Results: **5**

#### 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. ...

#### 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....

#### 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,...

#### 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 ...

#### 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