The multiple number field sieve for medium- and high-characteristic finite fields
نویسندگان
چکیده
منابع مشابه
The Multiple Number Field Sieve for Medium and High Characteristic Finite Fields
In this paper, we study the discrete logarithm problem in medium and high characteristic finite fields. We propose a variant of the Number Field Sieve (NFS) based on numerous number fields. Our improved algorithm computes discrete logarithms in Fpn for the whole range of applicability of NFS and lowers the asymptotic complexity from Lpn(1/3, (128/9)1/3) to Lpn(1/3, (213/36)1/3) in the medium ch...
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In this paper, we study several variations of the number field sieve to compute discrete logarithms in finite fields of the form Fpn , with p a medium to large prime. We show that when n is not too large, this yields a Lpn(1/3) algorithm with efficiency similar to that of the regular number field sieve over prime fields. This approach complements the recent results of Joux and Lercier on the fu...
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Let p be a prime number and n a positive integer, and let q D p. Let Fq be the field of q elements and denote by F q the multiplicative subgroup of Fq . Assume t and u are elements in F q with the property that u is in the subgroup generated by t . The discrete logarithm of u with respect to the base t , written logt u, is the least non-negative integer x such that t x D u. In this paper we des...
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The selection of polynomials to represent number fields crucially determines the efficiency of the Number Field Sieve (NFS) algorithm for solving the discrete log problem in a finite field. An important recent work due to Barbulescu et al builds upon existing works to propose two new methods for polynomial selection when the target field has a composite order. These methods are called the gener...
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ژورنال
عنوان ژورنال: LMS Journal of Computation and Mathematics
سال: 2014
ISSN: 1461-1570
DOI: 10.1112/s1461157014000369