Public-key cryptography from different assumptions: A multi-bit version

At STOC 2010, Applebaum, Barak and Wigderson introduced three new public-key cryptosystems based on combinatorial assumptions. In their paper, only encryption of bits has been considered. In this paper, we focus on one of their schemes and adapt it to encrypt a constant number of bits in a single ciphertext without changing the size of the public key. We add wire-tap channel techniques to improve the security level of our scheme, thus reaching indistinguishability. We show that it is homomorphic for the XOR operation on bit strings. We also suggest concrete parameters for a first instantiation of our scheme.