Geometric Key Establishment

Arkady Berenstein; Leon Chernyak

Paper 2004/239

Geometric Key Establishment

Arkady Berenstein and Leon Chernyak

Abstract

We propose a new class of key establishment schemes which are based on geometric generalizations of the classical Diffie-Hellman. The simplest of our schemes – based on the geometry of the unit circle – uses only multiplication of rational numbers by integers and addition of rational numbers in its key creation. Its first computer implementation works significantly faster than all known implementations of Diffie-Hellman. Preliminary estimations show that our schemes are resistant to attacks. This resistance follows the pattern of the discrete logarithm problem and hardness of multidimensional lattice problems

Note: a few comments added and a few typos corrected

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. to appear in the AMS series ''Comtemporary Mathematics''
Keywords: a new class of key establishment protocols
Contact author(s): arkadiy @ math uoregon edu
History: 2006-01-27: last of 3 revisions; 2004-09-16: received; See all versions
Short URL: https://ia.cr/2004/239
License: CC BY

BibTeX

@misc{cryptoeprint:2004/239,
      author = {Arkady Berenstein and Leon Chernyak},
      title = {Geometric Key Establishment},
      howpublished = {Cryptology {ePrint} Archive, Paper 2004/239},
      year = {2004},
      url = {https://eprint.iacr.org/2004/239}
}