Proceedings of the
The Nineteenth International Conference on Computational Intelligence and Security (CIS 2023)
December 1 – 4, 2023, Haikou, China
Improved Circular Secure Homomorphic Encryption Scheme
PLA Strategic Support Force Information Engineering University, Zhengzhou, China.
ABSTRACT
Fully homomorphic encryption can perform various operations on encrypted data without decryption, and the decryption result is the same as that of corresponding operations on plaintext. Therefore, fully homomorphic encryption can be applied to privacy protection of cloud data and ciphertext computing. In order to realize the "homomorphism", module-switching technology, key-switching technology and relinearization technology are often used to construct homomorphic encryption schemes. It is necessary to encrypt the function of the private key as the evaluate key. Therefore, there is a circular secure assumption in construction of fully homomorphic encryption scheme. The homomorphic encryption scheme satisfying circular secure can remove the assumption, that is, the scheme still satisfies provable semantic security when encrypting the function of private key. In this paper, the improved public key homomorphic encryption scheme with circular secure is proposed. The encryption process without rejection sampling technology, which leads to the optimization of the encryption algorithm. At the same time, Rényi divergence is introduced into the circular secure proof of the scheme, which reduces the system parameters from super-polynomial level to polynomial level. Accordingly, the public key and ciphertext size are effectively reduced, the computational complexity of ciphertext homomorphic operation is optimized, and the performance of homomorphic encryption scheme is improved. The encryption cost of the optimized scheme is about 20% ∼ 33% of that of RS.KDM.PKFHE scheme.
Keywords: Homomorphic encryption, Circular secure, Noise flooding technique, Rényi divergence.
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PLA Strategic Support Force Information Engineering University, Zhengzhou, China.
ABSTRACT
Fully homomorphic encryption can perform various operations on encrypted data without decryption, and the decryption result is the same as that of corresponding operations on plaintext. Therefore, fully homomorphic encryption can be applied to privacy protection of cloud data and ciphertext computing. In order to realize the "homomorphism", module-switching technology, key-switching technology and relinearization technology are often used to construct homomorphic encryption schemes. It is necessary to encrypt the function of the private key as the evaluate key. Therefore, there is a circular secure assumption in construction of fully homomorphic encryption scheme. The homomorphic encryption scheme satisfying circular secure can remove the assumption, that is, the scheme still satisfies provable semantic security when encrypting the function of private key. In this paper, the improved public key homomorphic encryption scheme with circular secure is proposed. The encryption process without rejection sampling technology, which leads to the optimization of the encryption algorithm. At the same time, Rényi divergence is introduced into the circular secure proof of the scheme, which reduces the system parameters from super-polynomial level to polynomial level. Accordingly, the public key and ciphertext size are effectively reduced, the computational complexity of ciphertext homomorphic operation is optimized, and the performance of homomorphic encryption scheme is improved. The encryption cost of the optimized scheme is about 20% ∼ 33% of that of RS.KDM.PKFHE scheme.
Keywords: Homomorphic encryption, Circular secure, Noise flooding technique, Rényi divergence.
Download PDF