Ant Colony Optimization （AGO） 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.
Wireless sensor networks are a favorite target of Byzantine malicious attackers because of their limited energy, low calculation capability, and dynamic topology, and other important characteristics. The Byzantine Generals Problem is one of the classical problems in the area of fault tolerance, and has wide application, especially in distributed databases and systems. There is a lot of research in agreement and replication techniques that tolerate Byzantine faults. However, most of this work is not suited to large-scale wireless sensor networks, due to its high computational complexity. By introducing Fast ECDSA(Elliptic Curve Digital Signature Algorithm), which can resist timing and energy attacks, and reduce the proportion of verifying signature algorithm to generating signature algorithm to 1.2 times, we propose a new Byzantine fault-tolerant routing algorithm for large-scale wireless sensor networks with double-level hierarchical architecture. In different levels, the algorithm runs different BFT protocols.Theory and simulation results have proved that this algorithm has high security and the number of communication rounds between clusters is reduced by 1/3, which balances the network load. At the same time, the application of Fast ECDSA improves the security level of the network without burdening it.
