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, SpringerVerlag 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 7bit 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 kth bit of xth 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

