Public key cryptosystems based on Boolean permutations and their applications

In this paper we propose the use of Boolean permutations to design public key cryptosystems. The security of the cryptosystems is based on the difficulty of inverting Boolean permutations. Using two Boolean permutations for which the inverses are easy to find, one can construct a composite Boolean permutation which is hard to invert. The paper proposes three such Boolean permutation based public key systems. The paper also consider applications of a Boolean permutation based public key system to digital signatures and shared signatures.