Hybrid Differential Evolutionary Algorithms for Koblitz Elliptic Curves Generating

Elliptic curve cryptography(ECC) is one of the most important public key cryptography. The koblitz curve is a special kind of elliptic curve in ECC. The elliptic curve cryptosystem (ECC) which is based on elliptic curve discrete logarithm problem. As of today the security of an ECC is determined by the cardinality of E(F-q) (the set of rational points of E over F-q). Based on the hybrid differential evolutionary algorithms and the evolutionary cryptography theory, we proposed a new algorithm to generate secure Koblitz ECC. Traveling Salesman Problems (TSP) is the well-known combinatorial optimization problem. And the optimal solution can not be found in polynomial time. So the approximation algorithm with polynomial algorithm for TSP has been an important topic in this field. PODE was proposed for TSP by incorporating Position-Order Encoding(POE) into DE. PODE is effective for small-size TSP and less effective for middle-size TSP. We deveplp a new hybrid differential evolution algorithm, which improves PODE by using hill-climbing operator as the local search algorithm, is proposed for middle-size TSP. The experimental results show that the generation efficiency of secure curves generated is superior to the parameters recommended by NIST.