Security analysis of homomorphic encryption scheme for cloud computing: Known-plaintext attack

We consider cryptosystems for homomorphic encryption schemes based on the Residue Number System (RNS) and Secret Sharing Schemes. One of their disadvantages is that they are directly related to data redundancy, and hence, increasing the size of the storage. To minimize it, homophonic encryption can be combined with the arithmetic coding known as Chinese remainder theorem. We describe a new method of cryptanalysis based on a property of RNS and theory of numbers. We prove that an attacker needs only η · [log
₂
log
₂
(k · p
_n
)l arbitrary generated input files that form the “known-plaintext”, where p
_i
is moduli RNS, to calculate the secret key required to decrypt the entire data.