Shorter Compact Representations in Real Quadratic Fields

Compact representations are explicit representations of algebraic numbers with size polynomial in the logarithm of their height. These representations enable much easier manipulations with larger algebraic numbers than would be possible using a standard representation and are necessary, for example,...

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Bibliographic Details
Published inNumber Theory and Cryptography pp. 50 - 72
Main Authors Silvester, Alan K., Jacobson, Michael J., Williams, Hugh C.
Format Book Chapter
LanguageEnglish
Published Berlin, Heidelberg Springer Berlin Heidelberg 2013
SeriesLecture Notes in Computer Science
Subjects
compact representation
fundamental unit
infrastructure
real quadratic field
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Summary:Compact representations are explicit representations of algebraic numbers with size polynomial in the logarithm of their height. These representations enable much easier manipulations with larger algebraic numbers than would be possible using a standard representation and are necessary, for example, in short certificates for the unit group and ideal class group. In this paper, we present two improvements that can be used together to reduce significantly the sizes of compact representations in real quadratic fields. We provide analytic and numerical evidence demonstrating the performance of our methods, and suggesting that further improvements using obvious extensions are likely not possible.
ISBN:9783642420009
3642420001
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-642-42001-6_5