Document Type : Original Article
Department of Mathematics, Islamic Azad university, Shahr-e-Qods Branch, Tehran, Iran.
Pairings are particular bilinear maps, and they have been defined based on elliptic curves which
are abelian groups. In cryptography and security problems use these pairings. Mrabet et al. proposed
pairings from a tensor product of groups in 2013. Also Mahalanobis et al. proposed bilinear cryptography
using groups of nilpotency class two in 2017. In this paper, I develop a novel idea of a bilinear cryptosystem
using 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.