Optimal Asymmetric Encryption-How to Encrypt with RSA

TLDR: A slightly enhanced scheme is shown to have the property that the adversary can create ciphertexts only of strings for which the adversary knows the corresponding plaintexts, and is not only semantically secure but also non-malleable and secure against chosen-ciphertext attack.

Abstract: Given an arbitrary k-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. Department of Computer Science & Engineering, Mail Code 0114, University of California at San Diego, 9500 Gilman Drive, La Jolla, CA 92093. E-mail: mihir@cs.ucsd.edu † Department of Computer Science, University of California at Davis, Davis, CA 95616, USA. E-mail: rogaway@cs.ucdavis.edu