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**2016/338**

**Title:**

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

**Authors:**
Siwei Sun, Lei Hu, Peng Wang, Meiqin Wang, Danping Shi, Xiaoshuang Ma, Qianqian Yang, Kai Fu

**Abstract:**

Inspired by Fu et al. work 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 (\alpha, \beta, \gamma)'s, such that {\rm adp}^\oplus(\alpha, \beta \rightarrow \gamma) = {\rm Pr}_{x,y}[((x + \alpha) \oplus (y + \beta))-(x \oplus y) = \gamma] > 0. We expect that this may be useful in automatic differential analysis with additive difference.

**ePrint:**
https://eprint.iacr.org/2016/338

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