A Cryptanalysis of the Original Domingo-Ferrer's Algebraic Privacy Homomophism

We propose a cryptanalysis of the original Domingo-Ferrer’s algebraic privacy homomorphism. We show that the scheme over Zn can be broken by d + 1 known plaintexts in O(d3 log n) time when it has d times expansion through the encryption. Furthermore even when the public modulus n is kept secret, it can be broken by d + 2 known plaintexts in time at most O(d5 log(dn)).