discrete logarithm problem
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 ...
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Generic Hardness of the Multiple Discrete Logarithm Problem
... multiple discrete logarithm problem, where the solver has to solve n instances of the discrete logarithm problem ...computational problem which we call the ...
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Quantum algorithm for the discrete logarithm problem for matrices over finite group rings
... the discrete logarithm problem in matrices over finite group ...this problem was recently employed in the design of a key-exchange protocol proposed by ...
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New algorithm for the discrete logarithm problem on elliptic curves
... curve discrete logarithm problem by decomposing points via computing zeroes of these ...the problem was proved to be sub-exponential, ...
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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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A Las Vegas algorithm to solve the elliptic curve discrete logarithm problem
... There are two kinds of attack on the discrete logarithm problem. One is generic. This kind of attack works in any group. Examples of such attacks are the baby-step giant-step attack [7, Proposition ...
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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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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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Some experiments investigating a possible L(1/4) algorithm for the discrete logarithm problem in algebraic curves
... The L(1/3) subexponential complexity of the function field sieve was first improved by Joux [18] to L(1/4 + o(1)), and then by G¨ olo˘ glu, Granger, McGuire, and Zumbr¨ agel [10] to L(1/4). Shortly thereafter, B˘ ...
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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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On Discrete Logarithm Problem based on Algebraic Varieties over Finite Field and Public Key Cryptosystem
... In this chapter, we propose new DLPs for exponential subfield as a base field and extension of this base field by the product operators over finite fields whic[r] ...
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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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A NEW APPROACH TO THE DISCRETE LOGARITHM PROBLEM WITH AUXILIARY INPUTS
... The rest of the paper is organized as follows: We begin with the description of the algorithm and present complexity analysis in Section 2. In Section 3, we present a fast multipoint evaluation method on exponents. The ...
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On the discrete logarithm problem in finite fields of fixed characteristic
... define discrete logarithms – or indices, as he called them, with respect to a primitive root – noting their usefulness for computing n-th roots modulo primes [19, ...the logarithm of a target element h ...
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A Digital Signature Scheme for Long-Term Security
... the discrete logarithm problem on this group, we have to define a hash function into the group G, namely a map to point ...This problem was studied by various authors giving their own method, ...
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Linearly Homomorphic Encryption from DDH
... Abstract. We design a linearly homomorphic encryption scheme whose security relies on the hardness of the decisional Diffie-Hellman problem. Our approach requires some special features of the underlying group. In ...
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A Security Proof of KCDSA using an extended Random Oracle Model
... This paper has described a tight security reduction for a generalised KCDSA scheme with Randomized Hashing to the discrete logarithm problem. Thus security parameters for the two problems can be ...
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Blockchain as cryptanalytic tool
... Abstract One approach for blockchain based applications to provide a proof-of-work is the computation of hash-values. In our opinion 1 these computations are a waste of energy. It would be highly desirable to find an ...
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A Riddle Wrapped in an Enigma
... For many years it has been known [55] that both the integer factorization problem, upon which RSA is based, and the elliptic curve discrete logarithm problem (ECDLP), upon which ECC is b[r] ...
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Using Symmetries in the Index Calculus for Elliptic Curves Discrete Logarithm
... A major application of the DLP is to design cryptographic protocols whose secu- rity depends on the difficulty of solving the DLP. A cryptosystem has to be secure and fast. Hence we have to consider groups with an ...
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