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.
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.
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.
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.
Abstract: Using the Bonsai trees primitive and Gentry’s CPA-secure (chosen-plaintext attack) public-key encryption (PKE) scheme, we propose an efficient chosen-ciphtertext secure PKE scheme over lattice. If the decision variant of the learning with errors (LWE) problem is hard and the one-time signature used in this scheme is strong unforgeable, the proposed PKE scheme is indistinguishable against the adaptive chosen-ciphtertext attack (IND-CCA2). One of the characters for this scheme is that, before any encryption operation, the encryption algorithm uses a new choice rule to fix the public parameter matrixes used in the encryption operation. With the help of this new choice rule, we can achieve the chosen-ciphtertext security with much shorter the public key size in contrast to the lattice-based encryption scheme proposed in STOC’09 by Peikert. Moreover, as a CCA-secure PKE scheme, the message-tociphtertext expanse factor of this scheme which is controlled efficiently is nearly closed to the message-to-ciphtertext expanse factor of Gentry’s scheme which is CPA secure. Due to the quantum intractability of the LWE problem on which the scheme is based, the proposed PKE scheme is secure even in quantum-era.
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 lattice basis delegation in a fixed dimension, we propose an efficient lattice-based hierarchical identity based encryption (HIBE) scheme in the standard model whose public key size is only ( dm 2 + mn ) log q bits and whose message-ciphertext expansion factor is only log q , where d is the maximum hierarchical depth and ( n , m , q ) are public parameters. In our construction, a novel public key assignment rule is used to averagely assign one random and public matrix to two identity bits, which implies that d random public matrices are enough to build the proposed HIBE scheme in the standard model, compared with the case in which 2 d such public matrices are needed in the scheme proposed at Crypto 2010 whose public key size is (2 dm 2 + mn + m ) log q . To reduce the message-ciphertext expansion factor of the proposed scheme to log q , the encryption algorithm of this scheme is built based on Gentry’s encryption scheme, by which m 2 bits of plaintext are encrypted into m 2 log q bits of ciphertext by a one time encryption operation. Hence, the presented scheme has some advantages with respect to not only the public key size but also the message-ciphertext expansion factor. Based on the hardness of the learning with errors problem, we demonstrate that the scheme is secure under selective identity and chosen plaintext attacks.
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 l' 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 l' 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.