Results: **4**

#### 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 p-rank one and their cryptographic applications

... Higher-dimensional 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, p-rank, embedding degree, bilinear pairings, Tate-Lichtenbaum pairing, Ate pairing, twisted Ate pairing, Weil pairing
155-161

#### 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
.
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.....
...

#### 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 functions (VDF’s), since ...