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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)

Many pairing-based protocols require the computation of the product and/or of a quotient of n pairings where n > 1 is a natural integer. Zhang et al.[1] recently showed that the Kachisa-Schafer and Scott family of elliptic curves with embedding degree 16 denoted KSS16 at the 192-bit security level is suitable for such protocols comparatively to the… (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)

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)

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