Chosen-ciphertext security for any one-way cryptosystem

Abstract

For two years, public key encryption has become an essential topic in cryptography, namely with security against chosen-ciphertext attacks. This paper presents a generic technique to make a highly secure cryptosystem from any partially trapdoor one-way function, in the random oracle model. More concretely, any suitable problem providing a one-way cryptosystem can be efficiently derived into a chosen-ciphertext secure encryption scheme. Indeed, the overhead only consists of two hashing and a XOR. As application, we provide the most efficient El Gamal encryption variant, therefore secure relative to the computational Diffie- Hellman problem. Furthermore, we present the first scheme whose security is relative to the factorization of large integers, with a perfect reduction (factorization is performed within the same time and with identical probability of success as the security break).