The Discrete Logarithm Problem as an Optimization Task: A First Study

E.C. Laskari, G.C. Meletiou, and M.N. Vrahatis (Greece)


Cryptography, Evolutionary Algorithms, Discrete Loga rithm, Integer Programming


Most of the contemporary cryptographic systems are based on mathematical problems whose solutions are generally intractable in polynomial time; such problems are the dis crete logarithm problem and the integer factorization prob lem. In this contribution we consider the discrete logarithm problem as an Integer Programming Problem. Two Evolu tionary Computation methods, namely the Particle Swarm Optimization and the Differential Evolution algorithm, as well as the Random Search technique, are employed as a first approach to tackle this new Integer Programming Problem. Primitive results indicate that this new approach seems promising.

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