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Generalized Mersenne Numbers in Pairing-Based Cryptography
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The author’s home country, the United States, and some of the characters from the film adaptation are fictitious.Abstract:
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Book ChapterDOI
Comparison of Three Modular Reduction Functions
TL;DR: In this paper, three modular reduction algorithms for large integers are compared with respect to their performance in portable software: the classical algorithm, Barrett's algorithm and Montgomery's algorithm, and three modular exponentiation algorithms are compared.
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Discrete Logarithms: The Effectiveness of the Index Calculus Method
TL;DR: This article surveys recent developments concerning the discrete logarithm problem in the case of finite fields, and in particular, recent modifications of the index calculus method, including the number field sieve and the function field sieves.
Journal Article
Comparison of three modular reduction functions
TL;DR: Three modular reduction algorithms for large integers are compared with respect to their performance in portable software: the classical algorithm, Barrett's algorithm and Montgomery's algorithm, whose application in the modular exponentiation operation is considered.
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Function Field Sieve Method for Discrete Logarithms over Finite Fields
TL;DR: This method is an analog of the number field sieve method originally developed for factoring integers and is asymptotically faster than the previously known algorithms when applied to finite fields Fpn, where p6?n.
Book ChapterDOI
High security pairing-based cryptography revisited
TL;DR: In this article, the Tate pairing is shown to be more efficient than the Weil pairing for all such security levels of the security level of the Tate-Weil pairings, using efficient exponentiation techniques in the cyclotomic subgroup.