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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., Kawazoe M., Takahashi T.
Suitable curves for genus-4 HCC over prime fields: point counting formulae for hyperelliptic curves of type.....
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Analysis of Algorithms for Computing in Jacobian of a Picard Curve
... for Hyperelliptic Curves of Genus 3 //
ANTS XIII. 2019. P. 425—442.
7. Thakur S. Abelian varieties in pairing-based cryptography. 2019. aXiv:1812. 11479v2 [math.NT].
Aleshnikov S. I.,Tkachenko S. N., Stolyarchuk S. V., Shpilevoy A. A.
divisor, Jacobian of a curve, Picard curve, reduction of a divisor
5-12
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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, therefore it is more favorable ...
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About pairing on abelian varieties p-rank one and their cryptographic applications
Described and analyzed in terms of computational efficiency different types of pairings on hyperelliptic curves, especially on curves of genus 2 and p-rank one for the cryptographic applications.... ... Transactions on Information Theory. 2006. Vol. 52. P. 4595—4602.
9. Koblitz N., Menezes A. Pairing-based cryptography at high seccurity levels //Cryptography and Coding. LNCS... ... 2008/274, 2008
Aleshnikov S., Aleshnikova M.
algebraic curves, hyperelliptic curves, Jacobians of curves, abelian varieties, p-rank, embedding degree, bilinear pairings...
