Improving a Compact Cipher Based on Non Commutative Rings of Quaternion

Abstract

Asymmetric cryptography is required to start encrypted communications. Most protocols are based on modular operations over integer's rings. Many are vulnerable to sub-exponential attacks or by using a quantum computer. Cryptography based on non-commutative algebra is a growing trend arising as a solid choice that strengthens these protocols. In particular, Hecht (2009) has presented a key exchange model based on the Diffie-Hellman protocol using matrices of order four with elements in Z256, that provides 128-bits keys also to devices with low computing power. Quaternions are four-component's vectors. These also form non-commutative rings structures, with compact notation and lower run-times in many comparable operations. Kamlofsky et al (2015) presented a model using quaternions with elements in Z256. To provide a 128-bit key is required 4 rounds of 32-bits. However, a gain of 42% was obtained. This paper presents an improvement of this cipher that reduces even more the run-times.