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Binary derivatives of bit output sequences probabilities


This family of tests was inspired by Jovan Dj. Golic's "Linear Statistical Weakness of Alleged RC4 Keystream Generator" (EUROCRYPT 1997), LNCS, vol. 1233, Springer-Verlag 1997, where the author describes a statistical bias in the second binary derivative of the least significant bit output sequence of RC4.

Output generated by the VMPC Stream Cipher showed no bias in this family of tests. The following objectives were taken in testing VMPC here:

First, second and third binary derivatives of all 7 bits output sequences (for 7-bit word size) were tested (21 frequencies of (Output[x]k + Output[x+A]k=1) were measured for k = {0,1,...,6}, A = {1,2,3}, where Output[x]k denotes k-th bit of x-th output word)

In a sequence of 2^44.8 (about 10^13.5) VMPC outputs tested according to this approach none of the measured frequencies showed a statistically significant deviation from its expected value of 0.5.

by Bartosz Zoltak

Copyright © 1999-2018 by Bartosz Zoltak