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, and 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)
PDF
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
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2016/338,
      author = {Siwei Sun and Lei Hu and Peng Wang and Meiqin Wang and Danping Shi and Xiaoshuang Ma and Qianqian Yang and Kai Fu},
      title = {Mixed Integer Programming Models for Finite Automaton and Its Application to Additive Differential Patterns of Exclusive-Or},
      howpublished = {Cryptology ePrint Archive, Paper 2016/338},
      year = {2016},
      note = {\url{https://eprint.iacr.org/2016/338}},
      url = {https://eprint.iacr.org/2016/338}
}
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