منابع مشابه
Computing discrete logarithms in an interval
The discrete logarithm problem in an interval of size N in a group G is: Given g, h ∈ G and an integer N to find an integer 0 ≤ n ≤ N , if it exists, such that h = gn. Previously the best low-storage algorithm to solve this problem was the van Oorschot and Wiener version of the Pollard kangaroo method. The heuristic average case running time of this method is (2 + o(1)) √ N group operations. We...
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We propose some new baby-step giant-step algorithms for computing “low-weight” discrete logarithms; that is, for computing discrete logarithms in which the radix-b representation of the exponent is known to have only a small number of nonzero digits. Prior to this work, such algorithms had been proposed for the case where the exponent is known to have low Hamming weight (i.e., the radix-2 case)...
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Computations of small discrete logarithms are feasible even in “secure” groups, and are used as subroutines in several cryptographic protocols in the literature. For example, the Boneh–Goh–Nissim degree2-homomorphic public-key encryption system uses generic square-root discrete-logarithm methods for decryption. This paper shows how to use a small group-specific table to accelerate these subrout...
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where q is the cardinality of the base field. The algorithm given follows the index calculus or relation generation and linear algebra strategy and as usual for such algorithms for the discrete logarithm problem for curves of a fixed genus, the so-called factor base consists of a subset of the set of rational points of the curve. Moreover, a so-called double large prime relation is used, where ...
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At present, there are two competing index calculus variants for computing discrete logarithms in (Z/pZ)* in practice. The purpose of this paper is to summarize the recent practical experience with a generalized implementation covering both a variant of the Number Field Sieve and the Gaussian integer method. By this implementation we set a record with p consisting of 85 decimal digits. With rega...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2012
ISSN: 0025-5718,1088-6842
DOI: 10.1090/s0025-5718-2012-02641-x