Asymptotically Optimal Communication for Torus-Based Cryptography View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2004

AUTHORS

Marten van Dijk , David Woodruff

ABSTRACT

We introduce a compact and efficient representation of elements of the algebraic torus. This allows us to design a new discrete-log based public-key system achieving the optimal communication rate, partially answering the conjecture in [4]. For n the product of distinct primes, we construct efficient ElGamal signature and encryption schemes in a subgroup of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$F_{q^n}^*$\end{document} in which the number of bits exchanged is only a φ(n)/n fraction of that required in traditional schemes, while the security offered remains the same. We also present a Diffie-Hellman key exchange protocol averaging only φ(n)log2q bits of communication per key. For the cryptographically important cases of n=30 and n=210, we transmit a 4/5 and a 24/35 fraction, respectively, of the number of bits required in XTR [14] and recent CEILIDH [24] cryptosystems. More... »

PAGES

157-178

Book

TITLE

Advances in Cryptology – CRYPTO 2004

ISBN

978-3-540-22668-0
978-3-540-28628-8

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-540-28628-8_10

DOI

http://dx.doi.org/10.1007/978-3-540-28628-8_10

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1034131114


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