<span style="color: black; mso-themecolor: text1;">Lattice-Based Multi-Key Homomorphic Encryption Scheme Without CRS

Multi-key homomorphic encryption is widely applied into outsourced computing and privacy-preserving applications in multi-user scenarios. However, the existence of CRS weakens the ability of users to independently generate public keys, and it is difficult to implement in decentralized systems or scenarios with low trust requirements. In order to reduce excessive reliance on public parameters, a multi-key homomorphic encryption scheme without pre-setting CRS is proposed based on a distributed key generation protocol. The proposed scheme does not require the pre-generation and distribution of CRS, which enhances the security and decentralization of the scheme. Furthermore, in order to further protect the plaintext privacy from each user, by embedding the specified target user into the ciphertext, this paper proposes an enhanced multi-key homomorphic encryption scheme that only allows only the target user to decrypt. Finally, this paper applies the proposed lattice-based multi-key homomorphic encryption scheme into the data submission stage of the perceived users, and thereby proposes a crowd-sensing scheme with privacy preservation.