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Overview of effective point counting algorithms for Jacobian of hyperelliptic curve over finite field
Various algorithms for finding of the order of Jacobian, their range of use and efficiency are considered.
1.
Colm
O
hEigeartaigh
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A comparison of point counting methods for hyperelliptic curves over prime fields and fields of characteristic 2 // Cryptology ePrint Archive. 2004.
2.
Haneda M....
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Analysis of Algorithms for Computing in Jacobian of a Picard Curve
In this article a representation of the elements of the Jacobian of a Picard curve is considered, which allows us to construct an algorithm for the reduction of divisors with complexity O(deg(D)). Addition of divisors can be performed using the reduction algorithm.
1. Barreirol E. R., Sarlabous J. ...
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An efficient implementation of an exponential point-counting algorithm on Jacobians of genus 2 hyperelliptic curves
Computing the order of Jacobian of a hyperelliptic curve is a common number-theoretical problem that has lots of applications in modern cryptography. Namely, Jacobians are applicable to constructions of DLP-based cryptosystems, as well as constructions of verifiable delay ...
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Acceleration of Computations in Jacobian Hyperelliptic Curve
In article is stated the method of acceleration of procedures of addition and doubling points Jacobian of a hyperelliptic curve in affine and projective coordinates. Corresponding modified Miller algorithms are developed. In affine coordinates an expense for group operation of doubling there are more than expenses for group operation of addition,...
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About pairing on abelian varieties p-rank one and their cryptographic applications
... over finite fields. Summer school in Göttingen. 2007.
13. Zhang F. Twisted Ate pairing on hyperelliptic curves and applications.Cryptology ePrint Archive, Report 2008/274, 2008
Aleshnikov S., Aleshnikova M.
algebraic curves, hyperelliptic curves, Jacobians of curves, abelian varieties, p-rank, embedding degree, bilinear pairings, Tate-Lichtenbaum pairing, Ate pairing, twisted Ate pairing, Weil pairing
155-161
