Skew-Frobenius Maps on Hyperelliptic Curves

Kozaki, Shunji; Matsuo, Kazuto; Shimbara, Yasutomo

doi:10.1093/ietfec/e91-a.7.1839

Cited by 4 publications

(5 citation statements)

References 11 publications

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“…Afficionados will have noticed that Theorem 1 holds (with minor modifications to the second part of property (2)) for arbitrary abelian varieties. This has been noted by Kozaki, Matsuo and Shimbara [32], but they do not use it for the GLV method. We now present an analogue of Theorem 2 for hyperelliptic curves.…”

Section: Hyperelliptic Curvesmentioning

confidence: 98%

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Endomorphisms for Faster Elliptic Curve Cryptography on a Large Class of Curves

2010

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Efficiently computable homomorphisms allow elliptic curve point multiplication to be accelerated using the Gallant-Lambert-Vanstone (GLV) method. Iijima, Matsuo, Chao and Tsujii gave such homomorphisms for a large class of elliptic curves by working over F p 2 . We extend their results and demonstrate that they can be applied to the GLV method.In general we expect our method to require about 0.75 the time of previous best methods (except for subfield curves, for which Frobenius expansions can be used). We give detailed implementation results which show that the method runs in between 0.70 and 0.83 the time of the previous best methods for elliptic curve point multiplication on general curves.

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Section: Hyperelliptic Curvesmentioning

confidence: 98%

“…The proof generalises immediately to hyperelliptic curves (see Sect. 5 or Kozaki, Matsuo and Shimbara [32]).…”

Section: For Allmentioning

confidence: 99%

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Endomorphisms for Faster Elliptic Curve Cryptography on a Large Class of Curves

2010

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“…The proof generalises immediately to hyperelliptic curves (see the full version of this paper or [22]).…”

Section: The Homomorphismmentioning

confidence: 74%

Endomorphisms for Faster Elliptic Curve Cryptography on a Large Class of Curves

Galbraith

Lin

Scott

2009

Lecture Notes in Computer Science

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Efficiently computable homomorphisms allow elliptic curve point multiplication to be accelerated using the Gallant-Lambert-Vanstone (GLV) method. We extend results of Iijima, Matsuo, Chao and Tsujii which give such homomorphisms for a large class of elliptic curves by working over F p 2 and demonstrate that these results can be applied to the GLV method. In general we expect our method to require about 0.75 the time of previous best methods (except for subfield curves, for which Frobenius expansions can be used). We give detailed implementation results which show that the method runs in between 0.70 and 0.84 the time of the previous best methods for elliptic curve point multiplication on general curves.

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“…where c ∈ F p 2 is a quadratic non-residue over [26]. As in [11] we first generate a degenerate divisor class…”

Section: Using Degenerate Divisors and Denominator Eliminationmentioning

confidence: 99%

Speeding Up Pairing Computations on Genus 2 Hyperelliptic Curves with Efficiently Computable Automorphisms

Fan

Gong

Jao

Pairing-Based Cryptography – Pairing 2008

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Abstract. Pairings on the Jacobians of (hyper-)elliptic curves have received considerable attention not only as a tool to attack curve based cryptosystems but also as a building block for constructing cryptographic schemes with new and novel properties. Motivated by the work of Scott [34], we investigate how to use efficiently computable automorphisms to speed up pairing computations on two families of non-supersingular genus 2 hyperelliptic curves over prime fields. Our findings lead to new variants of Miller's algorithm in which the length of the main loop can be up to 4 times shorter than that of the original Miller's algorithm in the best case. We also implement the calculation of the Tate pairing on both a supersingular and a non-supersingular genus 2 curve with the same embedding degree of k = 4. Combining the new algorithm with known optimization techniques, we show that pairing computations on non-supersingular genus 2 curves over primes fields use up to 56.2% fewer field operations and run about 10% faster than supersingular genus 2 curves for the same security level.

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Skew-Frobenius Maps on Hyperelliptic Curves

Cited by 4 publications

References 11 publications

Endomorphisms for Faster Elliptic Curve Cryptography on a Large Class of Curves

Endomorphisms for Faster Elliptic Curve Cryptography on a Large Class of Curves

Endomorphisms for Faster Elliptic Curve Cryptography on a Large Class of Curves

Speeding Up Pairing Computations on Genus 2 Hyperelliptic Curves with Efficiently Computable Automorphisms

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