
Round[2] After Mix Columns
35753A83 4BB49FE7 0E95759C 90CABB51
Round[2] After Inverse Sub Bytes
D93FA241 CCC66EB0 D7AD3F1C 9610FE70
Round[2] After Inverse Shift Rows
D9103FB0 CC3FFE1C D7C6A270 96AD6E41
Round[1] After Add RoundKey
C62513B7 F75EF6CB FA5EB2D3 9FB9B1B5
Round[1] After Mix Columns
2B7E7062 E22FD089 2528FC34 42B028F8
Round[1] After Inverse Sub Bytes
0B8AD0AB 3B4E60F2 C2EE5528 F6FCEEE1
Round[1] After Inverse Shift Rows
0BFC55F2 3B8AEE28 C24ED0E1 F6EE60AB
Round[0] After Add Round Key
6BC1BEE2 2E409F96 E93D7E11 7393172A
Round[14] Input to Inverse Cipher
591CCB10 D410ED26 DC5BA74A 31362870
Round[14] After Add Round Key
A7545BC1 3208602D D836540E 415A4B6E
Round[14] After Inverse Sub Bytes
89FD57DD A1BF90FA 2D24FDD7 F846CC45
Round[14] After Inverse Shift Rows
8946FDFA A1FDCCD7 2DBF5745 F82490DD
Round[13] After Add RoundKey
43BC5719 452857E3 B7603D8B 453489D0
Round[13] After Mix Columns
B89DD541 9C9C27FE 581F1036 C99B552F
Round[13] After Inverse Sub Bytes
9A75B5F8 1C1C3D0C 5ECB7C24 12E8ED4E
Round[13] After Inverse Shift Rows
9AE87C0C 1C75ED24 5E1CB54E 12CB3DF8
Round[12] After Add RoundKey
EE743BA7 0425F0FE BC69CB01 66CAADA2
Round[12] After Mix Columns
8EBD5762 F7995D1C 2D6A643C E8737E46
Round[12] After Inverse Sub Bytes
E6CDDAAB 26F98DC4 FA588C6D C88F8A98
Round[12] After Inverse Shift Rows
E68F8CC4 26CD8A6D FAF9DA98 C8588DAB
Round[11] After Add RoundKey
BE094699 08E2BBBA 84F32B62 EF97FE68
Round[11] After Mix Columns
03E42BA4 CFD9B14C 35FFE612 844B5273
Round[11] After Inverse Sub Bytes
D5AE0B1D 5FE5565D D97DF539 4FCC488F
Round[11] After Inverse Shift Rows
D5CCF55D 5FAE4839 D9E50B8F 4F7D561D
Round[10] After Add RoundKey
0BDF9C3A 33621248 23C0681A D909B808
Round[10] After Mix Columns
1D2F6E2E 46797145 BCBBCE58 B03911F8
Round[10] After Inverse Sub Bytes
DE4E45C3 98AF2C68 78FEEC5E FC5BE3E1
Round[10] After Inverse Shift Rows
DE5BEC68 984EE35E 78AF45E1 FCFE2CC3
Round[9] After Add RoundKey
164F0E6C EEE718D4 288A85CC A53BAEFA
Round[9] After Mix Columns
3CB952EC BE79D9DB 076567EE 6EE3EAAD
Round[9] After Inverse Sub Bytes
6DDB4883 5AAFE59F 38BC0A99 454DBB18
Round[9] After Inverse Shift Rows
6D4D0A9F 5ADBBB99 38AF4818 45BCE583
Round[8] After Add RoundKey
054D7133 E804888F AE4671FC 29ED6803
Round[8] After Mix Columns
048C64E6 42EFEFA9 549641E6 05C90162
Round[8] After Inverse Sub Bytes
30F08CF5 F66161B7 FD35F8F5 361209AB
Round[8] After Inverse Shift Rows
3012F8B7 F6F009F5 FD618CAB 363561F5
Round[7] After Add RoundKey
A8D7477E 484D107B DBEDB70C 3FD523E1
Round[7] After Mix Columns
