Algorithms for improved performance in cryptographic protocols.

Public key cryptographic algorithms provide data authentication and non-repudiation for electronic transmissions. The mathematical nature of the algorithms, however, means they require a significant amount of computation, and encrypted messages and digital signatures possess high bandwidth. Accordingly, there are many environments (e.g. wireless, ad-hoc, remote sensing networks) where public-key requirements are prohibitive and cannot be used. The use of elliptic curves in public-key computations has provided a means by which computations and bandwidth can be somewhat reduced. We report here on the research conducted in an LDRD aimed to find even more efficient algorithms and to make public-key cryptography available to a wider range of computing environments. We improved upon several algorithms, including one for which a patent has been applied. Further we discovered some new problems and relations on which future cryptographic algorithms may be based