Cryptology ePrint Archive: Report 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

Category / Keywords: public-key cryptography / a new class of key establishment protocols

Publication Info: to appear in the AMS series ''Comtemporary Mathematics''

Date: received 14 Sep 2004, last revised 26 Jan 2006

Contact author: arkadiy at math uoregon edu

Available format(s): PDF | BibTeX Citation

Note: a few comments added and a few typos corrected

Version: 20060127:005007 (All versions of this report)

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