Blog Entry © Wednesday, June 4, 2025, Differential Cryptanalysis of DES by James Pate Williams, Jr.

Below are outputs from three different apps perform differential cryptanalysis on three, four, and six round DES algorithms. Three round is first etc.

E  = 007e0e80 680c0000
E* = bf02ac05 40520000
C' = 965d5b67
E  = a0bff415 02f60000
E* = 8a6a5ebf 28aa0000
C' = 9c9c1f56
E  = ef15068f 695f0000
E* = 05e9a2bf 56040000
C' = d575db2b

1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0
0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 3
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

0 0 0 1 0 3 0 0 1 0 0 1 0 0 0 0
0 1 0 0 0 2 0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 1 0 0 1 0 1 0 0 0 1 0
0 0 1 1 0 0 0 0 1 0 1 0 2 0 0 0

0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0
0 0 0 3 0 0 0 0 0 0 0 0 0 0 1 1
0 2 0 0 0 0 0 0 0 0 0 0 1 1 0 0
0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0

3 1 0 0 0 0 0 0 0 0 2 2 0 0 0 0
0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 1
1 1 1 0 1 0 0 0 0 1 1 1 0 0 1 0
0 0 0 0 1 1 0 0 0 0 0 0 0 0 2 1

0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0
0 0 0 0 2 0 0 0 3 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 2 0 0 0 0 0 0 1 0 0 0 0 2 0

1 0 0 1 1 0 0 3 0 0 0 0 1 0 0 1
0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0
1 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0

0 0 2 1 0 1 0 3 0 0 0 1 1 0 0 0
0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1
0 0 2 0 0 0 2 0 0 0 0 1 2 1 1 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1
0 3 0 0 0 0 1 0 0 0 0 0 0 0 0 0

47 05 19 00 24 07 07 49
J = bc54c060 71f10000
key = 0001101P0110001P01?01?0P1?00100P0101001P0000??0P111?11?P?100011P
88
Unknown bit count = 8

key = 0001101001100010010011001000100101010010000011011110110001000110
key = 1a624c89 520dec46
E  = f069a40a a8a70000
E* = c0e9f28f 810f0000
C' = fa719d15

E  = dabefbef 01a70000
E* = c03fa95f 29570000
C' = ea5605a1

E  = ca7d095a 815f0000
E* = d57d094a 800f0000
C' = 0b00c0cb

E  = 7fbf56aa 43050000
E* = 65945eba 55550000
C' = 0923cbd6

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0

2 0 2 1 1 0 0 0 2 1 0 0 1 0 0 0
1 0 0 1 1 0 0 2 0 1 0 1 0 0 0 2
4 1 1 0 2 0 1 0 1 1 1 0 1 0 1 0
1 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0

1 1 2 1 1 1 1 2 3 2 1 2 1 1 2 1
1 1 2 1 1 1 1 2 1 2 2 1 1 2 1 2
2 3 1 1 4 2 2 2 1 1 1 1 2 2 1 1
1 2 1 1 1 2 1 1 1 1 1 1 1 1 2 2

1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1
1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1
1 1 1 2 2 4 1 1 1 1 2 1 2 2 1 2
1 1 1 2 1 2 1 2 1 2 1 1 2 1 1 1

0 1 1 0 0 0 1 0 0 1 0 0 1 1 1 0
0 1 0 1 0 0 0 1 2 0 1 0 3 0 1 0
4 0 1 1 2 1 1 0 0 0 1 1 1 0 0 2
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 2 1 2 1 1 1 1 1 1 1 1 2 4 1 2
1 1 1 1 1 1 1 1 1 1 2 2 1 2 1 3
1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 1
1 2 1 2 3 1 3 1 1 1 1 1 1 1 1 1

1 0 2 2 0 0 0 1 0 2 1 0 2 0 0 0
1 1 0 0 0 1 0 0 0 1 4 1 0 0 0 1
1 1 1 0 0 2 0 1 0 0 1 0 1 0 0 0
0 0 1 1 0 0 0 0 1 1 0 0 1 0 0 0

0 0 0 0 0 0 0 0 1 0 4 2 1 1 1 0
0 0 0 0 0 0 0 1 0 0 3 2 0 1 0 1
1 0 1 1 1 0 1 0 0 0 2 0 0 1 0 0
0 0 0 1 0 0 0 1 0 0 2 0 0 1 0 1

00 32 36 37 32 13 26 10
J = 02092580 d68a0000
key = 10?10?0P???1101P0011000P0000??0P00??01?P??00100P?101000P11?0101P

Unknown bit Count = 14

7774

key = 1001010011111011001100010000000100100110110010001101000011001011
key = 94fb3101 26c8d0cb
Plaintext-Ciphertext Pairs:
0       748502cd        38451097        03c70306        d8a09f10
0       38747564        38451097        78560a09        60e6d4cb
1       48691102        6acdff31        45fa285b        e5adc730
1       375bd31f        6acdff31        134f7915        ac253457
2       357418da        013fec86        d8a31b2f        28bbc5cf
2       12549847        013fec86        0f317ac2        b23cb944

Possible J Values:
J #     J Cnt   J-Value(s):
0       1       47
1       1        5
2       1       19
3       1        0
4       1       24
5       1        7
6       1        7
7       1       49

key = 0001101001100010010011001000100101010010000011011110110001000110
tst = 0001101001100010010011001000100101010010000011011110110001000110
key = 1a624c89 520dec46
tst = 1a624c89 520dec46

J #     J-Value True J-Value:
 0      47      47
 1       5       5
 2      19      19
 3       0       0
 4      24      24
 5       7       7
 6       7       7
 7      49      49

Tested Keys #             = 1073
Runtime (s)               = 0

Runtime per test (s)      = 0.000028
Runtime max estimated (s) = 0.029784

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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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