Elliptic divisibility sequences over the Edwards model of elliptic curves

Abstract

In this work, we use division polynomials on Edwards elliptic curves to construct elliptic nets of rank one called elliptic divisibility sequence on this curve. Introduced by Morgan Ward, elliptic divisibility sequence on elliptic curve are used for solving the elliptic curve discrete logarithm problem (ECDLP). Moved on rank 2, Elliptic Nets algorithm via elliptic nets associated to Weierstrass elliptic curves are useful for the computation of bilinear maps (called pairings) defined on the groups of points of elliptic curves and very useful to the construction of cryptographic protocols.