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Generalized Mersenne Numbers in Pairing-Based Cryptography
TLDR
The author’s home country, the United States, and some of the characters from the film adaptation are fictitious.Abstract:
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Square-root algorithms for the discrete logarithm problem (a survey)
TL;DR: A smoking and cooking apparatus operable to overlay a cooking surface including a closed heat reflective member, support members connected to and downwardly extending from the closed heat reflector for supporting the member above the cooking surface, is described in this paper.
Book ChapterDOI
Key Improvements to XTR
Arjen K. Lenstra,Eric R. Verheul +1 more
TL;DR: Improved methods for XTR key representation and parameter generation are described and the trace of a proper subgroup generator can, with very high probability, be computed directly, thus avoiding the probabilistic approach from [4].
Book ChapterDOI
Modular number systems: beyond the mersenne family
TL;DR: A new representation, called Modular Number System (MNS), is proposed, which allows efficient implementation of the modular arithmetic operations required in cryptography, and is more efficient than Montgomery for a very large class of numbers that do not belong to the large Mersenne family.
Book ChapterDOI
Fast Irreducibility and Subgroup Membership Testing in XTR
Arjen K. Lenstra,Eric R. Verheul +1 more
TL;DR: In this paper, a new general method to perform part of the set-up stage of the XTR system, namely finding the trace of a generator of a XTR group, is described.