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On the use of continued fractions for mutual authentication

The purpose of this paper is to present an improvement of the Needham-Schroder public key protocol. This new protocol will use partial quotients issue from the continued fraction expansion of some irrational numbers to secure the authentication between two principals. We introduce a new approach in the use of pseudo-random numbers, because besides using these numbers to provide uniqueness and timeliness guarantees, we use them to ensure that nobody can guess the identity of the sender. We also keep this new protocol secure against the Lowe attack, without taking the solution suggested by Lowe. This protocol remains fast although we compute some partial quotients during the authentication process.