Nonlinearly balanced Boolean functions and their propagation characteristics
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
Handbook of Applied Cryptography
Handbook of Applied Cryptography
A D. C. Optimization Algorithm for Solving the Trust-Region Subproblem
SIAM Journal on Optimization
Solving a Class of Linearly Constrained Indefinite QuadraticProblems by D.C. Algorithms
Journal of Global Optimization
Genetic Algorithms: Principles and Perspectives: A Guide to GA Theory
Genetic Algorithms: Principles and Perspectives: A Guide to GA Theory
Construction of nonlinear boolean functions with important cryptographic properties
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Propagation characteristics and correlation-immunity of highly nonlinear boolean functions
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Exact penalty and error bounds in DC programming
Journal of Global Optimization
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Substitution boxes, aka S-boxes, are a key component of modern crypto-systems. Several studies and developments were carried out on the problem of building high-quality S-boxes in the last few years. Qualities of such boxes, such as nonlinearity and balance, steer the robustness of modern block ciphers. This work is concerned with the construction of highly nonlinear balanced Boolean functions. A deterministic optimization model which is the minimization of a polyhedral convex function on a convex polytope with 0---1 variables is introduced. A local deterministic optimization approach called DCA (Difference of Convex functions Algorithm) is investigated. For finding a good starting point of DCA we propose two versions of a combined DCA---GA (Genetic Algorithm) method. Numerical simulations prove that DCA is a promising approach for this problem. Moreover the combination of DCA---GA improves the efficiency of DCA and outperforms other standard approaches.