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Fine Tuning the Function Field Sieve Algorithm for the Medium Prime Case
Discrete Log Finite fields Function Field Sieve Cryptography
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2016/1/26
This work builds on the variant of the function field sieve (FFS) algorithm for the
medium prime case introduced by Joux and Lercier in 2006. We make several contributions.
The first contribution us...
FFS Factory: Adapting Coppersmith's "Factorization Factory" to the Function Field Sieve
Discrete logarithm Function field sieve Cryptanalysis
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2016/1/9
In 1993, Coppersmith introduced the “factorization factory”
approach as a means to speed up the Number Field Sieve algorithm
(NFS) when factoring batches of integers of similar size: at the expense
...
Selecting polynomials for the Function Field Sieve
public-key cryptography
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2013/4/18
The Function Field Sieve algorithm is dedicated to computing discrete logarithms in a finite field GF(q^n) , where q is a small prime power. The scope of this article is to select good polynomials for...
Relation collection for the Function Field Sieve
function field sieve discrete logarithm polynomial arithmetic finite-field arithmetic
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2013/4/18
In this paper, we focus on the relation collection step of the Function Field Sieve (FFS), which is to date the best algorithm known for computing discrete logarithms in small-characteristic finite fi...
On the Function Field Sieve and the Impact of Higher Splitting Probabilities: Application to Discrete Logarithms in $\F_{2^{1971}}$
DLP
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2013/4/18
In this paper we propose a binary field variant of the Joux-Lercier medium-sized Function Field Sieve, which results not only in complexities as low as $L_{q^n}(1/3,2/3)$ for computing arbitrary logar...