Revisiting boomerang attacks on lightweight ARX and AND-RX ciphers with applications to KATAN, SIMON and CHAM

Abstract

In this paper, we investigate the security of lightweight block ciphers, focusing on those that utilize the ADD-Rotate-XOR (ARX) and AND-Rotate-XOR (AND-RX) design paradigms. More specifically, we examine their resilience against boomerang-style attacks. First, we propose an automated search strategy that leverages the boomerang connectivity table (BCT) for AND operations ($\wedge BCT$) to conduct a complete search for boomerang and rectangle distinguishers for AND-RX ciphers. The proposed search strategy automatically considers all possible $\wedge BCT$ switches in the middle of the boomerang to optimize distinguishing probability. The correctness of the search strategy was verified experimentally. We were able to find the best boomerang and rectangle distinguishers to date in the single-key model for lightweight block ciphers KATAN32/48/64 and SIMON32/48. Next, we investigated BCT properties of ARX ciphers and discovered that a truncated boomerang switch could be formulated for the lightweight ARX cipher, CHAM. We were able to find the best single-key and related-key rectangle distinguishers to date for CHAM. Our findings provide more accurate security margins of these lightweight ciphers against boomerang-style attacks.