Research on algorithms of data encryption scheme that supports homomorphic arithmetical operations

An efficient homomorphic encryption scheme called CESIL was proposed to meet the requirements of operating on encrypted data when protecting users' privacy in computing services. CESIL included key generation algorithm, encryption algorithm, decryption algorithm and calculation algorithm. In CESIL, a polynomial coefficient vector ring was established by defining addition and multiplication using polynomial ring; by using ideal lattice, the vector ring was partitioned into many residue classes to produce a quotient ring and its representative set; the plaintext was encrypted by mapping it to a representative and replacing the representative with another element in the same residue class. The features of operations in quotient ring ensured CESIL operate on encrypted data. Furthermore, the fast Fourier transform (FFT) algorithm was used to increase the efficiency and decrease the length of key. Theoretical analysis and experimental results show that CESIL is semantically secure, and can do addition and multiplication operations on encrypted data homomorphically in a specific scope. Comparing to some existing homomorphic encryption schemes, the CESIL runs efficiently, and has shorter length in key and ciphertext. Thus, the CESIL fits the practical applications better.