A Provably Secure Additive and Multiplicative Privacy Homomorphism

Privacy homomorphisms (PHs) are encryption transformations mapping a set of operations on cleartext to another set of operations on ciphertext. If addition is one of the ciphertext operations, then it has been shown that a PH is insecure against a chosen-cleartext attack. Thus, a PH allowing full arithmetic on encrypted data can be at best secure against known-cleartext attacks. We present one such PH (none was known so far) which can be proven secure against known-cleartext attacks, as long as the ciphertext space is much larger than the cleartext space. Some applications to delegation of sensitive computing and data and to e-gambling are briefly outlined.