On the Function Field Sieve and the Impact of Higher Splitting Probabilities: Application to Discrete Logarithms in $\mathbb{F}_{2^{1971}}$ and $\mathbb{F}_{2^{3164}}$
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Nowadays, the most popular public-key cryptosystems are based on either the integer factorization or the discrete logarithm problem. The feasibility of solving these mathematical problems in practice is studied and techniques are presented to speed-up the ...
In 2013 the Discrete Logarithm Problem in finite fields of small characteristic enjoyed a rapid series of developments, starting with the heuristic polynomial-time relation generation method due to Gologlu, Granger, McGuire and Zumbragel, and culminating w ...
The discrete logarithm problem (DLP) in finite fields of small characteristic recently enjoyed a dramatic series of breakthrough results and computational records, with its (heuristic) complexity dropping from subexponential to quasi-polynomial. While thes ...
We reconsider the provably collision resistant Very Smooth Hash and propose a small change in the design aiming to improve both performance and security. While the original proofs of security based on hardness of factoring or discrete logarithms are preser ...
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Motivated by the advantages of using elliptic curves for discrete logarithm-based public-key cryptography, there is an active research area investigating the potential of using hyperelliptic curves of genus 2. For both types of curves, the best known algor ...
In this paper we show how some recent ideas regarding the discrete logarithm problem (DLP) in finite fields of small characteristic may be applied to compute logarithms in some very large fields extremely efficiently. By combining the polynomial time relat ...
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We show that the binary logarithm of the nonnegative rank of a nonnegative matrix is, up to small constants, equal to the minimum complexity of a randomized communication protocol computing the matrix in expectation. We use this connection to prove new con ...
For q a prime power, the discrete logarithm problem (DLP) in Fq consists in finding, for any g∈Fq× and h∈⟨g⟩, an integer x such that gx=h. We present an algorithm for computing discrete log ...
In late 2012 and early 2013 the discrete logarithm problem (DLP) in finite fields of small characteristic underwent a dramatic series of breakthroughs, culminating in a heuristic quasi-polynomial time algorithm, due to Barbulescu, Gaudry, Joux and Thomé. U ...