873EE41B 0A1C8EF6 9579F899 F381BFE5
Round[7] After Inverse Sub Bytes
EAD1AE44 A3C4E6D6 ADAFE1F9 7E91F42A
Round[7] After Inverse Shift Rows
EA91E1D6 A3D1F4F9 ADC4AE2A 7EAFE644
Round[6] After Add RoundKey
6BBD607B 790EBC43 89F2A4D8 84175220
Round[6] After Mix Columns
0FD68591 0AFAC4BC F4C9D7ED 64E96B07
Round[6] After Inverse Sub Bytes
FB4A67AC A3148878 BA120D53 8CEB0538
Round[6] After Inverse Shift Rows
FBEB0D78 A34A0553 BA146738 8C1288AC
Round[5] After Add RoundKey
4E423FF2 8532A314 22254511 A37EF11F
Round[5] After Mix Columns
1ADDF2F4 68934EB5 56C8975A E154D553
Round[5] After Inverse Sub Bytes
43C904BA F722B6D2 B9B18546 E0FDB550
Round[5] After Inverse Shift Rows
43FD85D2 F7C9B546 B9220450 E0B1B6BA
Round[4] After Add RoundKey
9667696A AC3A7C51 47CB4618 3E3F082C
Round[4] After Mix Columns
9D6C9D9E E2155F13 58B3E6DF F20B8E52
Round[4] After Inverse Sub Bytes
75B875DF 3B2F8482 5E4BF5EF 049EE648
Round[4] After Inverse Shift Rows
759EF582 3BB8E6EF 5E2F7548 044B84DF
Round[3] After Add RoundKey
DD2E6998 A8697222 E066F126 B316DF45
Round[3] After Mix Columns
D45C64EE 011DE26F 5CA7EF45 95148739
Round[3] After Inverse Sub Bytes
19A78C99 09DE3B06 A7896168 AD9BEA5B
Round[3] After Inverse Shift Rows
199B6106 09A7EA68 A7DE8C5B AD893B99
Round[2] After Add RoundKey
82383517 87CECFC7 02C40704 8DEEC747
Round[2] After Mix Columns
33AAAFAE 51979B1C 36C3A292 C29455E0
Round[2] After Inverse Sub Bytes
66621BBE 7085E8C4 24331A74 A8E7EDA0
Round[2] After Inverse Shift Rows
66E71AC4 7062ED74 24851BA0 A833E8BE
Round[1] After Add RoundKey
79D236C3 4B03E5A3 091D0B03 A127374A
Round[1] After Mix Columns
8BDD7870 2B1C99A0 D5B5EF93 BACAC14A
Round[1] After Inverse Sub Bytes
CEC9C1D0 0BC4F947 B5D26122 C010DD5C
Round[1] After Inverse Shift Rows
CE106147 0BC9DD22 B5C4C15C C0D2F9D0
Round[0] After Add Round Key
AE2D8A57 1E03AC9C 9EB76FAC 45AF8E51
Round[14] Input to Inverse Cipher
B6ED21B9 9CA6F4F9 F153E7B1 BEAFED1D
Round[14] After Add Round Key
48A5B168 7ABE79F2 F53E14F5 CEC38E03
Round[14] After Inverse Sub Bytes
D42956F7 BD5AAF04 77D19B77 EC33E6D5
Round[14] After Inverse Shift Rows
D4339B04 BD29E677 775A56D5 ECD1AFF7
Round[13] After Add RoundKey
1EC931E7 59FC7D43 ED853C1B 51C1B6FA
Round[13] After Mix Columns
1E9333BF B700BE92 55A31AA3 BDA5F93D
Round[13] After Inverse Sub Bytes
E92266F4 20525A74 ED714371 CD29698B
Round[13] After Inverse Shift Rows
E9294374 20226971 ED52668B CD715AF4
Round[12] After Add RoundKey
9DB504DF 387274AB 0F2718C4 B970CAAE
Round[12] After Mix Columns
B555D1C2 D666AB8E 16EDF2FD 55F86767
