Discrete Logarithm
Discrete Logarithm in Galois Rings
... the discrete logarithm in Galois fields to the one in Galois rings? That concept of the discrete logarithm in Galois rings is a little bi t different from the one in Galois ...the ...
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A Simplified Approach to Rigorous Degree 2 Elimination in Discrete Logarithm Algorithms
... equations. Following [1], we can find a non-zero element in the kernel of the (row-)matrix of exponents modulo Q k 0 − 1, which is non-trivial thanks to a dimension argument. Taking the product corresponding to this ...
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A Las Vegas algorithm to solve the elliptic curve discrete logarithm problem
... the index-calculus algorithm, and our algorithm. In an index-calculus algorithm, the discrete logarithm problem is reduced to a linear algebra problem. Similar is the case with our algorithm. However, in ...
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Practical IBC Using Hybrid-Mode Problems: Factoring and Discrete Logarithm
... In 1991, Maurer and Yacobi [23] developed a non-interactive ID-based public-key distribution system. In their scheme, the public keys are self-authenticated and require no further authentication by certificates. However, ...
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Solving the Discrete Logarithm of a 113-bit Koblitz Curve with an FPGA Cluster
... the discrete logarithm was actually com- puted without knowing it in advance, a point generation function was ...their discrete logarithm is ...the discrete logarithm ...
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Multi-user collisions: Applications to Discrete Logarithm, Even-Mansour and PRINCE
... Attacking Even-Mansour using distinguished points methods. In order to attack Even-Mansour using a distinguished point methodas recalled in Appendix C, we would like to construct a set of chains using the public ...
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Group Signature Member Deletion Scheme Based on Discrete Logarithm and Factorization
... on discrete logarithm and the difficulty of factorization, two kinds improvement schemes on the secret property key updating algorithm are given and they requires lower computing power for member and ...
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Hybrid Authentication Cybersystem Based on Discrete Logarithm, Factorization and Array Entanglements
... the discrete logarithm problem, complexity of integer factorization of a product of two large primes and a combination of symmetric and asymmetric ...
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Modified Baby Step Giant Step Algorithm to Solve Elliptic Curve Discrete Logarithm Problem (ECDLP)
... Giant-step Algorithm to solve the Elliptic Curve Discrete Logarithm Problem is presented in this work. The algorithm is illustrated with numerical examples. The proposed algorithm is found to be more ...
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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 Problem (ECDLP). A wide research has ...
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Solving the Elliptic Curve Discrete Logarithm Problem Using Semaev Polynomials, Weil Descent and Grbner Basis Methods -- an Experimental Study
... Abstract. 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 ...
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Improving the Polynomial time Precomputation of Frobenius Representation Discrete Logarithm Algorithms - Simplified Setting for Small Characteristic Finite Fields
... crete logarithm algorithms. We show that a simplified description of the algorithm, together with some additional ideas, permits to obtain an im- proved complexity for the polynomial time precomputation that ...
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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- mation ...
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Quantum algorithm for the discrete logarithm problem for matrices over finite group rings
... Abstract. We propose a polynomial time quantum algorithm for solv- ing the discrete logarithm problem in matrices over finite group rings. The hardness of this problem was recently employed in the design of ...
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Polynomial Time Bounded Distance Decoding near Minkowskis Bound in Discrete Logarithm Lattices
... [BGJT14] Razvan Barbulescu, Pierrick Gaudry, Antoine Joux, and Emmanuel Thomé. A heuristic quasi-polynomial algorithm for discrete logarithm in finite fields of small characteristic. In Advances in ...
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Harder, Better, Faster, Stronger - Elliptic Curve Discrete Logarithm Computations on FPGAs
... Certicom [10] introduced ECC challenges in 1997 to in- crease industry acceptance of cryptosystems based on the elliptic curve discrete logarithm problem. They pub- lished challenges for di↵erent security ...
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Recent progress on the elliptic curve discrete logarithm problem
... each discrete logarithm computation, even if several take place in the same ...the discrete logarithms of all the factor base elements with a right-kernel computation is guaranteed only if the matrix ...
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The Discrete-Logarithm Problem with Preprocessing
... the discrete-log problem, and algorithms for the multiple-discrete-log problem—in which the task is to compute many discrete logarithms at ...the discrete logarithm in ...i ...
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Comparing the Difficulty of Factorization and Discrete Logarithm: a 240-digit Experiment
... Comparing the Difficulty of Factorization and Discrete Logarithm: a 240-digit Experiment 9/23.. Paying attention to the combination cost.. Relations with 2 LPs or less are a blessing..[r] ...
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The Discrete Logarithm Problem in non-representable rings
... any discrete logarithm algorithm with non-negligible success probability to become arbitrarily close to ...the Discrete Logarithm Problem in E p ...
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