On the Security of Williams Based Public Key Encryption Scheme

In 1984, H.C. Williams introduced a public key cryptosystem whose security is as intractable as factorization. Motivated by some strong and interesting cryptographic properties of the intrinsic structure of this scheme, we present a practical modification thereof that has very strong security properties. We establish, and prove, a generalization of the “sole-samplability” paradigm of Zheng-Seberry (1993) which is reminiscent of the plaintext-awareness concept of Bellare et. al. The assumptions that we make are both well-defined and reasonable. In particular, we do not model the functions as random oracles. In essence, the proof of security is based on the factorization problem of any large integer n = pq and Canetti’s “oracle hashing” construction introduced in 1997. Another advantage of our system is that we do not rely on any special structure of the modulus n = pq, nor do we require any specific form of the primes p and q. As our main result we establish a model which implies security attributes even stronger than semantic security against chosen ciphertext attacks.