TY - JOUR
TI - Refined Probability of Differential Characteristics Including Dependency Between Multiple Rounds
PY - 2017/06/19
Y2 - 2024/10/15
JF - IACR Transactions on Symmetric Cryptology
JA - ToSC
VL - 2017
IS - 2
SE - Articles
DO - 10.13154/tosc.v2017.i2.203-227
UR - https://doi.org/10.13154/tosc.v2017.i2.203-227
SP - 203-227
AB - The current paper studies the probability of differential characteristics for an unkeyed (or with a fixed key) construction. Most notably, it focuses on the gap between two probabilities of differential characteristics: probability with independent S-box assumption, pind, and exact probability, pexact. It turns out that pexact is larger than pind in Feistel network with some S-box based inner function. The mechanism of this gap is then theoretically analyzed. The gap is derived from interaction of S-boxes in three rounds, and the gap depends on the size and choice of the S-box. In particular the gap can never be zero when the S-box is bigger than six bits. To demonstrate the power of this improvement, a related-key differential characteristic is proposed against a lightweight block cipher RoadRunneR. For the 128-bit key version, pind of 2−48 is improved to pexact of 2−43. For the 80-bit key version, pind of 2−68 is improved to pexact of 2−62. The analysis is further extended to SPN with an almost-MDS binary matrix in the core primitive of the authenticated encryption scheme Minalpher: pind of 2−128 is improved to pexact of 2−96, which allows to extend the attack by two rounds.
ER -