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Communications in computer and information science

An Efficient Lattice-Based IBE Scheme Using Combined Public Key

Yanfeng Shi, Shuo Qiu, Jiqiang Liu

Published Jan 1, 2020• 2 citations
Publisher
DOI
10.1007/978-981-15-7530-3_1

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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.

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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.

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

Yanfeng Shi, Shuo Qiu, Jiqiang Liu +1 more

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.

Mathematical Biosciences & Engineering•Jan 1, 2020•2 citations
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.
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.
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.