Optimal asymmetric encryption

Abstract

Given an arbitrary fc-bit to k-bit trapdoor permutation f and a hash function, we exhibit an encryption scheme for which (i) any string x of length slightly less than k bits can be encrypted as f(rx), where rx is a simple probabilistic encoding of x depending on the hash function; and (ii) the scheme can be proven semantically secure assuming the hash function is “ideal.” Moreover, a slightly enhanced scheme is shown to have the property that the adversary can create ciphertexts only of strings for which she “knows” the corresponding plaintexts— such a scheme is not only semantically secure but also non-malleable and secure against chosen-ciphertext attack.