# Hacking of the AES with Boolean Functions

### Michel Dubois, Eric Filiol

#### Abstract

One of the major issues of cryptography is the cryptanalysis of cipher algorithms. Some mechanisms for breaking codes include differential cryptanalysis, advanced statistics and brute-force. Recent works also attempt to use algebraic tools to reduce the cryptanalysis of a block cipher algorithm to the resolution of a system of quadratic equations describing the ciphering structure. In our study, we will also use algebraic tools but in a new way: by using Boolean functions and their properties. A Boolean function is a function from Fn 2 !F2 with n > 1. The arguments of Boolean functions are binary words of length n. Any Boolean function can be represented, uniquely, by its algebraic normal form which is an equation which only contains additions modulo 2—the XOR function—and multiplications modulo 2—the AND function. Our aim is to describe the AES algorithm as a set of Boolean functions then calculate their algebraic normal forms by using the Moebius transforms. After, we use a specific representation for these equations to facilitate their analysis and particularly to try a combinatorial analysis. Through this approach we obtain a new kind of equations system.

#### References

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#### Paper Citation

#### in Harvard Style

Dubois M. and Filiol E. (2017). **Hacking of the AES with Boolean Functions** . In *Proceedings of the 3rd International Conference on Information Systems Security and Privacy - Volume 1: ForSE, (ICISSP 2017)* ISBN 978-989-758-209-7, pages 599-609. DOI: 10.5220/0006091305990609

#### in Bibtex Style

@conference{forse17,

author={Michel Dubois and Eric Filiol},

title={Hacking of the AES with Boolean Functions},

booktitle={Proceedings of the 3rd International Conference on Information Systems Security and Privacy - Volume 1: ForSE, (ICISSP 2017)},

year={2017},

pages={599-609},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0006091305990609},

isbn={978-989-758-209-7},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 3rd International Conference on Information Systems Security and Privacy - Volume 1: ForSE, (ICISSP 2017)

TI - Hacking of the AES with Boolean Functions

SN - 978-989-758-209-7

AU - Dubois M.

AU - Filiol E.

PY - 2017

SP - 599

EP - 609

DO - 10.5220/0006091305990609