Differential Analysis of ARX Block Ciphers Based on an Improved Genetic Algorithm

Differential cryptanalysis is one of the most critical analysis methods to evaluate the security strength of cryptographic algorithms. This paper first applies the genetic algorithm to search for differential characteristics in differential cryptanalysis. A new algorithm is proposed as the fitness function to generate a high-probability differential characteristic from a given input difference. Based on the differential of the differential characteristic found by genetic algorithm, Boolean satisfiability (SAT) is used to search all its differential characteristics to calculate the exact differential probability. In addition, a penalty-like function is also proposed to guide the search direction for the application of the stochastic algorithm to differential cryptanalysis. Our new automated cryptanalysis method is applied to SPECK32 and SPECK48. As a result, the 10-round differential probability of SPECK32 is improved to 2(-30.34), and a 12-round differential of SPECK48 with differential probability 2(-46.78) is achieved. Furthermore, the corresponding differential attacks are also performed. The experimental results show our method's validity and outstanding performance in differential cryptanalysis.