An Improved Real-Quadratic-Field-Based Key Exchange Procedure

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.

• Type: Journal
• Year: 2006
• Where: JOC
• Authors: Michael J. Jacobson Jr., Renate Scheidler, Hugh C. Williams
• Keywords: Diffie-Hellman Type, Diffie-Hellman Type Protocol, JOC 2006, Real Quadratic Number