Evolutionary cryptography theory-based generating method for secure ECs

Ant Colony Optimization (ACO) has the character of positive feedback, distributed searching, and greedy searching. It is applicable to optimization grouping problems. Traditional cryptographic research is mainly based on pure mathematical methods which have complicated theories and algorithm. It seems that there is no relationship between cryptography and ACO. Actually, some problems in cryptography are due to optimization grouping problems that could be improved using an evolutionary algorithm. Therefore, this paper presents a new method of solving secure curve selection problems using ACO. We improved Complex Multiplication (CM) by combining Evolutionary Cryptography Theory with Weber polynomial solutions. We found that ACO makes full use of valid information generated from factorization and allocates computing resource reasonably. It greatly increases the performance of Weber polynomial solutions. Compared with traditional CM, which can only search one root once time, our new method searches all roots of the polynomial once, and the average time needed to search for one root reduces rapidly. The more roots are searched, the more ECs are obtained.