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IET Information Security

Efficient batch identity‐based fully homomorphic encryption scheme in the standard model

Mingxing Hu, Qing Ye, Yongli Tang

Published Apr 5, 2018• 5 citations
Publisher

Abstract

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.

DOI
10.1049/iet-ifs.2017.0567

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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.
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.
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.
Abstract Based on the learning with errors over rings (RLWE) assumption, a leveled fully homomorphic encryption (FHE) by the approximate eigenvector method under the same public key is proposed, which security can be reduced to the shortest vector problem on ideal lattices in the worst case. And the leveled FHE under different public keys is realized by the secret key switching without dimension reduction. Combine the public key of leveled FHE with the identity, we bring forward an efficient identity‐based leveled FHE scheme from the RLWE assumption. The security analysis shows that our identity‐based leveled FHE scheme is selective‐ID secure against chosen‐plaintext attacks in the random oracle model. And the efficiency analysis and simulation results show that the proposed identity‐based leveled FHE scheme is much more efficient than Gentry's and Wang's identity‐based cryptosystems based on the learning with errors assumption. Copyright © 2016 John Wiley & Sons, Ltd.
There has been a great deal of work on improving the efficiency of fully homomorphic encryption (FHE) scheme. Our approach, in this regard, is to use the idea of packed ciphertexts to construct a multi-bit FHE with a short public key on the basis of the learning with errors (LWE) problem. More specifically, our FHE scheme builds on a basic encryption scheme that chooses LWE samples from the Gaussian distribution and adds Gaussian error to it. This results in decreasing the number of LWE samples from 2nlogq to n + 1. We prove that our FHE scheme is pragmatically feasible and its security relies on the hardness of the LWE problem. In addition, we form a new process of key switching for multi-bit FHE based on the ideas adopted by Brakerski et al. for optimizing the process of key switching. Finally, we analyze and compare the concrete parameters between our FHE scheme and BGH13 scheme. The result shows that compared with the BGH13 scheme, our scheme has a smaller public key by a factor about logq.
In this work, we present the first lattice-based construction of batched IBE in the standard model, whose security is proven under the succinct LWE assumption. Prior batched IBE schemes are only known either based on pairing-based assumptions or in the random oracle model. Moreover, our scheme is shown to be highly efficient, as the master public key, decryption key, and ciphertext are independent of the batch size B. Technically, we mainly rely on an insightful observation: batched IBE can be obtained solely from Inner-Product Encryption (IPE). To satisfy the efficiency requirements of batched IBE, we require an IPE scheme that owns two important features: decomposable key generation and compact components. Finally, we show how to construct such an IPE scheme from the well-known BGG+14 IPE scheme via careful modification.
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.