How to Compress Rabin Ciphertexts and Signatures (and More)

Ordinarily, RSA and Rabin ciphertexts and signatures are log N bits, where N is a composite modulus; here, we describe how to “compress” Rabin ciphertexts and signatures (among other things) down to about (2/3)log N bits, while maintaining a tight provable reduction from factoring in the random oracle model. The computational overhead of our compression algorithms is small. We also improve upon Coron’s results regarding partial-domain-hash signature schemes, reducing by over 300 bits the hash output size necessary to prove adequate security.