
Overview of effective point counting algorithms for Jacobian of hyperelliptic curve over finite field
...
Counting points for hyperelliptic curves of type.....
// Ibid. 2002.
4.
Haloui S.
The minimum and maximum number of rational points on jacobian surfaces over finite fields. URL: http://arxiv. org/abs/1002.3683.2010.
5.
Ravnshoj C. R.
Generators of Jacobians of genus two curves // Cryptology ePrint Archive. 2008.
6.
Ravnshoj C. R.
Noncyclic subgroups of Jacobians of genus two curves // Ibid.
7.
Ravnshoj C. R.
Noncyclic subgroups of Jacobians of genus two curves with complex multiplication // Ibid.
8.
Dechene ...

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 pairingbased 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
512

An efficient implementation of an exponential pointcounting algorithm on Jacobians of genus 2 hyperelliptic curves
Computing the order of Jacobian of a hyperelliptic curve is a common numbertheoretical problem that has lots of applications in modern cryptography. Namely, Jacobians are applicable to constructions of DLPbased cryptosystems, as well as constructions of verifiable delay functions (VDF’s), since ...

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 ...

About pairing on abelian varieties prank 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, prank, embedding degree, bilinear pairings, TateLichtenbaum pairing, Ate pairing, twisted Ate pairing, Weil pairing
155161