Bilinear cryptography using Lie algebras from p-groups

Abstract

Pairings are particular bilinear maps, and they have been defined based on elliptic curves whichare abelian groups. In cryptography and security problems use these pairings. Mrabet et al. proposedpairings from a tensor product of groups in 2013. Also Mahalanobis et al. proposed bilinear cryptographyusing groups of nilpotency class two in 2017. In this paper, I develop a novel idea of a bilinear cryptosystemusing Lie algebras from p-groups. First the researcher proposes pairing on Lie algebras from elliptic curves,and then pairings that can be constructed on Lie algebras from some of the non-abelian p-groups.

Keywords

• lie algebra
• bilinear map
• p-group