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CRYPTO
2004
Springer

Asymptotically Optimal Communication for Torus-Based Cryptography

11 years 7 months ago
Asymptotically Optimal Communication for Torus-Based Cryptography
Abstract. We introduce a compact and efficient representation of elements of the algebraic torus. This allows us to design a new discretelog 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 F ∗ qn 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) log2 q 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.
Marten van Dijk, David P. Woodruff
Added 01 Jul 2010
Updated 01 Jul 2010
Type Conference
Year 2004
Where CRYPTO
Authors Marten van Dijk, David P. Woodruff
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