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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...
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...
Recent progress on the elliptic curve discrete logarithm problem
Recent progress the elliptic curve discrete logarithm problem
2015/12/22
We survey recent work on the elliptic curve discrete logarithm problem.
In particular we review index calculus algorithms using summation polynomials, and
claims about their complexity.
Solving the Elliptic Curve Discrete Logarithm Problem Using Semaev Polynomials, Weil Descent and Gr鯾ner Basis Methods -- an Experimental Study
public-key cryptography Elliptic curve discrete logarithm problem
2014/3/8
At ASIACRYPT 2012, Petit and Quisquater suggested that there may be a subexponential-time index-calculus type algorithm for the Elliptic Curve Discrete Logarithm Problem (ECDLP) in characteristic two ...
Elliptic divisibility sequences and the elliptic curve discrete logarithm problem
elliptic divisibility sequences elliptic curve cryptography elliptic curve discrete logarithm problem
2009/6/9
We use properties of the division polynomials of an elliptic
curve E over a finite field Fq together with a pure result about elliptic
divisibility sequences from the 1940s to construct a very simpl...
The elliptic curve discrete logarithm problem and equivalent hard problems for elliptic divisibility sequences
elliptic curve discrete logarithm problem equivalent hard problems elliptic divisibility sequences
2009/6/3
We define three hard problems in the theory of elliptic divisibility
sequences (EDS Association, EDS Residue and EDS Discrete
Log), each of which is solvable in sub-exponential time if and only if t...