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

Le Hoai Minh (), Le Thi Hoai An (), Pham Dinh Tao () and Pascal Bouvry ()
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Le Hoai Minh: University of Paul Verlaine – Metz, Laboratory of Theoretical and Applied Computer Science (LITA EA 3097)
Le Thi Hoai An: University of Paul Verlaine – Metz, Laboratory of Theoretical and Applied Computer Science (LITA EA 3097)
Pham Dinh Tao: National Institute for Applied Sciences-Rouen, Laboratory of Modelling, Optimization & Operations Research
Pascal Bouvry: University of Luxembourg, Computer Science Research Unit

A chapter in Modeling, Simulation and Optimization of Complex Processes, 2008, pp 381-391 from Springer

Abstract: 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.

Keywords: Boolean Function; Hill Climbing; Preliminary Numerical Result; Lower Semicontinuous Proper Convex Function; Local Optimality Condition (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-79409-7_26

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

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