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IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences

More Efficient Adaptively Secure Lattice-Based IBE with Equality Test in the Standard Model

Kyoichi Asano, Keita Emura, Atsushi Takayasu

Published Oct 4, 2023• 1 citation
Publisher

Abstract

Identity-based encryption with equality test (IBEET) is a variant of identity-based encryption (IBE), in which any user with trapdoors can check whether two ciphertexts are encryption of the same plaintext. Although several lattice-based IBEET schemes have been proposed, they have drawbacks in either security or efficiency. Specifically, most IBEET schemes only satisfy selective security, while public keys of adaptively secure schemes in the standard model consist of matrices whose numbers are linear in the security parameter. In other words, known lattice-based IBEET schemes perform poorly compared to the state-of-the-art lattice-based IBE schemes (without equality test). In this paper, we propose a semi-generic construction of CCA-secure lattice-based IBEET from a certain class of lattice-based IBE schemes. As a result, we obtain the first lattice-based IBEET schemes with adaptive security and CCA security in the standard model without sacrificing efficiency. This is because, our semi-generic construction can use several state-of-the-art lattice-based IBE schemes as underlying schemes, e.g. Yamada's IBE scheme (CRYPTO'17).

DOI
10.1587/transfun.2023cip0021

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Identity-based encryption with equality test (IBEET) is a variant of identity-based encryption (IBE), in which any user with trapdoors can check whether two ciphertexts are encryption of the same plaintext. Although several lattice-based IBEET schemes have been proposed, they have drawbacks in either security or efficiency. Specifically, most IBEET schemes only satisfy selective security, while public keys of adaptively secure schemes in the standard model consist of matrices whose numbers are linear in the security parameter. In other words, known lattice-based IBEET schemes perform poorly compared to the state-of-the-art lattice-based IBE schemes (without equality test). In this paper, we propose a semi-generic construction of CCA-secure lattice-based IBEET from a certain class of lattice-based IBE schemes. As a result, we obtain the first lattice-based IBEET schemes with adaptive security and CCA security in the standard model without sacrificing efficiency. This is because, our semi-generic construction can use several state-of-the-art lattice-based IBE schemes as underlying schemes, e.g. Yamada's IBE scheme (CRYPTO'17).
Public key encryption with equality test (PKEET) enables the testing whether two ciphertexts encrypt the same message. Identity-based encryption with equality test (IBEET) simplify the certificate management of PKEET, which leads to many potential applications such as in smart city applications or Wireless Body Area Networks. Lee et al. (ePrint 2016) proposed a generic construction of IBEET scheme in the standard model utilising a 3-level hierachy IBE together with a one-time signature scheme, which can be instantiated in lattice setting. Duong et al. (ProvSec 2019) proposed the first direct construction of IBEET in standard model from lattices. However, their scheme achieve CPA security only. In this paper, we improve the Duong et al.'s construction by proposing an IBEET in standard model which achieves CCA2 security and with smaller ciphertext and public key size.
Identity-based encryption with equality test (IBEET) provides a feasible way for cloud server partitioning or searching on ciphertexts in the cloud. In that case, the server can judge if two different ciphertexts encrypt the same plaintexts or not. In response to threats posed by quantum computers, lattice-based IBEET schemes have been proposed to make cloud service post-quantum secure. However, those schemes are inefficient and can hardly meet the needs of resource-constrained devices. In this article, an efficient post-quantum IBEET scheme is introduced, which achieves testability by embedding the hash value of plaintext into testing trapdoor instead of encrypting it directly and doubling the size of ciphertext. We also prove that, with the Learning With Errors (LWE) problem assumption, the new scheme is one-way secure against selective identity and chosen ciphertext attacks (OW-sID-CCA) in quantum secure model. Furthermore, we evaluate the performance of the new construction and demonstrate its efficiency by showing that it only costs about half storage comparing with other lattice-based IBEET schemes. The execution time of encryption and decryption phrases in the new scheme reduce by 50%, while the computational cost in test algorithm keeps the same. Therefore, the new proposed IBEET is much more practical for working in post-quantum cloud computing scenarios.
Identity-based encryption with equality test (IBE-ET) allows the detection of whether two different ciphertexts encrypt the same plaintext without decryption within the conventional identity-based encryption (IBE) model. This property ensures the confidentiality of communication and reduces the storage overhead of ciphertexts in cryptosystems. However, IBE-ET schemes based on traditional assumptions, such as discrete logarithm and integer factoring, are vulnerable to quantum algorithm attacks, highlighting the importance of designing lattice-based IBE-ET schemes. To address this, researchers have proposed several lattice-based IBE-ET schemes that utilize outdated lattice IBE paradigms and are inefficient in terms of parameter size. In this work, we construct a new lattice-based IBE-ET scheme using the most compact lattice IBE framework known to date. Our new proposal significantly improves the parameters compared to previous constructions. Furthermore, we provide a security reduction in the random oracle model, along with corresponding parameter selection and the comparison between our scheme and known constructions. The results imply that our scheme is efficient.
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.
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.
At present, most of the identity based encryption (IBE) schemes from the lattice originate from the results of Gentry et.al., and regard each identity as a bit string with equal length and then map a matrix to every bit of identity string. Consequently, they are considerably less efficient. In our paper, we construct an IBE which is efficient from standard learning with errors problem and handles identities as a chunk for performance. In the standard model, our paper gives a proof which our IBE is IND-sID-CCA secure. Mean-while, we also show which our IBE construction is also IND-ID-CCA secure via the technique i.e., imposing additional restrictions on the identities, presented by Boyen and Boneh.