An Overview of Gaussian Integer Approaches for Classical and Post-Quantum Asymmetric Cryptography

Abstract

Asymmetric cryptography or public key cryptography is a popular measure employed to keep information secure.  For a long time, it was thought to be very difficult to attack; hence, highly secure.  However, the advent of quantum-based attacking algorithms drastically reduces the difficulties of attacking. This leads to the development of the post-quantum cryptography.  Classical and post-quantum asymmetric cryptography systems are based on one-dimension integer. The utilization of Gaussian integer, a two-dimension number system, to enhance the complexity in order to resist the attacks is therefore an interesting topic.  In this paper, we have surveyed and summarized the various approaches in applying Gaussian integer with classical and post-quantum cryptography.