Round[12] After Inverse Sub Bytes
D2ED51A8 4AD30EE6 FF530421 EDE10A0A
Round[12] After Inverse Shift Rows
D2E104E6 4AED0A21 FFD3510A ED530EA8
Round[11] After Add RoundKey
8A67CEBB 64C23BF6 81D9A0F0 CA9C7D6B
Round[11] After Mix Columns
74471BB0 4AE5C307 FDC7CCFE FAC2CDB5
Round[11] After Inverse Sub Bytes
CA1644FC 5C2A3338 2131270C 14A880D2
Round[11] After Inverse Shift Rows
CAA82738 5C16800C 212A44D2 143133FC
Round[10] After Add RoundKey
14BB4E5F 30DADA7D DB0F2747 8245DDE9
Round[10] After Mix Columns
1BCE264D 6963195E D607593C 5AC2F893
Round[10] After Inverse Sub Bytes
44EC2365 E4008E9D 4A38156D 46A8E122
Round[10] After Inverse Shift Rows
44A8159D E4ECE16D 4A002322 46388E65
Round[9] After Add RoundKey
8CBCF799 92451AE7 1A25E30F 1FFD0C5C
Round[9] After Mix Columns
832644BF 50248CD2 BC0BF89C D9E3B53D
Round[9] After Inverse Sub Bytes
412386F4 6CA6F07F 789EE11C E54DD28B
Round[9] After Inverse Shift Rows
414DE17F 6C23D21C 78A6868B E59EF0F4
Round[8] After Add RoundKey
294D9AD3 DEFCE10A EE4FBF6F 89CF7D74
Round[8] After Mix Columns
45E8AC2C BDE80B97 3CE08F22 F96B934E
Round[8] After Inverse Sub Bytes
68C8AA42 CDC89E85 6DA07394 690522B6
Round[8] After Inverse Shift Rows
68057385 CDC82294 6DC8AAB6 69A09E42
Round[7] After Add RoundKey
F0C0CC4C 73753B1A 4B449111 6040DC56
Round[7] After Mix Columns
2799606E 404A466B 8B215471 6BB698EF
Round[7] After Inverse Sub Bytes
3DF99045 725C9805 CE7BFD2C 0579E261
Round[7] After Inverse Shift Rows
3D79FD05 72F9E22C CE5C9061 057B9845
Round[6] After Add RoundKey
BC557CA8 A826AA96 EA6A9A93 FFC32C21
Round[6] After Mix Columns
96102C97 F2868F49 87F5FE05 4401F581
Round[6] After Inverse Sub Bytes
357C4285 04DC73A4 EA770C36 86097791
Round[6] After Inverse Shift Rows
35090CA4 047C7736 EADC4291 86777385
Round[5] After Add RoundKey
80A03E2E 2204D171 72ED60B8 A91B0A36
Round[5] After Mix Columns
A5227BCC 55A0B1C2 56EACA31 FE1F5A35
Round[5] After Inverse Sub Bytes
29940327 ED4756A8 B9BB102E 0CCB46D9
Round[5] After Inverse Shift Rows
29CB10A8 ED94462E B94703D9 0CBB5627
Round[4] After Add RoundKey
FC51FC10 B6678F39 47AE4191 D235E8B1
Round[4] After Mix Columns
C27040B3 99BD6E2D 7C7D0830 D68B8B68
Round[4] After Inverse Sub Bytes
A8D0724B F9CD45FA 0113BF08 4ACECEF7
Round[4] After Inverse Shift Rows
A8CEBFFA F9D0CE08 01CD72F7 4A13454B
Round[3] After Add RoundKey
007E23E0 6A015AC5 BF84F699 FD4E1ED1
Round[3] After Mix Columns
52A81057 699FAAA8 34D6D563 90158B72
Round[3] After Inverse Sub Bytes
486F7CDA E46E626F 284AB500 962FCE1E
Round[3] After Inverse Shift Rows
