搜索结果: 1-15 共查到“discrete logarithm”相关记录50条 . 查询时间(0.059 秒)
A New Method for Geometric Interpretation of Elliptic Curve Discrete Logarithm Problem
Intersection of Curves Grobner Basis Vanishing Ideals
2019/9/19
In this paper, we intend to study the geometric meaning of the discrete logarithm problem defined over an Elliptic Curve. The key idea is to reduce the Elliptic Curve Discrete Logarithm Problem (EC-DL...
Algorithmic aspects of elliptic bases in finite field discrete logarithm algorithms
discrete logarithm problem finite fields elliptic representation
2019/7/10
Elliptic bases, introduced by Couveignes and Lercier in 2009, give an elegant way of representing finite field extensions. A natural question which seems to have been considered independently by sever...
A Simplified Approach to Rigorous Degree 2 Elimination in Discrete Logarithm Algorithms
Discrete Logarithm Algorithms discrete logarithm problem
2018/5/14
we revisit the ZigZag strategy of Granger, Kleinjung and Zumbrägel. In particular, we provide a new algorithm and proof for the so-called degree 2 elimination step. This allows us to provide a st...
Polynomial Time Bounded Distance Decoding near Minkowski’s Bound in Discrete Logarithm Lattices
lattice techniques Bounded Distance Decoding Minkowski's bound
2018/2/9
We propose a concrete family of dense lattices of arbitrary dimension n in which the lattice Bounded Distance Decoding (BDD) problem can be solved in deterministic polynomial time. This construction i...
A Las Vegas algorithm to solve the elliptic curve discrete logarithm problem
public-key cryptography algorithm depends
2018/2/8
In this paper, we describe a new Las Vegas algorithm to solve the elliptic curve discrete logarithm problem. The algorithm depends on a property of the group of rational points of an elliptic curve an...
The Discrete-Logarithm Problem with Preprocessing
discrete logarithm problem generic-group model
2017/11/21
This paper studies discrete-log algorithms that use preprocessing. In our model, an adversary may use a very large amount of precomputation to produce an "advice" string about a specific group (e.g., ...
Threshold Kleptographic Attacks on Discrete Logarithm Based Signatures
kleptography threshold cryptography information hidding
2017/9/28
In an ℓℓ out of nn threshold scheme, ℓℓ out of nn members must cooperate to recover a secret. A kleptographic attack is a backdoor which can be implemented in an algorithm and ...
A Quantum “Magic Box'' for the Discrete Logarithm Problem
discrete logarithm problem elliptic curve cryptosystem quantum cryptanalysis
2017/8/10
In their foundational paper on pseudorandom bit generation, Blum and Micali showed that the discrete logarithm problem could be solved efficiently given a ``magic box'' oracle that computes the most s...
On Improving Integer Factorization and Discrete Logarithm Computation using Partial Triangulation
RSA factoring discrete logarithm problem
2017/8/8
The number field sieve is the best-known algorithm for factoring integers and solving the discrete logarithm problem in prime fields. In this paper, we present some new improvements to various steps o...
On the discrete logarithm problem for prime-field elliptic curves
elliptic curve discrete logarithm problem prime field
2017/6/27
In recent years several papers have appeared investigating the classical discrete logarithm problem for elliptic curves by means of the multivariate polynomial approach based on the celebrated summati...
FHPKE based on multivariate discrete logarithm problem
fully homomorphic public-key encryption multivariate discrete logarithm problem octonion ring
2017/5/23
Previously I proposed fully homomorphic public-key encryption (FHPKE) based on discrete logarithm problem which is vulnerable to quantum computer attacks. In this paper I propose FHPKE based on multiv...
The discrete logarithm problem over prime fields: the safe prime case. The Smart attack, non-canonical lifts and logarithmic derivatives
non-canonical lifts logarithmic derivatives
2017/3/6
The discrete logarithm problem over prime fields: the safe prime case. The Smart attack, non-canonical lifts and logarithmic derivatives.
Horizontal isogeny graphs of ordinary abelian varieties and the discrete logarithm problem
Isogeny expander graph hyperelliptic curve cryptography
2017/2/20
Fix an ordinary abelian variety defined over a finite field. The ideal class group of its endomorphism ring acts freely on the set of isogenous varieties with same endomorphism ring, by complex multip...
This paper reports on the number field sieve computation of a 768-bit prime field discrete logarithm, describes the different parameter optimizations and resulting algorithmic changes compared to the ...
The Discrete Logarithm Problem over Prime Fields can be transformed to a Linear Multivariable Chinese Remainder Theorem
Discrete logarithm Hensel lift Multivaraible Chinese Remainder theorem
2016/12/10
The Discrete Logarithm Problem over Prime Fields can be transformed to a Linear Multivariable Chinese Remainder Theorem.