Efficient Computation of Boomerang Connection Probability for ARX-Based Block Ciphers with Application to SPECK and LEA

Abstract

The boomerang connectivity table (BCT) was introduced by C. Cid et al. Using the BCT, for SPN block cipher, the dependency between sub-ciphers in boomerang structure can be computed more precisely. However, the existing method to generate BCT is difficult to be applied to the ARX-based cipher, because of the huge domain size. In this paper, we show a method to compute the dependency between sub-ciphers in boomerang structure for modular addition. Using bit relation in modular addition, we compute the dependency sequentially in bitwise. And using this method, we find boomerang characteristics and amplified boomerang characteristics for the ARX-based ciphers LEA and SPECK. For LEA-128, we find a reduced 15-round boomerang characteristic and reduced 16-round amplified boomerang characteristic which is two rounds longer than previous boomerang characteristic. Also for SPECK64/128, we find a reduced 13-round amplified boomerang characteristic which is one round longer than previous rectangle characteristic.