482FB56F E46FCE00 286E7C1E 964A62DA
Round[2] After Add RoundKey
D38CE17E 6A06EBAF 8D74F741 B62D9E04
Round[2] After Mix Columns
3F299640 F32622DF 96BC7217 32FD18D6
Round[2] After Inverse Sub Bytes
254C3572 7E2394EF 35781E87 A121344A
Round[2] After Inverse Shift Rows
25211EEF 7E4C3487 3523354A A1789472
Round[1] After Add RoundKey
3A1432E8 452D3C50 18BB25E9 A86C4B86
Round[1] After Mix Columns
5390A89F 4EC43FB1 8BF56879 DBE62A1E
Round[1] After Inverse Sub Bytes
50966F6E B6882556 CE77F7AF 9FF595E9
Round[1] After Inverse Shift Rows
50F5F756 B69695AF CE886FE9 9F77256E
Round[0] After Add Round Key
30C81C46 A35CE411 E5FBC119 1A0A52EF
Round[14] Input to Inverse Cipher
23304B7A 39F9F3FF 067D8D8F 9E24ECC7
Round[14] After Add Round Key
DD78DBAB DFE17EF4 02107ECB EE488FD9
Round[14] After Inverse Sub Bytes
C9C19F0E EFE08ABA 6A7C8A59 99D473E5
Round[14] After Inverse Shift Rows
C9D48ABA EFC17359 6AE09FE5 997C8A0E
Round[13] After Add RoundKey
032E2059 0B14E86D F03FF52B 246C9303
Round[13] After Mix Columns
17379CE8 B22E7E78 F879DF4F 1C6C00A8
Round[13] After Inverse Sub Bytes
87B21CC8 3EC38AC1 E1AFEF92 C4B8526F
Round[13] After Inverse Shift Rows
87B8EFC1 3EB25292 E1C31C6F C4AF8AC8
Round[12] After Add RoundKey
F324A86A 26E24F48 03B66220 B0AE1A92
Round[12] After Mix Columns
8CB9FDDD 8BBC7F8B E3657706 5867C56C
Round[12] After Inverse Sub Bytes
F0DB21C9 CE786BCE 4DBC02A5 5E0A07B8
Round[12] After Inverse Shift Rows
F00A02CE CEDB07A5 4D7821B8 5EBC6BC9
Round[11] After Add RoundKey
A88CC893 E0F43672 3372D042 7973180A
Round[11] After Mix Columns
D1D24F33 5BA32D85 01FC5F71 2A827BCB
Round[11] After Inverse Sub Bytes
517F9266 5771FA67 0955842C 95110359
Round[11] After Inverse Shift Rows
51118467 577F032C 09719259 9555FA66
Round[10] After Add RoundKey
8F02ED00 3BB3595D F354F1CC 03211473
Round[10] After Mix Columns
5082F240 23694284 8875A5C2 4043DD9B
Round[10] After Inverse Sub Bytes
6C110472 32E4F64F 973F29A8 7264C9E8
Round[10] After Inverse Shift Rows
6C64294F 3211C9A8 97E404E8 723FF672
Round[9] After Add RoundKey
A470CB4B 44B83222 C7C1C4C5 2BFA744B
Round[9] After Mix Columns
7233B5A0 A9241C7D F8E4F5EE 2AD0B2A6
Round[9] After Inverse Sub Bytes
1E66D247 B7A6C413 E1AE7799 95603EC5
Round[9] After Inverse Shift Rows
1E607713 B7663E99 E1A6D2C5 95AEC447
Round[8] After Add RoundKey
76600CBF 05B90D8F 774FEB21 F9FF49C7
Round[8] After Mix Columns
5313789D 93C7E78D 629C010D A7CC1CFF
Round[8] After Inverse Sub Bytes
5082C175 2231B0B4 AB1C09F3 8927C47D
Round[8] After Inverse Shift Rows
