Efficient algorithms for Koblitz curves over fields of characteristic three
نویسندگان
چکیده
منابع مشابه
Efficient Arithmetic on Elliptic Curves over Fields of Characteristic Three
This paper presents new explicit formulae for the point doubling, tripling and addition for ordinary Weierstraß elliptic curves with a point of order 3 and their equivalent Hessian curves over finite fields of characteristic three. The cost of basic point operations is lower than that of all previously proposed ones. The new doubling, mixed addition and tripling formulae in projective coordinat...
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We consider digital expansions of scalars for supersingular Koblitz curves in characteristic three. These are positional representations of integers to the base of τ , where τ is a zero of the characteristic polynomial T 2 ± 3T + 3 of a Frobenius endomorphism. They are then applied to the improvement of scalar multiplication on the Koblitz curves. A simple connection between τ -adic expansions ...
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Let C be a supersingular genus-2 curve over an algebraically closed field of characteristic 3. We show that if C is not isomorphic to the curve y = x + 1 then up to isomorphism there are exactly 20 degree-3 maps φ from C to the elliptic curve E with j-invariant 0. We study the coarse moduli space of triples (C, E, φ), paying particular attention to questions of rationality. The results we obtai...
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In this work, we retake an old idea that Koblitz presented in his landmark paper [21], where he suggested the possibility of defining anomalous elliptic curves over the base field F4. We present a careful implementation of the base and quadratic field arithmetic required for computing the scalar multiplication operation in such curves. In order to achieve a fast reduction procedure, we adopted ...
متن کاملEfficient Arithmetic on Koblitz Curves
It has become increasingly common to implement discrete-logarithm based public-key protocols on elliptic curves over finite fields. The basic operation is scalar multiplication: taking a given integer multiple of a given point on the curve. The cost of the protocols depends on that of the elliptic scalar multiplication operation. Koblitz introduced a family of curves which admit especially fast...
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ژورنال
عنوان ژورنال: Journal of Discrete Algorithms
سال: 2005
ISSN: 1570-8667
DOI: 10.1016/j.jda.2004.04.011