搜索结果: 1-15 共查到“军事学 Genus 3 Curves”相关记录26条 . 查询时间(0.14 秒)
Hash functions from superspecial genus-2 curves using Richelot isogenies
isogeny-based cryptography genus 2 hyperelliptic curve CGL hash function
2019/3/21
Last year Takashima proposed a version of Charles, Goren and Lauter’s hash function using Richelot isogenies, starting from a genus-2 curve that allows for all subsequent arithmetic to be performed ov...
We construct a genus 2 curve inside the product of 2 elliptic curves. The formula for this construction has appeared in a previous paper. The current paper discusses how this formula arises naturally ...
This paper presents a new projective coordinate system and new explicit
algorithms which together boost the speed of arithmetic in the divisor class group of
genus 2 curves. The proposed formulas ge...
A New Method for Decomposition in the Jacobian of Small Genus Hyperelliptic Curves
Discrete Log Index calculus Hyperelliptic curve
2016/1/6
Decomposing a divisor over a suitable factor basis in the Jacobian of a hyperelliptic
curve is a crucial step in an index calculus algorithm for the discrete log problem in the
Jacobian. For small g...
Counting Points on Genus 2 Curves with Real Multiplication
2 Curves Real Multiplication Counting Points
2011/7/25
We present an accelerated Schoof-type point-counting algorithm for curves of genus 2 equipped with an efficiently computable real multiplication endomorphism.
We present an accelerated Schoof-type point-counting algorithm for curves of genus 2 equipped with an efficiently computable real multiplication endomorphism. Our new algorithm reduces the complexity ...
Counting Points on Genus 2 Curves with Real Multiplication
finite field algorithm prime-order Jacobian
2011/6/9
We present an accelerated Schoof-type point-counting algorithm for curves of genus 2 equipped with an efficiently computable real multiplication endomorphism. Our new algorithm reduces the complexity ...
Computing Discrete Logarithms in the Jacobian of High-Genus Hyperelliptic Curves over Even Characteristic Finite Fields
Computing Discrete Logarithms High-Genus Hyperelliptic Curves Characteristic Finite Fields
2011/3/10
We describe improved versions of index-calculus algorithms for
solving discrete logarithm problems in Jacobians of high-genus hyperelliptic
curves de ned over even characteristic elds. Our rst imp...
Computing Discrete Logarithms in the Jacobian of High-Genus Hyperelliptic Curves over Even Characteristic Finite Fields
foundations / hyperelliptic curves discrete logarithm problem sieving, Weil descent
2012/3/29
We describe improved versions of index-calculus algorithms for solving discrete logarithm problems in Jacobians of high-genus hyperelliptic curves defi ned over even characteristic fields. Our first i...
Generating Pairing-friendly Parameters for the CM Construction of Genus 2 Curves over Prime Fields
hyperelliptic curve cryprography pairing-friendly parameters
2010/10/20
We present two contributions in this paper. First, we give a quantitative analysis of the scarcity of pairing-friendly genus 2 curves, assuming the Riemann Hypothesis. This result is an improvement re...
Computing genus 2 curves from invariants on the Hilbert moduli space
public-key cryptography Hyperelliptic curve cryptography
2010/7/13
We give a new method for generating genus 2 curves over a finite field with a given number of points on the Jacobian of the curve. We define two new invariants for genus 2 curves as values of modular ...
The elliptic curve method (ECM) is one of the best factorization
methods available. It is possible to use hyperelliptic curves instead of elliptic
curves but it is in theory slower. We use special h...
EFFICIENT HALVING FOR GENUS 3 CURVES OVER BINARY FIELDS
Efficient Halving Genus 3 Curves Binary Fields
2009/6/12
In this article, we deal with fast arithmetic in the Picard group
of hyperelliptic curves of genus 3 over binary fields. We investigate both the
optimal performance curves, where h(x) = 1, and the m...
We present an algorithm for constructing cryptographic hyperelliptic
curves of genus 2 and p-rank 1, using the CM method. We
also present an algorithm for constructing such curves that, in addition,...
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 ...