Generalized Public Key Transformations with Side Information

This paper presents results on generalized public key cryptography with exponentials modulo primes and composite numbers where the mapping is not one-to-one and the uniqueness is achieved by additional side information. Such transformations may be used for oblivious transfer and generate events of specific probabilities. Introduction This paper presents generalized public key transformations that require side information as extension to earlier proposals on cubic and quartic transformations [1],[2],[3]. Specifically, we present results on quintic and sextic transformations and then show how further generalizations may be made. For background papers on cryptographic protocols, the reader may see [4]-[7]. The properties of the quintic transformation For quintic transformation c = m5 mod p, five different values of message m would give the same cipher c, where the value of prime p is given by p = 5k + 1. The quintic roots of 1 would be 1, α, α2, α3 and α4 and they are calculated by solving the equation x5 − 1 = 0 (1) (x − 1)(x4 + x3 + x2 + x1 + 1)=0 (2) One of the roots is 1, and the other four roots are obtained by the following equation: (x4 + x3 + x2 + x1 + 1)=0 We convert the above quartic equation into depressed quartic equation by substituting