Tate Pairing Computation on Jacobi’s Elliptic Curves

Duquesne, Sylvain; Fouotsa, Emmanuel

doi:10.1007/978-3-642-36334-4_17

Cited by 7 publications

(3 citation statements)

References 20 publications

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“…12-BS01-0010-01 "PEACE", INS 2012 SIMPATIC project and LIRIMA 2013 MACISA project. This work is an improved and extended version of [10]. group law.…”

Section: Introductionmentioning

confidence: 97%

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Efficient computation of pairings on Jacobi quartic elliptic curves

Duquesne

Mrabet

Fouotsa

2014

Journal of Mathematical Cryptology

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International audienceThis 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 point representation to obtain the best result to date among curves with quartic twists. For the doubling and addition steps in Miller's algorithm for the computation of the Tate pairing, we obtain a theoretical gain up to 27% and 39%, depending on the embedding degree and the extension field arithmetic, with respect to Weierstrass curves and previous results on Jacobi quartic curves. Furthermore and for the first time, we compute and implement Ate, twisted Ate and optimal pairings on the Jacobi quartic curves. Our results are up to 27% more efficient compared to the case of Weierstrass curves with quartic twists

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“…12-BS01-0010-01 "PEACE", INS 2012 SIMPATIC project and LIRIMA 2013 MACISA project. This work is an improved and extended version of [10]. group law.…”

Section: Introductionmentioning

confidence: 97%

“…As a second contribution of this work, we extend the results on the special Jacobi quartic in [10] to the computation of the Ate pairing and its variations. We show that among known curves with quartic twists, the Jacobi model Y 2 D dX 4 C Z 4 offers the best performances for all these different pairings.…”

Section: Introductionmentioning

confidence: 98%

Efficient computation of pairings on Jacobi quartic elliptic curves

Duquesne

Mrabet

Fouotsa

2014

Journal of Mathematical Cryptology

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“…Originally defined over elliptic curves in Weierstrass model [19], pairings have been computed in other models of elliptic curves (for example Edwards [13], Huff [14], Jacobi [5]). They have also been studied in different systems of coordinates such as affine [16], Jacobian, projective, Chudnovsky [3] or in original representation of finite fields RNS [2].…”

Section: Introductionmentioning

confidence: 99%

Side Channel Attacks against Pairing over Theta Functions

Mrabet¹

2013

Algebraic Informatics

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Abstract. In [17], Lubicz and Robert generalized the Tate pairing over any abelian variety and more precisely over Theta functions. The security of the new algorithms is an important issue for the use of practical cryptography. Side channel attacks are powerful attacks, using the leakage of information to reveal sensitive data. The pairings over elliptic curves were sensitive to side channel attacks. In this article, we study the weaknesses of the Tate pairing over Theta functions when submitted to side channel attacks.

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