The Cubic Public-Key Transformation

Abstract

This note proposes the use of the cubic transformation for public-key applications and random event and number generation, in a manner akin to the Rabin cipher. Transformations modulo a prime p or a composite n = pq, where p and q are primes, are so used that each transformed value has only three roots. Such a transformation, together with additional tag information, makes it possible to uniquely invert each transformed value. The effectiveness of the method as a random number generator (used in a variant with nine roots) comes from the fact that the cryptanalyst must contend with a ninefold branching at each step.