Abstract
Aiming at the problems of large ciphertext size and low efficiency in the current secure multi-party computation (SMC) protocol based on fully homomorphic encryption (FHE), the paper proves that the fully homomorphic encryption scheme that supports multi-bit encryption proposed by Chen Li et al. satisfies the key homomorphism. Based on this scheme and threshold decryption, a three-round, interactive, leveled, secure multi-party computation protocol under the Common Random String (CRS) model is designed. The protocol is proved to be safe under the semi-honest model and the semi-malicious model. From the non-interactive zero-knowledge proof, it can be concluded that the protocol is also safe under the malicious model. Its security can be attributed to the Decisional Learning With Errors (DLWE) and a variant of this problem (some-are-errorless LWE). Compared with the existing secure multi-party computation protocol based on fully homomorphic encryption under the CRS model, the ciphertext size of this protocol is smaller, the efficiency is higher, the storage overhead is smaller, and the overall performance is better than the existing protocol.
Highlights
Due to the secure multi-party computation (SMC) protocol under the Common Random String (CRS) model, if the protocol is proven to be safe under the semi-malicious model, the protocol can be converted into a protocol under the malicious model by non-interactive zero-knowledge proofs (NIZKs) [21]
Based on the efficient Fully Homomorphic Encryption (FHE) scheme, a leveled, multi-bit, multi-key, secure multi-party computation protocol under the CRS model is constructed in this paper
This protocol has a total of three rounds of communication, which is proven to be safe in a semi-honest and semi-malicious environment, and the security is based on Decisional Learning With Errors (DLWE) and the some-are-errorless
Summary
2021, Tang et al [16] proved the key homomorphism of the multi-bit fully homomorphic encryption scheme proposed by Li [17] Based on this scheme, a three-round, secure, multi-party computation protocol that could support multi-bit encryption under the CRS model was designed, which further reduced the complexity of the NAND gate. To solve the problems mentioned above, a three-round secure multi-party computation protocol that can resist malicious opponents under the CRS model is designed in this paper with the help of the New Fully Homomorphic Encryption (NFHE) scheme [18] and threshold decryption. Compared with the existing secure multi-party computation protocol under the CRS model, the ciphertext size of the protocol is smaller, and the overall performance is better than the existing protocol
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