Post-Quantum Cryptography Using Hyper-Complex Numbers

Abstract

Encrypted communications are performed using symmetric ciphers, which require asymmetric cryptography for safe initiation. Asymmetric cryptography was seriously weakened after the presentation of Shor’s algorithm (1997) and others for quantum computers. New algorithms are generalized as post quantum cryptography. Asymmetric cryptography based on noncommutative algebra is a growing trend arising as a solid choice that strengthens these protocols. Hyper-complex numbers generated by the Cayley-Dickson construction forms non-commutative algebras. This paper focus on the use of these numbers in post-quantum cryptography.