S-box-and-bit-sliced analysis of DES (VI): information -theoretic sensitivity analysis of last-round-key of DES using

摘要

Dual representation of 2-round DES characteristics, denoted by (S{sub}i), is introduced whose input and output random vectors consist of 6-dimensional lefthalf bit and 12-dimensional righthalf bit. We can observe frequencies between an output random variable, being EOR-operated with an input left half bit and its input random 6-dimensional vector observed in the last-round S-box, referred to as a dual trellis module. We introduce the likelihood function for input lefthalf bit sequence, based on the binomial distribution with probability 1/2 + δ to guess the associated key vector. It is shown from the statistical point of view that the precise estimate of δ requires δ{sup}(-2) ciphertexts only. Simple numerical simulation results show that the χ{sup}2 statistics play an important role in determining the last-round-key vectors correctly.