搜索结果: 1-15 共查到“军事学 Genus 2”相关记录67条 . 查询时间(0.109 秒)
Hash functions from superspecial genus-2 curves using Richelot isogenies
isogeny-based cryptography genus 2 hyperelliptic curve CGL hash function
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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...
Genus 2 curves with given split Jacobian
given split Jacobian elliptic Kummer surfaces
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2018/11/29
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
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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
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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
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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...
Kummer for Genus One over Prime Order Fields
Kummer Line Field Arithmetic SIMD
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2016/12/8
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 ...
Constructing genus 3 hyperelliptic Jacobians with CM
CM explicit method
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2016/3/28
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
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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
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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
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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 ...
Jacobian Coordinates on Genus 2 Curves
Genus 2 hyperelliptic curves explicit formulas
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2016/1/9
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
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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
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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
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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
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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...