A symmetric additive homomorphic encryption scheme based on NTRU proxy rekeys

To address the problems that homomorphic encryption cannot achieve secret sharing and existing Paillier cryptosystems cannot resist quantum attacks and are not suitable for scenarios where encrypted data is only uploaded by the data owner, this paper designs an NTRU (number theory research unit) based symmetric additive homomorphic encryption-proxy rekey (PAHE-PRK) scheme using the ideas of proxy rekeying and symmetric encryption based on the approximate convention number problem and the ring fault-tolerant learning problem. research unit) Proxy ReKey-based Symmetric Additive Homomorphic Encryption scheme (Partially Additive Homomorphic Encryption-Proxy ReKey, PAHE-PRK). The proxy can not only perform homomorphic computation on the original ciphertext, but also re-encrypt the homomorphic key so that the trusted user can obtain the homomorphic key to decrypt the ciphertext, thus achieving secret sharing and privacy protection. Finally, the performance and security of the proposed scheme are discussed in comparison with the traditional Paillier cryptosystem and the proxy re-encryption scheme based on the fault-tolerant learning problem, showing that the proposed scheme is faster in encryption and decryption, has less computation and storage overhead, and is resistant to the indistinguishability under chosen plaintext attack (IND-CPA).