Differential analysis of lightweight cipher algorithm ACE based on MILP - Shuai LIU; Jie GUAN; Bin HU; Sudong MA (Tongxin xuebao)
The differential property of the lightweight cipher algorithm ACE was researched.n-dimension ring AND-gate combination was defined and its differential property was described accurately by only O(n) expressions with the MILP method by analyzing the relationship among AND gates.The nonlinear operation of ACE was transformed to the 32-dimension ring AND-gate combination and the MILP differential model of ACE was proposed.According to the characteristics of Gurobi solver, a model for fast solving the MILP differential model of ACE was given.For ACE permutation with 3 to 6 steps, the optimal differential characteristic was obtained and its probability was improved by multi-difference technique.The differential forge attack on authenticated encryption algorithm ACE- AE-128 and the differential collision attack on hash algorithm ACE- H-256 was given with 3-step ACE permutation, and the success probability was 2-90.52.And it was proved that the 4-steps ACE permutation arrived the differential security bound of 128 bit.Actually, the MILP differential description of ring AND-gate combination can be applied on more cipher algorithms, such as SIMON, Simeck.