Paper 2019/025

STP Models of Optimal Differential and Linear Trail for S-box Based Ciphers

Yu Liu, Huicong Liang, Muzhou Li, Luning Huang, Kai Hu, Chenhe Yang, and Meiqin Wang

Abstract

Automatic tools have played an important role in designing new cryptographic primitives and evaluating the security of ciphers. Simple Theorem Prover constraint solver (STP) has been used to search for differential/linear trails of ciphers. This paper proposes general STP-based models searching for differential and linear trails with the optimal probability and correlation for S-box based ciphers. In order to get trails with the best probability or correlation for ciphers with arbitrary S-box, we give an efficient algorithm to describe probability or correlation of S-Box. Based on the algorithm we present a search model for optimal differential and linear trails, which is efficient for ciphers with S-Boxes whose DDTs/LATs contain entities not equal to the power of two. Meanwhile, the STP-based model for single-key impossible differentials considering key schedule is proposed, which traces the propagation of values from plaintext to ciphertext instead of propagations of differences. And we found that there is no 5-round AES-128 single-key truncated impossible differential considering key schedule, where input and output differences have only one active byte respectively. Finally, our proposed models are utilized to search for trails of bit-wise ciphers GIFT-128, DES, DESL and ICEBERG and word-wise ciphers ARIA, SM4 and SKINNY-128. As a result, improved results are presented in terms of the number of rounds or probabilities/correlations.