搜索结果: 1-15 共查到“Endomorphism”相关记录17条 . 查询时间(0.062 秒)
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Fields with a generic multiplicative endomorphism
通用乘法 自同态 域
2023/5/4
The theory of fields expanded by a unary function symbol for a multiplicative endomorphism admits a model-companion, we denote it ACFH. It is a new example of an NSOP1 theory which is not simple. I wi...
Supersingular isogeny graphs and endomorphism rings: reductions and solutions
post-quantum cryptography isogeny-based cryptography cryptanalysis
2018/4/26
In this paper, we study several related computational problems for supersingular elliptic curves, their isogeny graphs, and their endomorphism rings. We prove reductions between the problem of path fi...
On the Hardness of Computing Endomorphism Rings of Supersingular Elliptic Curves
Supersingular isogeny based cryptography number theory
2017/10/10
Cryptosystems based on supersingular isogenies have been proposed recently for use in post-quantum cryptography. Three problems have emerged related to their hardness: computing an isogeny between two...
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 ...
The Q-curve Construction for Endomorphism-Accelerated Elliptic Curves
Elliptic curve cryptography endomorphism exponentiation
2016/1/7
We give a detailed account of the use of Q-curve reductions
to construct elliptic curves over Fp2 with efficiently computable endomorphisms,
which can be used to accelerate elliptic curve-based cryp...
VLSI Implementation of Double-Base Scalar Multiplication on a Twisted Edwards Curve with an Efficiently Computable Endomorphism
Multiple-precision arithmetic Pseudo-Mersenne prime
2015/12/30
The verification of an ECDSA signature requires a double-base scalar multiplication, an operation of the form k⋅G+l⋅Q where G is a generator of a large elliptic curve group of prime order ...
Pairing-based algorithms for jacobians of genus 2 curves with maximal endomorphism ring
Pairing-based algorithms jacobians of genus 2 curves maximal endomorphism ring Number Theory
2012/4/17
Using Galois cohomology, Schmoyer characterizes cryptographic non-trivial self-pairings of the $\ell$-Tate pairing in terms of the action of the Frobenius on the $\ell$-torsion of the Jacobian of a ge...
Computing endomorphism rings of elliptic curves under the GRH
endomorphism elliptic the GRH
2011/2/23
We design a probabilistic algorithm for computing endomorphism rings of ordinary elliptic curves defined over finite fields that we prove has a subexponential runtime in the size of the base field, as...
Computing endomorphism rings of elliptic curves under the GRH
foundations / endomorphism rings GRH
2012/3/30
We design a probabilistic algorithm for computing endomorphism rings of ordinary elliptic curves defined over finite fields that we prove has a subexponential runtime in the size of the base field, as...
Fast Endomorphism for any Genus 2 Hyperelliptic Curve over a Finite Field of Even Characteristic
Hyperelliptic cryptosystem Jacobian efficiently computable endomorphism
2010/11/26
In EUROCRYPT 2009, Galbraith, Lin and Scott constructed an efficiently computable endomorphism for a large family of elliptic curves defined over finite fields of large characteristic. They demonstrat...
We prove that the mass endomorphism associated to the Dirac operator on a Riemannian manifold is non-zero for generic Riemannian metrics.The proof involves a study of the mass endomorphism under surge...
The Bergman property for endomorphism monoids of some Fraïssé limits
Bergman property for endomorphism monoids Fraï ssé limits
2010/12/3
Based on an idea of Y. P´eresse and some results ofMaltcev, Mitchell and Ruˇskuc,we present sufficient conditions under which the endomorphism monoid of an ultrahomogeneous first-order structure...
A universality result for endomorphism monoids of some ultrahomogeneous structures
endomorphism monoid Fra¨ı ss´ e limit pushout
2010/12/7
We devise a fairly general sufficient condition ensuring that the endomorphism monoid of a countably infinite ultrahomogeneous structure (i.e. a Fra¨ıss´e limit) embeds all countable semigr...
Pairing computation on curves with efficiently computable endomorphism and small embedding degree
elliptic curves pairings isogenies
2010/7/14
Scott uses an efficiently computable isomorphism in order to optimize pairing computation on a particular class of curves with embedding degree 2. He pointed out that pairing implementation becomes th...
COMPUTING THE ENDOMORPHISM RING OF AN ORDINARY ELLIPTIC CURVE OVER A FINITE FIELD
endomorphism ring ordinary elliptic curve finite field
2009/6/12
We present two algorithms to compute the endomorphism ring
of an ordinary elliptic curve E defined over a finite field Fq. Under suitable
heuristic assumptions, both have subexponential complexity. ...