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A Privacy Homomorphism Allowing Field Operations on Encrypted Data

Privacy homomorphisms (PHs) are encryption transformations that allow direct computation on en-crypted data. Known secure PHs allow addition and multiplication to be carried out on encrypted data, but do not allow computation of inverses. We present in this paper a PH which allows addition, multiplication and multiplicative inverse computation to be performed on encrypted data. An additive PH can at most be secure against a known-cleartext attack; unfortunately, in its current state the new proposal is only secure against ciphertext-only attacks.