An improved real-quadratic-field-based key exchange procedure

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. Key words. Cryptographic key exchange, Real quadratic field, Reduced principa