Preliminary NIST FIPS 203 Results © Monday, February 16, 2026, by James Pate Williams, Jr. C Implementation

References:

  1. Module-Lattice-Based Key-Encapsulation Mechanism Standard
  2. Number-theoretic transform (integer DFT)
  3. chap2.pdf Chapter 2 of the Handbook of Applied Cryptography

I have two versions of the code using C long integers and another variant using Professor Emeritus Arjen K. Lenstra’s C Free Large Integer Package (lip).

Testing NIST BitRev
Primitive root = 17
Length = 7
n = 256
n / 2 = 128
q = 3329
BitRev(0) = 1
BitRev(1) = 1729
BitRev(2) = 2580
BitRev(3) = 3289
BitRev(4) = 2642
BitRev(5) = 630
BitRev(6) = 1897
BitRev(7) = 848
Testing NIST NTT
f[0] = 4        fhat[0] = 257
f[1] = 1        fhat[1] = 95
f[2] = 4        fhat[2] = 308
f[3] = 2        fhat[3] = 232
f[4] = 1        fhat[4] = 90
f[5] = 3        fhat[5] = 657
f[6] = 5        fhat[6] = 34
f[7] = 6        fhat[7] = 366
Testing NIST NTT^-1
fhat[0] = 257   copf[0] = 4
fhat[1] = 95    copf[1] = 1
fhat[2] = 308   copf[2] = 4
fhat[3] = 232   copf[3] = 2
fhat[4] = 90    copf[4] = 1
fhat[5] = 657   copf[5] = 3
fhat[6] = 34    copf[6] = 5
fhat[7] = 366   copf[7] = 6
Testing NIST NTT Multiplication
g[0] = 6        ghat[0] = 518   copg[0] = 6
g[1] = 1        ghat[1] = 661   copg[1] = 1
g[2] = 8        ghat[2] = 492   copg[2] = 8
g[3] = 0        ghat[3] = 339   copg[3] = 0
g[4] = 3        ghat[4] = 583   copg[4] = 3
g[5] = 3        ghat[5] = 91    copg[5] = 3
g[6] = 9        ghat[6] = 450   copg[6] = 9
g[7] = 8        ghat[7] = 259   copg[7] = 8
fhat[0] = 257   ghat[0] = 518   hhat[0] = 102
fhat[1] = 95    ghat[1] = 661   hhat[1] = 362
fhat[2] = 308   ghat[2] = 492   hhat[2] = 392
fhat[3] = 232   ghat[3] = 339   hhat[3] = 504
fhat[4] = 90    ghat[4] = 583   hhat[4] = 150
fhat[5] = 657   ghat[5] = 91    hhat[5] = 208
fhat[6] = 34    ghat[6] = 450   hhat[6] = 196
fhat[7] = 366   ghat[7] = 259   hhat[7] = 545

D:\NISTFIPS203\x64\Release\NISTFIPS203.exe (process 26656) exited with code 0 (0x0).
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Author: jamespatewilliamsjr

My whole legal name is James Pate Williams, Jr. I was born in LaGrange, Georgia approximately 70 years ago. I barely graduated from LaGrange High School with low marks in June 1971. Later in June 1979, I graduated from LaGrange College with a Bachelor of Arts in Chemistry with a little over a 3 out 4 Grade Point Average (GPA). In the Spring Quarter of 1978, I taught myself how to program a Texas Instruments desktop programmable calculator and in the Summer Quarter of 1978 I taught myself Dayton BASIC (Beginner's All-purpose Symbolic Instruction Code) on LaGrange College's Data General Eclipse minicomputer. I took courses in BASIC in the Fall Quarter of 1978 and FORTRAN IV (Formula Translator IV) in the Winter Quarter of 1979. Professor Kenneth Cooper, a genius poly-scientist taught me a course in the Intel 8085 microprocessor architecture and assembly and machine language. We would hand assemble our programs and insert the resulting machine code into our crude wooden box computer which was designed and built by Professor Cooper. From 1990 to 1994 I earned a Bachelor of Science in Computer Science from LaGrange College. I had a 4 out of 4 GPA in the period 1990 to 1994. I took courses in C, COBOL, and Pascal during my BS work. After graduating from LaGrange College a second time in May 1994, I taught myself C++. In December 1995, I started using the Internet and taught myself client-server programming. I created a website in 1997 which had C and C# implementations of algorithms from the "Handbook of Applied Cryptography" by Alfred J. Menezes, et. al., and some other cryptography and number theory textbooks and treatises.

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