A Deterministic Optimization Approach for Generating Highly Nonlinear Balanced Boolean Functions in Cryptography

Le Hoai Minh,Pham Dinh Tao,Pascal Bouvry,Le Thi Hoai An

doi:10.1007/978-3-540-79409-7_26

A Deterministic Optimization Approach for Generating Highly Nonlinear Balanced Boolean Functions in Cryptography

Le Hoai Minh, Pham Dinh Tao + Show 2 more

https://doi.org/10.1007/978-3-540-79409-7_26

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Publication Date: Jan 1, 2008

Citations: 7

Affiliation: Institut National des Sciences Appliquées de Rouen, Institut National des Sciences Appliquées de Toulouse, University of Luxembourg

#Difference Of Convex Functions Programming #Difference Of Convex Functions + Show 8 more

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Abstract

We propose in this work a deterministic continuous approach for constructing highly nonlinear balanced Boolean functions, which is an interesting and open question in Cryptography. Our approach is based on DC (Difference of Convex functions) programming and DCA (DC optimization Algorithms). We first formulate the problem in the form of a combinatorial optimization problem, more precisely a mixed 0–1 linear program. By using exact penalty technique in DC programming, this problem is reformulated as polyhedral DC program. We next investigate DC programming and DCA for solving this latter problem. Preliminary numerical results show that the proposed algorithm is promising and more efficient than somes heuristic algorithms.

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