Elliptic Curve Discrete Logarithm Problem
Elliptic divisibility sequences and the elliptic curve discrete logarithm problem
... an elliptic curve E over a finite field F q together with a pure result about elliptic divisibility sequences from the 1940s to construct a very simple alterna- tive to the Menezes-Okamoto-Vanstone ...
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A Las Vegas algorithm to solve the elliptic curve discrete logarithm problem
... the elliptic curve discrete logarithm problem to a problem in linear ...algebra problem, Problem ...solve Problem L will produce better algorithms to solve ...
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The Elliptic Curve Discrete Logarithm Problem and Equivalent Hard Problems for Elliptic Divisibility Sequences
... of elliptic di- visibility 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 ...
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A New Index Calculus Algorithm for the Elliptic Curve Discrete Logarithm Problem and Summation Polynomial Evaluation
... for elliptic curves by Semaev has opened up new avenues of investigation in index calcu- lus type algorithms for the elliptic curve discrete logarithm problem, and several recent ...
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Modified Baby Step Giant Step Algorithm to Solve Elliptic Curve Discrete Logarithm Problem (ECDLP)
... ------------------------------------------------------------------------***---------------------------------------------------------------------- Abstract - A Modified version of Shanks’ Baby-step Giant-step Algorithm to ...
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Solving the Elliptic Curve Discrete Logarithm Problem Using Semaev Polynomials, Weil Descent and Grbner Basis Methods -- an Experimental Study
... {mshantz,eteske}@uwaterloo.ca, University of Waterloo, Canada Johannes Buchmann zu Ehren Abstract. At ASIACRYPT 2012, Petit and Quisquater suggested that there may be a subexponential-time index-calculus type algorithm ...
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Recent progress on the elliptic curve discrete logarithm problem
... A natural question is to give a tight lower bound on the number of group operations for any algorithm of this type. The original baby-step-giant-step algorithm is non- optimal, since the DLP can only be solved when there ...
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Elliptic Curve Discrete Logarithm Problem over Small Degree Extension Fields. Application to the static Diffie-Hellman problem on $E(\F_{q^5})$
... the discrete logarithm on the group of points of an elliptic curve defined over a small degree extension field F q n ...the elliptic curve static Diffie-Hellman problem ...
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A brief survey of the discrete logarithm problem
... any elliptic curve discrete loga- rithm based ...the Elliptic Curve Discrete Logarithm Problem (ECDLP), the fastest algorithm currently available is the Pollard Rho ...
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New Random Walk Technique and Collision Detection Algorithm to Improve the Pollard RHO Attack of Solving Discrete Logarithm Problem on Elliptic Curves
... Abstract- Elliptic curve cryptography is a revolutionary in the history of public key cryptography that is protected by a hard problem Elliptic Curve Discrete Logarithm ...
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Elliptic Curve Cryptography
... of elliptic curves as groups, we can approach the elliptic curve discrete logarithm problem, from which elliptic curve cryptosystems draw their ...The ...
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Summation polynomials and the discrete logarithm problem on elliptic curves
... the discrete logarithm problem on elliptic ...the problem of finding bounded solutions to some explicit modular multivariate polynomial ...the elliptic curve summation ...
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New algorithm for the discrete logarithm problem on elliptic curves
... computing discrete logarithms on an elliptic curve over a field of size 2 n ...binary elliptic curves recommended by FIPS the new method performs better than ...
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Harder, Better, Faster, Stronger - Elliptic Curve Discrete Logarithm Computations on FPGAs
... Computing discrete logarithms takes ...compute discrete logarithms of Weierstrass curves defined over binary fields and Koblitz curves us- ing ...a discrete logarithm of the elliptic ...
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A Discrete Logarithm Attack on Elliptic Curves
... a discrete log- arithm problem from an elliptic curve to a higher genus curve is at the heart of a very deep problem in algebraic ...a curve serves as a platform to ...
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Generic Hardness of the Multiple Discrete Logarithm Problem
... cryptographic problem based on a group does not depend solely on the isomorphism class of the underlying ...an elliptic curve and a subgroup G of prime order p on it, then the discrete ...
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Cheon's algorithm, pairing inversion and the discrete logarithm problem
... [email protected] Abstract. We relate the fixed argument pairing inversion problems (FAPI) and the discrete logarithm problem on an elliptic curve. This is done using the ...
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Computing Elliptic Curve Discrete Logarithms with the Negation Map
... an elliptic curve defined over a finite field F q ...The problem of finding k, given P, Q, and the parameters of E, is known as the elliptic curve discrete logarithm prob- ...
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Cryptanalysing the Critical Group: Efficiently Solving Biggs's Discrete Logarithm Problem
... the discrete logarithm problem is efficiently solved by an application of the extended Euclidean ...the discrete logarithm problem is thought to be hard in ...an elliptic ...
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Isogenies and the Discrete Logarithm Problem on Jacobians of Genus 3 Hyperelliptic Curves
... particular curve has no rational isogenies if its hyperelliptic polynomial has an irreducible factor of degree 5 or 7 (or a single irreducible factor of degree ...a curve in this form if we are using the CM ...
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