LUC: A New Public Key System
Peter J. Smith, Mick Lennon · 1993
We describe public key cryptosystems and analyse the RSA cryptosystem, pointing out a weakness (already known) of the RSA system. We define Lucas functions and derive some of their properties. Then we introduce a public key system based on Lucas functions instead of exponentiation. The computational requirements of the new system are only a little greater than those for the RSA system, and we prove that the new system is cryptographically stronger than the RSA system. Finally, we present a Lucas function equivalent of the DiffieHellman key negotiation method. Keyword Codes: E.3; K.4.2; K.6.5 Keywords: Data Encryption; Social Issues; Security and Protection 1. Public Key Encryption Public-key encryption was first discussed by Diffie and Hellman [1] as a general principle. The new concept which they introduced was the use of trapdoor functions for cryptography. A trapdoor function is a computable function whose inverse can be computed in a reasonable amount of time only if a (small) amou...