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On the alpha value of polynomials in the tower number field sieve algorithm
number field sieve discrete logarithm pairing-friendly curve
2019/8/2
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...
A Generalisation of the Conjugation Method for Polynomial Selection for the Extended Tower Number Field Sieve Algorithm
finite fields discrete logarithm tower number field sieve
2016/6/2
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...
Extended Tower Number Field Sieve with Application to Finite Fields of Arbitrary Composite Extension Degree
Discrete Logarithm Problem Number Field Sieve Finite Fields
2016/5/30
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...
A General Polynomial Selection Method and New Asymptotic Complexities for the Tower Number Field Sieve Algorithm
Discrete Log Tower Number Field Sieve
2016/5/24
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...
Tower Number Field Sieve Variant of a Recent Polynomial Selection Method
TNFS Recent Polynomial Selection Method
2016/4/25
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...
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 ...
Extended Tower Number Field Sieve: A New Complexity for Medium Prime Case
Discrete Logarithm Problem Number Field Sieve Finite Fields Cryptanalysis
2015/12/22
In this paper, we extend the tower number field sieve~(TNFS) proposed by Barbulescu, Gaudry, and Kleinjung in Asaicrypt 2015. Our generalization based on the JLSV algorithm (by Joux, Lercier, Smart, a...