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Barreto, Lynn and Scott elliptic curves of embedding degree 12 denoted BLS12 have been proven to present fastest results on the implementation of pairings at the 192-bit security level [1]. The computation of pairings in general involves the execution of the Miller algorithm and the final exponentiation. In this paper, we improve the complexity of these two(More)
In this paper, we present an Edwards model for elliptic curves which is dened over any perfect eld and in particular over nite elds. This Edwards model is birationally equivalent to the well known Edwards model over non-binary elds and is ordinary over binary elds. For this, we use theta functions of level four to obtain an intermediate model that we call a(More)
This paper proposes the computation of the Tate pairing, Ate pairing and its variations on the special Jacobi quartic elliptic curve Y 2 = dX 4 + Z 4. We improve the doubling and addition steps in Miller's algorithm to compute the Tate pairing. We use the birational equivalence between Jacobi quartic curves and Weierstrass curves, together with a specific(More)
This paper proposes the computation of the Tate pairing, Ate pairing and its variations on the special Jacobi quartic elliptic curve Y 2 D dX 4 C Z 4. We improve the doubling and addition steps in Miller's algorithm to compute the Tate pairing. We use the birational equivalence between Jacobi quartic curves and Weierstrass curves, together with a specific(More)
Since the advent of pairing based cryptography, much attention has been given to efficient computation of pairings on elliptic curves with even embedding degrees. The few works that exist in the case of odd embedding degrees require some improvements. This paper considers the computation of optimal ate pairings on elliptic curves of embedding degrees k = 9,(More)