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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