Lattice-based Identity-based Encryption Scheme Research Articles

Quantum‐resistant anonymous identity‐based encryption with trable identities

Identity-based encryption (IBE), introduced by Shamir, eliminates the need for public-key infrastructure. The sender can simply encrypt a message by using the recipient's identity (such as email or IP address) without needing to look up the public key. In particular, when ciphertexts of an IBE do not reveal recipient's identity, this scheme is known as an anonymous IBE scheme. Recently, Blazy et al. (ARES '19) analysed the trade-off between public safety and unconditional privacy in anonymous IBE and introduced a new notion that incorporates traceability into anonymous IBE, called anonymous IBE with traceable identities (AIBET). However, their construction is based on the discrete logarithm assumption, which is insecure in the quantum era. In this paper, we first formalize the consistency of tracing key of the AIBET scheme to ensure that a ciphertext cannot be traced with the use of wrong tracing keys. Subsequently, we present a generic formulation concept that can be used to transform structure-specific lattice-based anonymous IBE schemes into an AIBET. Finally, we apply this concept to Katsumata and Yamada's compact anonymous IBE scheme (Asiacrypt '16) to obtain the first quantum-resistant AIBET scheme that is adaptively secure under the ring learning with errors assumption without random oracle.

Adaptively Secure Efficient (H)IBE over Ideal Lattice with Short Parameters.

Identity-based encryption (IBE), and its hierarchical extension (HIBE), are interesting cryptographic primitives that aim at the implicit authentication on the users’ public keys by using users’ identities directly. During the past several decades, numerous elegant pairing-based (H)IBE schemes were proposed. However, most pairing-related security assumptions suffer from known quantum algorithmic attacks. Therefore, the construction of lattice-based (H)IBE became one of the hot directions in recent years. In the setting of most existing lattice-based (H)IBE schemes, each bit of a user’s identity is always associated with a parameter matrix. This always leads to drastic but unfavorable increases in the sizes of the system public parameters. To overcome this issue, we propose a flexible trade-off mechanism between the size of the public parameters and the involved computational cost using the blocking technique. More specifically, we divide an identity into segments and associate each segment with a matrix, while increasing the lattice modulo slightly for maintaining the same security level. As a result, for the setting of 160-bit identities, we show that the size of the public parameters can be reduced by almost 89.7% (resp. 93.8%) while increasing the computational cost by merely 5.2% (resp. 12.25%) when is a set of 16 (resp. 8). Finally, our IBE scheme is extended to an HIBE scheme, and both of them are proved to achieve the indistinguishability of ciphertexts against adaptively chosen identity and chosen plaintext attack (IND-ID-CPA) in the standard model, assuming that the well-known ring learning with error (RLWE) problem over the involved ideal lattices is intractable, even in the post-quantum era.

Novel efficient lattice-based IBE schemes with CPK for fog computing.

The data security of fog computing is a key problem for the Internet of things. Identity-based encryption (IBE) from lattices is extremely suitable for fog computing. It is able to not only simplify certificate management, but also resist quantum attacks. In this paper, firstly, we construct a novel efficient lattice-based IBE scheme with Combined Public Key (CPK) technique by keeping from consumptive trapdoor generation algorithm and preimage sampling algorithm, which is required by the existing lattice-based IBE schemes based on learning with errors (LWE). In addition, its key storage cost is lower and it is IND-ID-CPA secure in the random oracle model. Furthermore, based on this, an enhanced lattice-based IBE scheme with IND-ID-CCA security is developed by employing strong one-time signature. Our schemes only need O(n3/log n) additions of vectors, while the existing schemes need at least O(n3) of additions and multiplications in Setup and Extract phase.

Full secure identity-based encryption scheme over lattices for wireless sensor networks in the standard model

This paper proposes a lattice-based identity-based encryption scheme which can be used in wireless sensor networks to achieve secure communication. More precisely, a known lattice-based chosen plain-text secure encryption scheme and the bonsai trees primitive are used to design an identity-based encryption (IBE) scheme in this paper. To reduce the public key size of the proposed IBE scheme, a public matrices chosen rule is used in this paper which reduces the public key size of proposed scheme to be close to half of that of a known lattice-based scheme. 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. 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.

Full secure identity-based encryption scheme with short public key size over lattices 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 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 matrix and vectors, compared with that the public keys of the known lattice-based IBE schemes all consist as a group of matrices. Hence, the public key size of this scheme is shorter than that of the known constructions.

An ideal lattice based IBE scheme in the standard model

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.