
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 genus4 HCC over prime fields: point counting formulae for hyperelliptic curves of type.....
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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 ...

About pairing on abelian varieties prank one and their cryptographic applications
... Higherdimensional varieties 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
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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 ...

Analysis of Algorithms for Computing in Jacobian of a Picard Curve
... Curves // Public Key Cryptography — PKC 2004. 2004. P. 55—68.
4. Oyono R. Arithmetik nichthyperelliptischer Kurven des Geschlechts 3 und ihre Anwendung in der Kryptographie : PhD Diss. Univ. DuisburgEssen, 2005.
5. Handbook of Elliptic and Hyperelliptic Curve Cryptography / ed. H. Cohen, G. Frey. Chapman & Hall, 2006
6. Sutherland A. V. Fast Jacobian Arithmetic for Hyperelliptic Curves of Genus 3 //
ANTS XIII. 2019. P. 425—442.
7. Thakur S. Abelian varieties in pairingbased cryptography. 2019. aXiv:1812....

About one algorithm of calculation of inverses in finite fields
... qn F developed, where q is power of the prime number. They are received by generalisation of algorithm of Wong for a field F2n with use of the main idea for fast algorithm of calculation of inverses in the field 2 F n .
1. Handbook of elliptic and hyperelliptic curve cryptography / Scientific editors, Henry Cohen & Gerhard Frey. Chapman & Hall/CRC, 2006.
2. Handbook of finite Fields / Scientific editors, Gary L. Mullen, Daniel Panario. CRC Press, Taylor & Francis Group, 2013.
3. Itoh T., Tsujii S. A fast algorithm ...