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IACR Communications in Cryptology

Efficient Batched IBE from Lattices in the Standard Model

Saisi Xiong, Yijian Zhang, Jie Chen

Published Aug 3, 2026• 2 citations
Publisher

Abstract

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.

DOI
10.62056/aksude-3

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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.
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.
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.
Under the standard model, an IND-sID-CPA secure IBE (Identity Based Encryption) scheme is proposed, which is based on an improved trapdoor generation function over ring and decisional R-LWE (ring-learning with errors) assumption, thus the hardness of recovering system master key can be reduced to solve the Ideal-SIS (small integer solution) problem, and the attack to the ciphertext is equivalent to solving the SVP (the shortest vector problem) in the worst case on ideal lattice to within a fixed poly( n ) factor. Moreover, the proposed scheme has advantages of high encryption and decryption speed and low encryption blowup factor compared with all known IBE scheme from the standard lattice under the standard model.
Recently,Identity-based Encryption(IBE) scheme based on lattices becomes one of the focuses of cryptographic research.But the IBE scheme based on standard lattice have large key size and high ciphertext expansion rate.So based on ideal lattices,this paper presents an efficient identity-based encryption scheme with small key size and low ciphertext expansion rate.The proposed scheme uses a method that combines the NTRU digital signature and the dual encryption based on ideal lattices.It is provably secure in the random oracle model.Analysis results show that the public key and the private key of key generation center contain one ring element and four ring elements respectively.The decryption key of each user is comprised of two ring elements.The ciphertext contains only two ring elements and the ciphertext expansion rate is a small constant.The encryption and decryption require four and two multiplications in the polynomial ring.Hence,the IBE scheme is more computationally efficient than that of traditional number theory based IBE scheme.
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.