Razvan Barbulescu

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The difficulty of computing discrete logarithms in fields Fqk depends on the relative sizes of k and q. Until recently all the cases had a sub-exponential complexity of type L(1/3), similar to the factorization problem. In 2013, Joux designed a new algorithm with a complexity of L(1/4 + ǫ) in small characteristic. In the same spirit, we propose in this(More)
The aim of this work is to investigate the hardness of the discrete logarithm problem in fields GF(p) where n is a small integer greater than 1. Though less studied than the small characteristic case or the prime field case, the difficulty of this problem is at the heart of security evaluations for torus-based and pairing-based cryptography. The best known(More)
We give details on solving the discrete logarithm problem in the 202-bit prime order subgroup of F2809 using the Function Field Sieve algorithm (FFS). To our knowledge, this computation is the largest discrete logarithm computation so far in a binary field extension of prime degree. The Function Field Sieve is the traditional approach for solving these(More)
We introduce a new variant of the number field sieve algorithm for discrete logarithms in Fpn called exTNFS. The most important modification is done in the polynomial selection step, which determines the cost of the whole algorithm: if one knows how to select good polynomials to tackle discrete logarithms in Fpκ , exTNFS allows to use this method when(More)
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 number field sieve (NFS) together with its many variants. When p has a special form (SNFS), as in many pairings constructions, NFS has a faster variant due to(More)
The difficulty of computing discrete logarithms in fields Fqk depends on the relative sizes of k and q. Until recently all the cases had a sub-exponential complexity of type L(1/3), similar to the factorization problem. In 2013, Joux designed a new algorithm with a complexity of L(1/4 + ǫ) in small characteristic. In the same spirit, we propose in this(More)
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(More)
We describe a unified framework to search for optimal formulae evaluating bilinear — or quadratic — maps. This framework applies to polynomial multiplication and squaring, finite field arithmetic, matrix multiplication, etc. We then propose a new algorithm to solve problems in this unified framework. With an implementation of this algorithm, we prove the(More)
The discrete logarithm problem (DLP) was first proposed as a hard problem in cryptography in the seminal article of Diffie and Hellman [DH76]. Since then, together with factorization, it has become one of the two major pillars of public key cryptography. As a consequence, the problem of computing discrete logarithms has attracted a lot of attention. From an(More)