Improved Conditional Differential Analysis on NLFSR-Based Block Cipher KATAN32 with MILP

Abstract

In this paper, a new method for constructing a Mixed Integer Linear Programming (MILP) model on conditional differential cryptanalysis of the nonlinear feedback shift register- (NLFSR-) based block ciphers is proposed, and an approach to detecting the bit with a strongly biased difference is provided. The model is successfully applied to the block cipher KATAN32 in the single-key scenario, resulting in practical key-recovery attacks covering more rounds than the previous. In particular, we present two distinguishers for 79 and 81 out of 254 rounds of KATAN32. Based on the 81-round distinguisher, we recover 11 equivalent key bits of 98-round KATAN32 and 13 equivalent key bits of 99-round KATAN32. The time complexity is less than $2^{31}$ encryptions of 98-round KATAN32 and less than $2^{33}$ encryptions of 99-round KATAN32, respectively. Thus far, our results are the best known practical key-recovery attacks for the round-reduced variants of KATAN32 regarding the number of rounds and the time complexity. All the results are verified experimentally.