The Discrete Logarithm Problem
A brief survey of the discrete logarithm problem
... Proof: We simply create a list of the values g x for x = 0; 1; 2; :::; N 1; where each successive value is obtained by multiplying the previous value by g: If a solution to g x = h exists, then h will certainly appear in ...
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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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Hard Instances of the Constrained Discrete Logarithm Problem
... The discrete logarithm problem (DLP) generalizes to the constrained DLP, where the secret exponent x belongs to a set known to the attacker. The complexity of generic algorithms for solving the ...
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Recent progress on the elliptic curve discrete logarithm problem
... 5 Pollard rho and kangaroo The baby-step-giant-step algorithm requires large storage and is hard to parallelise or distribute over the internet. The rho and kangaroo algorithms require less storage and can be ...
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New algorithm for the discrete logarithm problem on elliptic curves
... In this section an asymptotical complexity estimate for the discrete logarithm problem in E(F 2 n ) based on Assumption 1 is derived. The algorithm complexity is the sum of the complexity of two ...
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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 ...finds discrete logarithms faster than by means ...
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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 reduction from the DLP ...
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It is based on a computationally difficult problem - the discrete logarithm problem in multiplicative group
... Abstract. In this paper we describe a new method of encryption that orig- inates from the public key cryptography and number theory. Our algorithm was inspired by the RSA algorithm and Diffie-Hellman key exchange proto- ...
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The discrete logarithm problem in the group of non-singular circulant matrices
... the discrete logarithm problem in circulant matrices over F q with the discrete logarithm problem in the finite field F q d−1 , where F q is of characteristic ...
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Elliptic divisibility sequences and the elliptic curve discrete logarithm problem
... 2 University of Cape Town, Rondebosch, 7701, South Africa, [email protected]. Abstract. We use properties of the division polynomials of an elliptic curve E over a finite field F q together with a pure result ...
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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 ...
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The Discrete Logarithm Problem Modulo One: Cryptanalysing the Ariffin--Abu cryptosystem
... a discrete logarithm problem in the infinite (additive) group R / Z (the reals modulo ...this discrete logarithm problem can be efficiently solved in ...
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Solving a 676-bit Discrete Logarithm Problem in GF(3^{6n})
... 2 National Institute of Information and Communications Technology, Japan. Abstract. Pairings on elliptic curves over finite fields are crucial for con- structing various cryptographic schemes. The η T pairing on ...
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A Las Vegas algorithm to solve the elliptic curve discrete logarithm problem
... i=1 P i = O. 2.1 How to use the above theorem in our algorithm We choose k such that k = 3n 0 for some positive integer n 0 . Then we choose random points P 1 , P 2 , . . . , P s and Q 1 , Q 2 , . . . , Q t such that s + ...
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Integer Factorization: Solution via Algorithm for Constrained Discrete Logarithm Problem
... Abstract: Problem statement: During the last thirty years many public-key cryptographic protocols based on either the complexity of integer factorization of large semiprimes or the Discrete Logarithm ...
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Quantum algorithm for the discrete logarithm problem for matrices over finite group rings
... 5. Conclusion We presented a probabilistic polynomial-time quantum algorithm for solv- ing the discrete logarithm problem in the ring M n ( F p s [G]) for any fixed fi- nite group G. As a consequence ...
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Using Equivalence Classes to Accelerate Solving the Discrete Logarithm Problem in a Short Interval
... h), and the ‘type’ of the walk. When the same equivalence class is reached by walks of both types then the discrete logarithm problem is solved. To understand the algorithm it is necessary to ...
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The Elliptic Curve Discrete Logarithm Problem and Equivalent Hard Problems for Elliptic Divisibility Sequences
... EDS Discrete Log), each of which is solvable in sub-exponential time if and only if the elliptic curve discrete logarithm problem is solvable in sub-exponential ...the problem of EDS ...
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A New Index Calculus Algorithm for the Elliptic Curve Discrete Logarithm Problem and Summation Polynomial Evaluation
... curve discrete logarithm problem, and several recent papers have explored their ...Curve Discrete Logarithm Problem that makes use of a technique for fast evaluation of the sum- ...
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