This paper proposes an efficient identity-based leveled fully homomorphic encryption (IBFHE) scheme over ideal lattice. First, we achieve an identity-based encryption (IBE) scheme in dual-LWE cryptosystem. Then, we take advantage of the eigenvector method to compile the IBE scheme into an IBFHE scheme. Compared with the previous scheme, our scheme is of shorter key size, smaller storage, and higher efficiency, owing to a new trapdoor generation function and algebraic structure of ideal lattice. The security analysis shows that our scheme is selective-identity secure against chosen-plaintext attacks in the standard model.
This paper proposes an efficient identity-based leveled fully homomorphic encryption (IBFHE) scheme over ideal lattice. First, we achieve an identity-based encryption (IBE) scheme in dual-LWE cryptosystem. Then, we take advantage of the eigenvector method to compile the IBE scheme into an IBFHE scheme. Compared with the previous scheme, our scheme is of shorter key size, smaller storage, and higher efficiency, owing to a new trapdoor generation function and algebraic structure of ideal lattice. The security analysis shows that our scheme is selective-identity secure against chosen-plaintext attacks in the standard model.
An efficient identity-based encryption (IBE) scheme over lattice is proposed in this paper. Under the hardness of the learning with errors (LWE) problem, the proposed scheme is semantic secure against adaptive chosen identity and chosen plaintext attack in the standard model. To improve the efficiency of the lattice-based IBE scheme, unlike the identity string is encoded into a matrix by a group of public matrices in several known constructions, the identity string of l bits is encoded into a vector with the help of l+1 vectors in this paper. With the help of this idea, we achieve the private key extraction of IBE scheme at the same lattice. Then, the public key of the proposed scheme only consists of one n×m matrix and l+1 vectors, compared with that the public keys of the known lattice-based IBE schemes all consist as a group of n×m matrices. Hence, the public key size of this scheme is shorter than that of the known constructions.
Identity‐based fully homomorphic encryption (IBFHE) provided a fundamental solution to the problem of huge public key size that exposed in fully homomorphic encryption (FHE) schemes, thus it is significant to make FHE become more practical. In recent years, the construction of IBFHE schemes were mainly based on lattices due to their conjectured resistance against quantum cryptanalysis, however, which makes these cryptosystems further unpractical. The main reason is the trapdoor function on which the scheme was based is rather complex for practical and the ciphertext size is too large. In this study, the authors propose an efficient batch IBFHE scheme, which can be proven secure from the standard LWE assumption in the standard model. The first contribution of this work is that the authors construct an efficient batch version of MP12 preimage sampling algorithm, which can efficiently generate identity keys for multi‐bit IBE schemes. Based on that, the authors construct an asymptotically‐faster multi‐bit IBE scheme as the second contribution. The third contribution is that the authors transform the multi‐bit IBE scheme to batch IBFHE scheme which supports to encrypt any message in . Compared with the similar schemes, the authors show their schemes are essentially improved.
Using a known lattice-based chosen plain-text secure encryption scheme and the Bonsai trees primitive, a identity-based encryption (IBE) scheme is proposed in this paper. A public matrices chosen rule that has been used in a known efficient lattice-based chosen ciphtertext secure encryption scheme is used in this paper to reduce the public key size and the message-to ciphtertext expanse factor. Under the hardness of the decision variant of the learning with errors (LWE) problem, we prove that the proposed IBE scheme is indistinguishable against the adaptive chosen identities and chosen-plaintext attack in the standard model. Since a new public key chosen rule is used in our design scheme, the public key size of the proposed scheme would be short. Moreover, the message-to-ciphtertext expanse factor of this scheme is also controlled efficiently which is nearly closed to that of Gentry's scheme. Due to the quantum intractability of the LWE problem on which the scheme is based, the proposed IBE scheme is secure even in quantum-era.
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.
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).