Recent progress on NFS imposed a new estimation of the security of pairings. In this work
we study the best attacks against some of the most popular pairings and propose new key …

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 …

The selection of polynomials to represent number fields crucially determines the efficiency of
the Number Field Sieve (NFS) algorithm for solving the discrete logarithm in a finite field. An …

A recent NFS attack against pairings made it necessary to increase the key sizes of the most
popular families of pairings: BN, BLS12, KSS16, KSS18 and BLS24. The attack applies to …

We study the discrete logarithm problem at the boundary case between small and medium
characteristic finite fields, which is precisely the area where finite fields used in pairing …

With the rapid development of the world economy, some developing countries only pay
attention to the growth rate of GDP, but ignore the importance of sustainable development …

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 …

Cryptography concerns itself with the problem of exchanging encrypted, meaning
unintelligible, messages that only a legitimate receiver can decrypt, hence read. In order to …

Abstract At Eurocrypt 2015, Barbulescu et al. introduced two new methods of polynomial
selection, namely the Conjugation and the Generalised Joux-Lercier methods, for the …

The present work reports progress in discrete logarithm computation for the general medium
prime case using the function field sieve algorithm. A new record discrete logarithm …