Automatic Differential Analysis of ARX Block Ciphers with Application to SPECK and LEA

In this paper, we focus on the automatic differential cryptanalysis of ARX block ciphers with respect to XOR-difference, and develop Mouha et al.’s framework for finding differential characteristics by adding a new method to construct long characteristics from short ones. The new method reduces the searching time a lot and makes it possible to search differential characteristics for ARX block ciphers with large word sizes such as n = 48, 64. What’s more, we take the differential effect into consideration and find that the differential probability increases by a factor of 1.4 ∼ 8 for SPECK and about 2 for LEA when multiple characteristics are counted in. The efficiency of our method is demonstrated by improved attacks of SPECK and LEA, which attack 1, 1, 4 and 6 more rounds of SPECK48, SPECK64, SPECK96 and SPECK128, respectively, and 2 more rounds of LEA than previous works.