Compressible Multikey and Multi-Identity Fully Homomorphic Encryption

Abstract

With the development of new computing models such as cloud computing, user’s data are at the risk of being leaked. Fully homomorphic encryption (FHE) provides a possible way to fundamentally solve the problem. It enables a third party who does not know anything about the secret key and plaintexts to homomorphically perform any computable functions on the corresponding ciphertexts. In 2009, Gentry proposed the first FHE scheme. After that, its inefficiency has always been a bottleneck of the development of practical schemes and applications. At TCC 2019, Gentry and Halevi proposed the first compressible FHE scheme that enables the ratio of plaintext size to the ciphertext size (i.e., the compression rate) to reach1−εfor any smallε>0under the standard learning with errors (LWE) assumption. However, it is only a single-key one, where the homomorphic evaluation can only be performed over ciphertexts encrypted under the same key. Compared with single-key FHE, multikey FHE is more practical. Multikey FHE enables ciphertexts encrypted under different public keys to be homomorphically computed without having to decrypt these ciphertexts using their own private keys. In addition, in a multi-identity FHE scheme, only identity information and public parameters are required when encrypting, which simplifies certificate-based key management in public key infrastructure. In this paper, a new compressible ciphertext expansion technique is proposed. Then, we use this technique to construct a compressible multikey FHE scheme and a compressible multi-identity FHE scheme to overcome the bottleneck of bandwidth inefficiency in the multikey and multi-identity settings. The two schemes proposed in this paper make it possible that the objects of homomorphic operation can be the ciphertexts encrypted under different keys or different identities before compression, thus solving the single-key defect of the work of Gentry and Halevi.