MILP-Based Differential Cryptanalysis on IVLBC and Eslice-64

Abstract

Mixed integer linear programming (MILP) model was presented by Sun <italic>et al.</italic> at Asiacrypt 2014 to search for differential characteristics of block ciphers. Based on this model, it is easy to assess block ciphers against differential attack. In this paper, the MILP model is improved to search for differential trails of Midori64 which is a family of lightweight block ciphers provided by Banik <italic>et al.</italic> at Asiacrypt 2015. We find the best 5-round differential characteristics of Midori64 with MILP-based model, and the probabilities are <inline-formula> <tex-math notation="LaTeX">$2^{-52}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$2^{-58}$ </tex-math></inline-formula> respectively. Based on these distinguishers, we give key recovery attacks on the 11-round reduced Midori64 with data complexities of <inline-formula> <tex-math notation="LaTeX">$2^{55.6}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$2^{61.2}$ </tex-math></inline-formula>, and time complexities of <inline-formula> <tex-math notation="LaTeX">$2^{109.35}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$2^{100.26}$ </tex-math></inline-formula>.

Description