finding integral distinguisher and differential bound on present cipher based on mixed integer linear programming

Mixed integer linear programming (milp) is a powerful method for block ciphers analysis and optimization as it presents a flexible tool for solving some large, complex problems such as finding active substitution boxes, integral division property cryptanalysis and so on. in this paper, we introduce milp and supply it to find the number of active s-boxes into the model of block cipher as present and we discuss about integral analysis. as a new method, we also apply convex shell approach to reduce the complexity and find 8 round integral distinguisher with memory less than the other one and find 12 round differential characteristic on the present cipher.