Shantz, M., Teske, E.: Solving the elliptic curve discrete logarithm problem using semaev polynomials, weil descent and grobner basis methods - an experimental study. In: Fischlin, M., Katzenbeisser, S. (eds.) Number Theory and Cryptography. Lecture Notes in Computer Science, vol 8260, pp...
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 the elliptic curve discrete logarithm problem is sol...
well-known and widely accepted conjectures concerning the expected ranks of elliptic curves over the ra- tionals. Keyword: Elliptic curve cryptosystem, discrete logarithm, partial lift- ing. 1 Introduction The discrete logarithm problem over elliptic curves is a natural analog of the discrete ...
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 fields. This algorithm uses Semaev polynomials and Weil Descent to create a system of polynomial equati...
This is due to the apparently increased difficulty of the underlying mathematical problem, the Elliptic Curve Discrete Logarithm Problem (ECDLP). This problem is believed to require more time for its solution than the time required for the solution of its finite field analogue, the Discrete ...
Algebraic Approaches for the Elliptic Curve Discrete Logarithm Problem over Prime Fields Chapter © 2016 Technical history of discrete logarithms in small characteristic finite fields Article 24 November 2015 The Past, Evolving Present, and Future of the Discrete Logarithm Chapter © 2014 Ref...
The Discrete Logarithm Problem (DLP) 离散对数问题 (DLP) Okay, letGbe an abelian group. First we write the operation inGmultiplicatively. For anyg∈Gand any integer
Elliptic Curve Cryptography (ECC) is a relatively recent branch of cryptography based on the arithmetic of elliptic curves and the Elliptic Curve Discrete Logarithm Problem (ECDLP). Elliptic curve cryptographic schemes are public-key mechanisms that provide encryption, digital signature and key exchange ...
Certicom introduced the Elliptic Curve Cryptosystem (ECC) Challenge in November 1997. The first of its kind, the ECC Challenge was developed to increase industry understanding and appreciation for the difficulty of the elliptic curve discrete logarithm problem, and to encourage and stimulate further ...
P. Gaudry, Index calculus for abelian varieties of small dimension and the elliptic curve discrete logarithm problem. J. Symb. Comput. 44(12), 1690–1702 (2009) Article MATH MathSciNet Google Scholar P. Gaudry, E. Thomé, N. Thériault, C. Diem, A double large prime variation for ...