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Designs, Codes and Cryptography

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01.01.2016

Recent progress on the elliptic curve discrete logarithm problem

verfasst von: Steven D. Galbraith, Pierrick Gaudry

Erschienen in: Designs, Codes and Cryptography | Ausgabe 1/2016

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Abstract

We survey recent work on the elliptic curve discrete logarithm problem. In particular we review index calculus algorithms using summation polynomials, and claims about their complexity.

Vorheriger Artikel Four decades of research on bent functions

Nächster Artikel Technical history of discrete logarithms in small characteristic finite fields

This is sometimes called the “non-uniform” model, but we do not discuss such interpretations in this paper. Note that an algorithm that stores a table of all discrete logs does not fit the model since the program length is \(O( r \log (r) )\) bits.

It is not necessary that V be a subfield. If V is a one-dimensional subspace that is not a subfield then \(V^{(2)}\) is also a one-dimensional subspace, but \(V^{(2)} \ne V\).

And more, including the first author and his Ph.D. student Shishay Gebregiyorgis.

This is true only under genericity assumptions, and with appropriate monomial orderings.

And one must be careful not to be fooled by the Strong law of small numbers [57].

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Titel: Recent progress on the elliptic curve discrete logarithm problem
verfasst von: Steven D. Galbraith
Pierrick Gaudry
Publikationsdatum: 01.01.2016
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 1/2016
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-015-0146-7

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