Integer Factorization: Solution via Algorithm for Constrained Discrete Logarithm Problem
نویسندگان
چکیده
منابع مشابه
Integer Factorization: Solution via Algorithm for Constrained Discrete Logarithm Problem
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 Problem (DLP) have been developed. Approach: Although several factorization algorithms with subexponential complexity have been discovered, the recent RSA Factoring Challenge demonstrated that it was still n...
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These are notes for a lecture given at CIRM in 2014, for the Journées Nationales du Calcul Formel . We explain the basic algorithms based on combining congruences for solving the integer factorization and the discrete logarithm problems. We highlight two particular situations where the interaction with symbolic computation is visible: the use of Gröbner basis in Joux's algorithm for discrete lo...
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The security of most current public-key cryptosystems is based on the difficulty of finding discrete logarithms in large finite fields or factoring large integers. Most discrete logarithm and integer factoring algorithms, such as the Number Field Sieve (NFS) or the Function Field Sieve (FFS), can be described in 3 main steps: data collection, filtering and linear algebra. The goal of the filter...
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Though integer factorization and discrete logarithm problem are both practically and theoretically important, the computational complexity of these problems remained unknown. By comparing integer factorization problem with a problem in P and NP-complete problems, I show that the decision problem version of integer factorization problem is neither in P nor NP-complete. In addition, integer facto...
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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 constrained DLP depends on the choice of the set. Motivated by cryptographic applications, we study sets with succinct representation for which the constrained DLP is hard. We draw on earlier results due...
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ژورنال
عنوان ژورنال: Journal of Computer Science
سال: 2009
ISSN: 1549-3636
DOI: 10.3844/jcssp.2009.674.679