In this paper, we describe a new algorithm for discrete logarithms in small characteristic.
This algorithm is based on index calculus and includes two new contributions. The first is a …

An algorithm of digital logarithm calculation for the Galois field GF (257) is proposed. It is
shown that this field is coupled with one of the most important existing standards that uses a …

A popular approach to tweakable blockcipher design is via masking, where a certain
primitive (a blockcipher or a permutation) is preceded and followed by an easy-to-compute …

In this paper, we revisit the recent small characteristic discrete logarithm algorithms. We
show that a simplified description of the algorithm, together with some additional ideas …

We show that a Magma implementation of Joux's L 1/4+ o (1) algorithm can be used to
compute discrete logarithms in the 1303-bit finite field\mathbb F _ 3^ 6 ⋅ 137 and the 1551 …

Abstract In 2013, Joux, and then Barbulescu, Gaudry, Joux and Thomé, presented new
algorithms for computing discrete logarithms in finite fields of small and medium …

Due to its use in cryptographic protocols such as the Diffie–Hellman key exchange, the
discrete logarithm problem attracted a considerable amount of attention in the past 40 years …

In the past two years, there have been several dramatic improvements in algorithms for
computing discrete logarithms in small-characteristic finite fields. In this paper, we examine …

Computing discrete logarithms in finite fields is a main concern in cryptography. The best
algorithms in large and medium characteristic fields (eg, $\rm {GF}(p^ 2) $, $\rm {GF}(p^{12}) …

Pairing cryptosystems are extremely powerful mathematical tools for developing
cryptographic protocols that can provide end-to-end security for applications like Internet-of …