搜索结果: 1-15 共查到“军事学 Jacobians”相关记录21条 . 查询时间(0.123 秒)
Fast, uniform scalar multiplication for genus 2 Jacobians with fast Kummers
Hyperelliptic curve cryptography Kummer surface genus 2
2016/12/10
We give one- and two-dimensional scalar multiplication algorithms for Jacobians of genus~2 curves that operate by projecting to Kummer surfaces, where we can exploit faster and more uniform pseudomult...
Given a CM sextic field K, we give an explicit method for finding and constructing all genus 3 hyperelliptic curves whose Jacobians have complex multiplication by the maximal order of this field. Our ...
Fast, uniform, and compact scalar multiplication for elliptic curves and genus 2 Jacobians with applications to signature schemes
elliptic curve cryptography hyperelliptic curve cryptography scalar multiplication
2015/12/22
We give a general framework for uniform, constant-time oneand
two-dimensional scalar multiplication algorithms for elliptic curves
and Jacobians of genus 2 curves that operate by projecting to the x...
Easy scalar decompositions for efficient scalar multiplication on elliptic curves and genus 2 Jacobians
Elliptic curve cryptography number theory
2014/3/6
The first step in elliptic curve scalar multiplication algorithms based on scalar decompositions using efficient endomorphisms---including Gallant--Lambert--Vanstone (GLV) and Galbraith--Lin--Scott (G...
Group Law Computations on Jacobians of Hyperelliptic Curves
Hyperelliptic curves group law Jacobian arithmetic genus 2
2012/3/28
We derive an explicit method of computing the composition step in Cantor's algorithm for group operations on Jacobians of hyperelliptic curves. Our technique is inspired by the geometric description o...
Geometric Group Law Computations on Jacobians of Hyperelliptic Curves
foundations Hyperelliptic curves group law Jacobian arithmetic genus 2
2011/7/25
We derive a new method of computing the composition step in Cantor's algorithm for group operations on Jacobians of hyperelliptic curves.
Computing $(\ell,\ell)$-isogenies in polynomial time on Jacobians of genus~$2$ curves
public-key cryptography / elliptic curve cryptosystem
2012/3/29
In this paper, we compute $\ell$-isogenies between abelian varieties over a field of characteristic different from $2$ in polynomial time in $\ell$, when $\ell$ is an odd prime which is coprime to the...
GENERATORS OF JACOBIANS OF GENUS TWO CURVES
Jacobians genus two curves Frobenius endomorphism
2009/6/2
We prove that in most cases relevant to cryptography, the Frobenius
endomorphism on the Jacobian of a genus two curve is represented
by a diagonal matrix with respect to an appropriate basis of the ...
NON-CYCLIC SUBGROUPS OF JACOBIANS OF GENUS TWO CURVES
Jacobians hyperelliptic genus two curves pairings
2009/6/2
Let E be an elliptic curve de ned over a nite eld. Balasubramanian
and Koblitz have proved that if the `th roots of unity ` is not contained
in the ground eld, then a eld extension of the groun...
Pairing-friendly Hyperelliptic Curves with Ordinary Jacobians of Type y2 = x5 + ax
pairing-based cryptography hyperelliptic curves
2009/6/2
An explicit construction of pairing-friendly hyperelliptic curves
with ordinary Jacobians was firstly given by D. Freeman. In this paper,
we give other explicit constructions of pairing-friendly hyp...
NON-CYCLIC SUBGROUPS OF JACOBIANS OF GENUS TWO CURVES WITH COMPLEX MULTIPLICATION
Jacobians hyperelliptic curves embedding degree complex multiplication
2009/6/2
Let E be an elliptic curve de ned over a nite eld. Balasubramanian
and Koblitz have proved that if the `th roots of unity ` is not contained
in the ground eld, then a eld extension of the groun...
FAST ARITHMETIC ON JACOBIANS OF PICARD CURVES
Jacobians Picard curves algebraic curves cryptography
2009/4/8
In this paper we present a fast addition algorithm in the Jacobian of a Picard curve over a finite field Fq of characteristic different from 3. This algorithm has a nice geometric interpretation, comp...
Point Compression on Jacobians of Hyperelliptic Curves over Fq.
Point Compression Jacobians Hyperelliptic Curves Fq.
2009/3/20
Hyperelliptic curve cryptography recently received a lot of attention,
especially for constrained environments. Since there space is critical, compression
techniques are interesting. In this note we...
D´ech`ene has proposed generalized Jacobians as a source of groups for public-key
cryptosystems based on the hardness of the Discrete Logarithm Problem (DLP). Her specific
proposal gives rise ...
Arithmetic of Generalized Jacobians
Public-key cryptography Discrete logarithm problem generalized Jacobians
2008/10/23
This paper aims at introducing generalized Jacobians as a
new candidate for discrete logarithm (DL) based cryptography. The mo-
tivation for this work came from the observation that several practica...