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, 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.
Keywordscompact representation real quadratic field fundamental unit infrastructure
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