搜索结果: 1-15 共查到“军事学 Genus 2”相关记录67条 . 查询时间(0.062 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 ...
Fast FPGA Implementations of Diffie-Hellman on the Kummer Surface of a Genus-2 Curve
Diffie-Hellman key exchange hyperelliptic curve cryptography Kummer surface
2017/9/1
We present the first hardware implementations of Diffie-Hellman key exchange based on the Kummer surface of Gaudry and Schost's genus-22 curve targeting a 128128-bit security level. We describe a sing...
Reduced Mumford divisors of a genus 2 curve through its jacobian function field
hyperelliptic Mumford arithmetic
2017/2/20
We explore the function field of the jacobian JH of a hyperelliptic curve H of genus 2 in order to find reduced coordinates to represent points of JH and do arithmetic. We show how this relates to the...
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...
This work considers the problem of fast and secure scalar multiplication using curves of genus one defined over a field of prime order. Previous work by Gaudry and Lubicz had suggested the use of the ...
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 ...
Computing theta functions in quasi-linear time in genus 2 and above
number theory hyperelliptic curves theta functions
2016/2/24
We outline an algorithm to compute θ(z, τ ) in genus 2 in quasi-optimal time, borrowing
ideas from the algorithm for theta constants and the one for θ(z, τ ) in genus 1. Our
implementation shows a l...
Time-Memory Trade-offs for Index Calculus in Genus 3
discrete logarithm problem index calculus double large prime
2016/1/9
In this paper, we present a variant of Diem’s Oe(q) index calculus algorithm to attack
the discrete logarithm problem (DLP) in Jacobians of genus 3 non-hyperelliptic curves over a
finite field Fq. W...
Explicit endomorphism of the Jacobian of a hyperelliptic function field of genus 2 using base field operations
public-key cryptography hyperelliptic curves
2016/1/9
We present an efficient endomorphism for the Jacobian of a curve C of genus 2 for divisors having a Non
disjoint support. This extends the work of Costello in [12] who calculated explicit formul?for ...
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...
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...
Genus 2 Hyperelliptic Curve Families with Explicit Jacobian Order Evaluation and Pairing-Friendly Constructions
public-key cryptography / Hyperelliptic Curves Genus 2 Order Computation
2012/6/14
The use of (hyper)elliptic curves in cryptography relies on the ability to compute the Jacobian order of a given curve. Recently, Satoh proposed a probabilistic polynomial time algorithm to test wheth...