An Improved Real-Quadratic-Field-Based Key Exchange Procedure |
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Authors: | Michael J Jacobson Jr Renate Scheidler Hugh C Williams |
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Affiliation: | (1) University of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N 1N4, Canada |
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Abstract: | To date, the only non-group structure that has been suitably
employed as the key space for Diffie-Hellman-type cryptographic key
exchange is the infrastructure of a real quadratic (number or
function) field. We present an implementation of a Diffie-Hellman-type protocol based on real quadratic number field arithmetic
that
provides a significant improvement in performance over previous
versions of this scheme. This dramatic speed-up is achieved by
replacing the ordinary multiplication and reduction procedures for
reduced ideals by a new version of the NUCOMP algorithm due to Shanks. |
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Keywords: | Cryptographic key exchange Real quadratic field Reduced principal ideal NUCOMP |
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