An improved ellipticnet algorithm for tate pairing on weierstrass? curves, faster point arithmetic and pairing on selmer curves and a note on double scalar multiplication

Abstract

Elliptic Curve point arithmetic is at the heart of all cryptographic algorithms utilizing Elliptic Curves. Pairing based cryptography has been an area of intense research recently. In this context, we (i) present an improved version of Stange’s Elliptic Net Algorithm to compute the Tate Pairing, (ii) present an improved algorithm for Point arithmetic and Pairing on Selmer curves and (iii) show that Co-Z based precomputation algorithms for elliptic curve double scalar multiplication are not necessarily faster than Conjugate-addition based precomputation algorithms as claimed in the literature Show more