This paper proposes a generic construction of CCA-secure fully homomorphic encryption (FHE) scheme.First, we introduce a new primitive called multi-identity fully homomorphic encryption, which works in the multi-identity setting; that is, homomorphic evaluation can performed on ciphertexts created with different identities.Then, we propose an IND-sID-CPA secure multi-identity leveled FHE scheme over lattice.Finally, we present CCA-secure FHE from our proposed multi-identity FHE scheme and strongly EUF-CMA secure signature.The security analysis shows that our FHE scheme is CCA2-secure when the evaluation key is unavailable to the adversary, and remains CCA1-secure when the evaluation key is exposed in the standard model.
This paper proposes a generic construction of CCA-secure fully homomorphic encryption (FHE) scheme.First, we introduce a new primitive called multi-identity fully homomorphic encryption, which works in the multi-identity setting; that is, homomorphic evaluation can performed on ciphertexts created with different identities.Then, we propose an IND-sID-CPA secure multi-identity leveled FHE scheme over lattice.Finally, we present CCA-secure FHE from our proposed multi-identity FHE scheme and strongly EUF-CMA secure signature.The security analysis shows that our FHE scheme is CCA2-secure when the evaluation key is unavailable to the adversary, and remains CCA1-secure when the evaluation key is exposed in the standard model.
The lattice-based multi-identity fully homomorphic encryption scheme combines the quantum security of lattice cryptography with the advantage of identity-based encryption. However, existing schemes face challenges such as large key sizes, inefficient ciphertext expansion processes, and reliance on outdated trapdoor designs, limiting their compactness and practicality. In this study, we propose a novel Compact Multi-Identity Fully Homomorphic Encryption Scheme (WZ-MIBFHE) that eliminates the need for fresh ciphertexts during expansion. First, we construct a compact identity-based encryption scheme by combining the YJW23 trapdoor and ABB10 under the standard model, proving its IND-sID-CPA security. The scheme is then adapted to ensure correctness and security when integrated with the decomposition method for ciphertext expansion. This adaptation also utilizes approximation errors to reduce overall noise. Finally, we expand the modified IBE scheme’s ciphertext using the decomposition method to construct the WZ-MIBFHE scheme. Compared to existing methods, WZ-MIBFHE reduces the lattice dimension to nlogq+logbq, improves public and private key sizes, and significantly lowers ciphertext expansion rates by removing the need for fresh ciphertexts. These improvements enhance both the compactness and efficiency of the scheme, making it a promising solution for multi-identity homomorphic encryption.
Fully data using only public information. So far, most FHE schemes are CPA secure. In PKC 2017, Canetti et al. extended the generic transformation of Boneh, Canetti, Halevi and Katz to turn any multi-key identity-based FHE scheme into a CCA1-secure FHE scheme. Their main construction of multi-key identity-based FHE is from probabilistic indistinguishability obfuscation (PIO) and statistical trapdoor encryption. We show that the above multi-key identity-based FHE is not secure by giving an attack. Then we give a solution to avoid the attack and redesign a more succinct and efficient multi-key identity-based FHE scheme. Compared with the scheme of Canetti et al., ours has smaller secret key of one identity and more efficient homomorphic operations. Thus we obtain a more efficient CCA1 secure FHE scheme.
Multi-key fully homomorphic encryption (MKFHE), a generalization of fully homomorphic encryption (FHE), enables a computation over encrypted data under multiple keys. The first MKFHE schemes were based on the NTRU primitive, however these early NTRU based FHE schemes were found to be insecure due to the problem of over-stretched parameters. Recently, in the case of standard (non-multi key) FHE a secure version, called FINAL, of NTRU has been found. In this work we extend FINAL to an MKFHE scheme, this allows us to benefit from some of the performance advantages provided by NTRU based primitives. Thus, our scheme provides competitive performance against current state-of-the-art multi-key TFHE, in particular reducing the computational complexity from quadratic to linear in the number of keys.
Fully homomorphic encryption (FHE) has important applications in cloud computing. However, almost all fully homomorphic encryption schemes share two common flaws that they all use large-scale secret keys and some operations are inefficient. In this paper, the 'special b' variant of the learning with errors problem (bLWE) is presented, and helps us construct the first circularly secure key switching process which can replace the key switching process and similar re-linearisation process used by the existing FHE schemes. Then, we present an efficient FHE. Compared with Brakerski's scheme, our scheme reduces L secret keys to one and is more efficient. Finally, we prove the chosen-plaintext attack (CPA) security of the fully homomorphic scheme and the circular security of key switching process in standard model under the learning with errors problem (LWE) assumption.
With the development of quantum theory, traditional encryption algorithms are facing enormous challenges. Once quantum computers are available, existing encryption systems will no longer be secure. The lattice cipher is proven by theory to be a new type of encryption scheme, which can resist quantum algorithm. It has the property of fast computing speed and small space occupation, hence, it has become a hot issue in today??s research. The identity-based encryption scheme can improve the utilization of storage space and facilitate user public key management. Consequently, this paper based on the hard problem of learning with errors (LWE), constructs an identity-based matrix encryption scheme at first, then applies the improved key switching technology to reduce the dimension of homomorphic ciphertext to normal, and uses the mode conversion technique to reduce noise, realizing matrix homo-morphic operation, and getting an identity-based matrix (level) fully homomorphic encryption scheme. The scheme uses matrices as the storage structure, which has greatly improved the processing capability compared to other single-bit schemes. The scheme not only satisfies the addition and Hadamard product of the matrix, but also supports matrix dot multiplication. The experimental results show that compared with other methods, the improved key switching technology in this paper inputs less noise. Through the difficulty of the LWE problem, it is proven that the scheme satisfies IND-sID-CPA (indistinguishability-selective identity-chosen plaintext attack).