Abstract The Number Field Sieve and its numerous variants is the best algorithm to compute
discrete logarithms in medium and large characteristic finite fields. When the extension …

Solving the discrete logarithm problem in a finite prime field is an extremely important
computing problem in modern cryptography. The hardness of solving the discrete logarithm …

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

Cryptographic agility, the ability to easily and quickly modify cryptography in a sys-tem, is
one of the most important features of any cryptographic system. Any algorithm may be …

In this short paper we show how to apply Montgomery multiplication to the tag tracing variant
of the Pollard rho algorithm applied to prime order fields. This combines the advantages of …

We focus on improving the Gaudry-Schost algorithm, which solves multi-dimensional
discrete logarithm problem. We have proposed a modified algorithm that reduces the cost of …

The thesis focuses on two problems: The discrete logarithm problem (DLP) and the class
group com-putation problem. Besides the inherent mathematical appeal, both of these …