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Modeling, Simulation and Optimization of Complex Processes pp 381–391Cite as

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

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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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References

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Author information

Authors and Affiliations

  1. Laboratory of Theoretical and Applied Computer Science (LITA EA 3097), University of Paul Verlaine – Metz, Ile du Saulcy, 57045, Metz, France

    Le Hoai Minh & Le Thi Hoai An

  2. Laboratory of Modelling, Optimization & Operations Research, National Institute for Applied Sciences-Rouen, BP 08, Place Emile Blondel, 76131, Mont Saint Aignan Cedex, France

    Pham Dinh Tao

  3. Computer Science Research Unit, University of Luxembourg, Campus Kirchberg, 6 Rue Richard Coudenhove-Kalergi, L-1359, Luxembourg

    Pascal Bouvry

Authors
  1. Le Hoai Minh
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  2. Le Thi Hoai An
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  3. Pham Dinh Tao
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  4. Pascal Bouvry
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Editor information

Editors and Affiliations

  1. Interdisziplinäres Zentrum für Wissenschaftliches Rechnen (IWR), Universität Heidelberg, Im Neuenheimer Feld 368, 69120, Heidelberg, Germany

    Hans Georg Bock  & Rolf Rannacher  & 

  2. FB Mathematik und Informatik, Universität Marburg, Hans-Meerwein-Str., 35032, Marburg, Germany

    Ekaterina Kostina

  3. Institute of Mathematics, Vietnamese Academy of Science and Technology (VAST), 18 Hoang Quoc Viet Road, 10307, Hanoi, Vietnam

    Hoang Xuan Phu

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© 2008 Springer-Verlag Berlin Heidelberg

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Minh, L.H., An, L.T.H., Tao, P.D., Bouvry, P. (2008). A Deterministic Optimization Approach for Generating Highly Nonlinear Balanced Boolean Functions in Cryptography. In: Bock, H.G., Kostina, E., Phu, H.X., Rannacher, R. (eds) Modeling, Simulation and Optimization of Complex Processes. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79409-7_26

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