Paper 2016/338
Mixed Integer Programming Models for Finite Automaton and Its Application to Additive Differential Patterns of Exclusive-Or
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.
Metadata
- Available format(s)
- Publication info
- Preprint. MINOR revision.
- Keywords
- Finite automatonARX cipherModulo additionExclusive-orAdditive differentialInteger programmingAutomatic cryptanalysis
- Contact author(s)
- sunsiwei @ iie ac cn
- History
- 2016-03-30: received
- Short URL
- https://ia.cr/2016/338
- License
-
CC BY