Universal quantum computers are far from achieving practical applications. The D-Wave quantum computer is initially designed for combinatorial optimizations. Therefore, exploring the potential applications of the D-Wave device in the field of cryptography is of great importance. First, although we optimize the general quantum Hamiltonian on the basis of the structure of the multiplication table (factor up to 1 005 973), this study attempts to explore the simplification of Hamiltonian derived from the binary structure of the integers to be factored. A simple factorization on 143 with four qubits is provided to verify the potential of further advancing the integer-factoring ability of the D-Wave device. Second, by using the quantum computing cryptography based on the D-Wave 2000Q system, this research further constructs a simple version of quantum-classical computing architecture and a Quantum-Inspired Simulated Annealing (QISA) framework. Good functions and a high-performance platform are introduced, and additional balanced Boolean functions with high nonlinearity and optimal algebraic immunity can be found. Further comparison between QISA and Quantum Annealing (QA) on six-variable bent functions not only shows the potential speedup of QA, but also suggests the potential of architecture to be a scalable way of D-Wave annealer toward a practical cryptography design.

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.