Cryptography and the Discrete Logarithm Problem
A brief survey of the discrete logarithm problem
... The Discrete Logarithm Problem (DLP) has been the subject of interest among many mathematicians and cryptographers in recent times because of its computational di¢ ...the Discrete ...
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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 ...
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Recent progress on the elliptic curve discrete logarithm problem
... There are many excellent books that provide a detailed background to elliptic curve cryptography, for example [3, 12, 13, 42, 58, 114]. Hence, the goal of this article is to survey developments from within the ...
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On the discrete logarithm problem in finite fields of fixed characteristic
... Given the immense importance of the DLP to public key cryptography ever since its inception in 1976 [17], this plateau in progress could have been taken as strong evidence of the problem’s hardness. However, in ...
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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 ...
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Elliptic divisibility sequences and the elliptic curve discrete logarithm problem
... smaller keys. There are, however, some special cases of “weak curves” E/ F q that should not be used for cryptography because the discrete logarithm problem is no harder in them than in the ...
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Cryptanalysing the Critical Group: Efficiently Solving Biggs's Discrete Logarithm Problem
... Abstract Biggs has recently proposed the critical group of a certain class of finite graphs as a platform group for cryptosystems relying on the difficulty of the discrete log problem. The paper uses ...
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Isogenies and the Discrete Logarithm Problem on Jacobians of Genus 3 Hyperelliptic Curves
... Our results have a number of interesting implications for curve-based cryp- tography. First, the difficulty of the DLP in a subgroup G of J H depends not only on the size of the subgroup G, but upon the existence of ...
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The Discrete Logarithm Problem Modulo One: Cryptanalysing the Ariffin--Abu cryptosystem
... In Section 3 we show how to solve this discrete logarithm problem, thus breaking the scheme. (We derive the shared key in polynomial time, even in a passive adversary model.) We provide a short ...
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A Secure Anonymous E-Voting System based on Discrete Logarithm Problem
... Jinn-Ke Jan was born in Taiwan in 1951. He received the B.S. degree in physics from the Catholic Fu Jen University in 1974 and the M.S. degree in information and computer science from University of Tokyo in 1980. He ...
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Weakness of F_{3^{6*1429}} and F_{2^{4*3041}} for Discrete Logarithm Cryptography
... the discrete logarithm problem in these fields is necessary for the security of pairings derived from supersingular curves with embedding degree 6 and 4 defined, respectively, over F 3 1429 and F 2 ...
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Quantum algorithm for the discrete logarithm problem for matrices over finite group rings
... Currently quantum computers are weak, but a full scale quantum computer (if ever built) will defeat all DLP-based and factorization-based schemes. This is a powerful motivator for the design and construction of quantum ...
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An ID-Based Public Key Cryptosystem based on Integer Factoring and Double Discrete Logarithm Problem
... cryptography: one is in modular p, where p is a large prime number; the other is in modular N, where N = pq, and p and q are large primes. Blom [12] proposed a symmetric key generation system (SKGS) based on ...
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Time Stamped Proxy Blind Signature Scheme With Proxy Revocation Based on Discrete Logarithm Problem
... Acknowledgment First of all, I would like to express my deep sense of respect and gratitude towards my supervisor Prof. Ramesh Kumar Mohapatra, who has been the guiding force behind this work. I want to thank him for ...
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Modified Baby Step Giant Step Algorithm to Solve Elliptic Curve Discrete Logarithm Problem (ECDLP)
... The discrete logarithm computation in finite groups is of considerable importance in Public Key ...the discrete logarithm problem. The elliptic curve discrete logarithm ...
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Study of Matrices Related to Discrete Logarithm in Kummer Extensions
... The discrete logarithm problem has been studied during the past decades for its important application in cryptography and other ...key cryptography, which is widely used for Internet ...
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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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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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A NEW APPROACH TO THE DISCRETE LOGARITHM PROBLEM WITH AUXILIARY INPUTS
... using the fast Fourier transform multiplication. We note that the technique is also extended to the Sch¨ onhage-Strassen multiplication algorithm. If the size of the image of f is N , then the birthday paradox (under the ...
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