Mixed Integer Programming Models for Finite Automaton and Its Application to Additive Differential Patterns of Exclusive-Or [article]

Siwei Sun, Lei Hu, Peng Wang, Meiqin Wang, Danping Shi, Xiaoshuang Ma, Qianqian Yang, Kai Fu
2016 IACR Cryptology ePrint Archive  
Inspired by Fu et al. work [12] on modeling the exclusive-or differential property of the modulo addition as an mixed-integer programming problem, we propose a method with which any finite automaton can be formulated as an mixed-integer programming model. Using this method, we show how to construct a mixed integer programming model whose feasible region is the set of all differential patterns (α, β, γ)'s, such that adp ⊕ (α, β → γ) = Prx,y[((x + α) ⊕ (y + β)) − (x ⊕ y) = γ] > 0. We expect that
more » ... his may be useful in automatic differential analysis with additive difference.
dblp:journals/iacr/SunHWWSMYF16 fatcat:7licbqo3snfsphh36jnqxepfpe