The current multikey fully homomorphic encryption (MKFHE) needs to add exponential noise in the distributed decryption phase to ensure the simulatability of partial decryption. Such a large noise causes the ciphertext modulus of the scheme to increase exponentially compared to the single‐key fully homomorphic encryption (FHE), further reducing the efficiency of the scheme and making the hardness problem on the lattice on which the scheme relies have a subexponential approximation factor (which means that the security of the scheme is reduced). To address this problem, this paper analyzes in detail the noise in partial decryption of the MKFHE based on the learning with error (LWE) problem. It points out that this part of the noise is composed of private key and the noise in initial ciphertext. Therefore, as long as the encryption scheme is leak‐resistant and the noise in partial decryption is independent of the noise in the initial ciphertext, the semantic security of the ciphertext can be guaranteed. In order to make the noise in the initial ciphertext independent of the noise in the partial decryption, this paper proves the smudging lemma on discrete Gaussian distribution and achieves this goal by multiplying the initial ciphertext by a “dummy” ciphertext with a plaintext of 1. Based on the above method, this paper removes the exponential noise in the distributed decryption phase for the first time and reduces the ciphertext modulus of MKFHE from 2 ω ( λ L log λ ) to 2 O ( λ + L ) as the same level as the FHE.The current multikey fully homomorphic encryption (MKFHE) needs to add exponential noise in the distributed decryption phase to ensure the simulatability of partial decryption. Such a large noise causes the ciphertext modulus of the scheme to increase exponentially compared to the single‐key fully homomorphic encryption (FHE), further reducing the efficiency of the scheme and making the hardness problem on the lattice on which the scheme relies have a subexponential approximation factor (which means that the security of the scheme is reduced). To address this problem, this paper analyzes in detail the noise in partial decryption of the MKFHE based on the learning with error (LWE) problem. It points out that this part of the noise is composed of private key and the noise in initial ciphertext. Therefore, as long as the encryption scheme is leak‐resistant and the noise in partial decryption is independent of the noise in the initial ciphertext, the semantic security of the ciphertext can be guaranteed. In order to make the noise in the initial ciphertext independent of the noise in the partial decryption, this paper proves the smudging lemma on discrete Gaussian distribution and achieves this goal by multiplying the initial ciphertext by a “dummy” ciphertext with a plaintext of 1. Based on the above method, this paper removes the exponential noise in the distributed decryption phase for the first time and reduces the ciphertext modulus of MKFHE from 2 ω ( λ L log λ ) to 2 O ( λ + L ) as the same level as the FHE.

IET Information SecurityJan 1, 20251 citation

On the exact decryption range for Gentry–Halevi's implementation of fully homomorphic encryption

Masaya Yasuda, Kazuhiro Yokoyama, Takeshi Shimoyama +2 more

Abstract In this paper, we revisit the fully homomorphic encryption (FHE) scheme implemented by Gentry and Halevi, which is just an instantiation of Gentry's original scheme based on ideal lattices. Their FHE scheme starts from a somewhat homomorphic encryption (SHE) scheme, and its decryption range is deeply related with the FHE construction. Gentry and Halevi gave an experimental evaluation of the decryption range, but theoretical evaluations have not been given so far. Moreover, we give a theoretical upper bound, and reconsider suitable parameters for theoretically obtaining an FHE scheme. In particular, while Gentry and Halevi use the Euclidean norm evaluation in the noise management of ciphertexts, our theoretical bound enables us to use the ∞-norm evaluation, and hence it helps to lower the difficulty of controlling the noise density of ciphertexts.Abstract In this paper, we revisit the fully homomorphic encryption (FHE) scheme implemented by Gentry and Halevi, which is just an instantiation of Gentry's original scheme based on ideal lattices. Their FHE scheme starts from a somewhat homomorphic encryption (SHE) scheme, and its decryption range is deeply related with the FHE construction. Gentry and Halevi gave an experimental evaluation of the decryption range, but theoretical evaluations have not been given so far. Moreover, we give a theoretical upper bound, and reconsider suitable parameters for theoretically obtaining an FHE scheme. In particular, while Gentry and Halevi use the Euclidean norm evaluation in the noise management of ciphertexts, our theoretical bound enables us to use the ∞-norm evaluation, and hence it helps to lower the difficulty of controlling the noise density of ciphertexts.

Journal of Mathematical CryptologyMar 12, 20143 citations

Fully Homomorphic Encryption with Auxiliary Inputs

Fuqun Wang, Kunpeng Wang

Lecture notes in computer scienceJan 1, 20159 citations

Quantum fully homomorphic encryption on single qubit

Min Liang

Suppose some data have been encrypted, can you compute with the data without decrypting them? This problem has been studied as homomorphic encryption and blind computing. We consider this problem in the context of quantum information processing, and present the definitions of quantum homomorphic encryption (QHE) and quantum fully homomorphic encryption (QFHE). Then, based on quantum one-time pad (QOTP), we construct a symmetric QFHE scheme, where the evaluate algorithm depends on the secret key. This scheme permits any unitary transformation on any $n$ -qubit state that has been encrypted. Compared with classical homomorphic encryption, the QFHE scheme has perfect security. Finally, we also construct a QOTP-based symmetric QHE scheme, where the evaluate algorithm is independent of the secret key.Suppose some data have been encrypted, can you compute with the data without decrypting them? This problem has been studied as homomorphic encryption and blind computing. We consider this problem in the context of quantum information processing, and present the definitions of quantum homomorphic encryption (QHE) and quantum fully homomorphic encryption (QFHE). Then, based on quantum one-time pad (QOTP), we construct a symmetric QFHE scheme, where the evaluate algorithm depends on the secret key. This scheme permits any unitary transformation on any $n$-qubit state that has been encrypted. Compared with classical homomorphic encryption, the QFHE scheme has perfect security. Finally, we also construct a QOTP-based symmetric QHE scheme, where the evaluate algorithm is independent of the secret key.

Apr 18, 20130 citations

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-qubit state that has been encrypted. Compared with classical homomorphic encryption, the QFHE scheme has perfect security. Finally, we also construct a QOTP-based symmetric QHE scheme, where the evaluate algorithm is independent of the secret key.