Automatic search for differential characteristics in ARX ciphers

ARX operations are composed of only three operations: additions modulo 2ⁿ, bit rotations and XORs. Due to the widespread use of ARX, the study of its security is particularly important. This paper shows an algorithm to search for optimal differential characteristics in ARX ciphers. The algorithm is based on two related algorithms - the algorithm for finding all optimal output differences and the algorithm for differential probability of modular addition, and the idea of weight calculation. Finally, we apply this algorithm to three round Chacha, which is the compression algorithm of Blake, and show a differential characteristic with weight 36 for it. This result could contribute to the study of differential cryptanalysis of Chacha and Blake.