The 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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New algorithm for the discrete logarithm problem on elliptic curves
... computing discrete logarithms on elliptic curves defined over finite fields is ...binary elliptic curves one is to solve a cubic system of Boolean equa- ...
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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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Speeding Up Elliptic Curve Discrete Logarithm Computations with Point Halving
... computing elliptic curve dis- crete ...for elliptic curves over binary ...computing elliptic curve discrete logarithms over binary ...
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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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The Discrete-Logarithm Problem with Preprocessing
... Acknowledgements. We would like to thank Dan Boneh for encouraging us to undertake this project and for his advice along the way. We thank Omer Reingold, David Wu, and Benedikt Bünz for fruitful discussions during the ...
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Using Symmetries in the Index Calculus for Elliptic Curves Discrete Logarithm
... the curve to normalize the action of the 4-torsion, the corresponding factor base F 0 seems to contain the expected number of points and then can be choose for index calculus ...
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The Discrete Logarithm Problem in non-representable rings
... of discrete logarithm solvers. 1. introduction For Discrete Logarithm based cryptography, it is desirable to find efficiently implementable groups for which sub-exponential algorithms for the ...
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Generic Hardness of the Multiple Discrete Logarithm Problem
... the discrete logarithm problem [12], the Diffie-Hellman problem [12], the strong Diffie-Hellman problem [3], the decision linear problem [4], and many ...
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