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In this paper, we provide a notable step towards filling the gap between theory (estimates of running-time) and practice (a discrete logarithm record computation) for the Tower Number Field Sieve (TNF...
We propose the General Sieve Kernel (G6K, pronounced /ʒe.si.ka/), an abstract stateful machine supporting a wide variety of lattice reduction strategies based on sieving algorithms. Using the bas...
Since 2016 and the introduction of the exTNFS (extended Tower Number Field Sieve) algorithm, the security of cryptosystems based on non- prime finite fields, mainly the paring and torus-based one, is ...
Major substep in a lattice sieve algorithm which solves the Euclidean shortest vector problem (SVP) is the computation of sums and Euclidean norms of many vector pairs. Finding a solution to the SVP i...
In a recent work, Kim and Barbulescu showed how to combine previous polynomial selection methods with the extended tower number field sieve algorithm to obtain improved complexity for the discrete log...
In a recent work, Kim and Barbulescu~(CRYPTO~2016) proposed an algorithm, called exTNFS, that improves asymptotic complexity for the discrete logarithm problems over Fpn in medium prime case, when the...
In a recent work, Kim and Barbulescu had extended the tower number field sieve algorithm to obtain improved asymptotic complexities in the medium prime case for the discrete logarithm problem on Fpn w...
At Asiacrypt 2015, Barbulescu et al. performed a thorough analysis of the tower number field sieve (TNFS) variant of the number field sieve algorithm. More recently, Kim and Barbulescu combined the TN...
In order to assess the security of cryptosystems based on the discrete logarithm problem in non-prime finite fields, as are the torus-based or pairing-based ones, we investigate thoroughly the case ...
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...
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 improv...
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 ...
In this paper, we propose two variants of the Number Field Sieve (NFS) to compute discrete logarithms in medium characteristic finite fields. We consider algorithms that combine two ideas, namely th...
The security of pairing-based crypto-systems relies on the difficulty to compute discrete logarithms in finite fields Fpn where n is a small integer larger than 1. The state-of-art algorithm is the ...
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 importa...

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