502709B4 2282C4F3 AB31C17D 891CB075
Round[7] After Add RoundKey
C8E2B67D 9C3FDD7D 8DBDFADA 80FCF261
Round[7] After Mix Columns
D7A870EE C5E882AC BA24ED63 7D74CA2C
Round[7] After Inverse Sub Bytes
0D6FD099 07C811AA C0A65300 13CA1042
Round[7] After Inverse Shift Rows
0DCA53AA 076F1000 C0C8D042 13A61199
Round[6] After Add RoundKey
8CE6D207 DDB058BA E4FEDAB0 E91EA5FD
Round[6] After Mix Columns
0B173093 BEC83EC7 F5482BE6 97729ED4
Round[6] After Inverse Sub Bytes
9E870822 5AB1D131 77D40BF5 851EDF19
Round[6] After Inverse Shift Rows
9E1E0B31 5A87DFF5 77B10819 85D4D122
Round[5] After Add RoundKey
2BB739BB 7CFF79B2 EF802A30 AAB8A891
Round[5] After Mix Columns
AE6E805E 4BF9DE24 F8C9D793 EE54BA2B
Round[5] After Inverse Sub Bytes
BE453A9D CC699CA6 E1120D22 99FDC00B
Round[5] After Inverse Shift Rows
BEFD0DA6 CC45C022 E1693A0B 99129C9D
Round[4] After Add RoundKey
6B67E11E 97B60935 1F807843 479C220B
Round[4] After Mix Columns
47A53021 6E1CCAA5 4EB97A29 46B2DCDA
Round[4] After Inverse Sub Bytes
1629087B 45C41029 B6DBBD4C 983E937A
Round[4] After Inverse Shift Rows
163EBD29 4529934C B6C4087A 98DB107B
Round[3] After Add RoundKey
BE8E2133 D6F80781 088D8C14 2F864BE1
Round[3] After Mix Columns
BD2066D9 7C7DE64F CA28748B F69B94FA
Round[3] After Inverse Sub Bytes
CD54D3E5 0113F592 10EECACE D6E8E714
Round[3] After Inverse Shift Rows
CDE8CA92 0154E7CE 1013D314 D6EEF5E5
Round[2] After Add RoundKey
564B9E83 8F3DC261 B509584B F689093B
Round[2] After Mix Columns
61F7A93F 462A2954 EF18471F CA7FAF57
Round[2] After Inverse Sub Bytes
D826B725 98954CFD 613416CB 106B1BDA
Round[2] After Inverse Shift Rows
D86B16FD 98261BCB 6195B7DA 10344C25
Round[1] After Add RoundKey
C75E3AFA A347131C 4C0DA779 192093D1
Round[1] After Mix Columns
9097DF81 746A09FC 44828AD3 FB3A873D
Round[1] After Inverse Sub Bytes
9685EF91 CA584055 8611CFA9 63A2EA8B
Round[1] After Inverse Shift Rows
96A2CF55 CA85EAA9 8658EF8B 63114091
Round[0] After Add Round Key
F69F2445 DF4F9B17 AD2B417B E66C3710

Blog Entry © Monday, March 9, 2026, by James Pate Williams, Jr. Testing a Translation of My C# Advanced Encryption Standard (AES) to the Programming Language C

Blog Entry Monday March 9 2026Download

Blog Entry © Thursday, March 5, 2026, by James Pate Williams, Jr., Simple Filtering of a Noisy Signal in the Programming Language C

Blog Entry Thursday March 5 2026Download

Blog Entry © Friday, February 27, 2026, by James Pate Williams, Jr., C Pseudorandom Bit Generators and Four Statistical Tests

Blog Entry Friday February 27 2028Download