Elaheh Khamseh - 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 ۲۰۱۳. Also Mahalanobis et al. proposed bilinear cryptography using groups of nilpotency class two in ۲۰۱۷. 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.

Lie algebra, Bilinear map, p-group