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International Journal of Information and Computer Security

An IBE scheme based on hybrid sampler over NTRU lattice

Xiufeng Zhao, Yang Song, Aoyang Zhou, Haiying Gao, Shiyu Wang

Published Jan 1, 2025• 0 citations
Publisher

Abstract

The identity-based encryption (IBE) scheme takes the user's identity as the public key, which avoids the disadvantages of digital certificate management. Lattice-based IBE scheme has the advantages of resistant to quantum attack, high efficiency and simple structure, and has become a research hotspot in the field of post-quantum information security. In this paper, an IBE scheme is designed based on NTRU lattice, and the hybrid sampling algorithm proposed by Ducas and Prest is used in the private key extraction algorithm of the scheme, which improves the implementation efficiency of the key generation algorithm while ensuring the security of the private key. The encryption and decryption algorithm of the IBE scheme is designed by using the framework structure of the encryption algorithm based on the LWE problem. Under the condition that the NTRU difficulty hypothesis and the LWE difficulty hypothesis hold simultaneously, the scheme is proved to have indistinguishability under chosen plaintext attack with identity-based encryption (IND-ID-CPA). The software implementation of the scheme and the efficiency under the specific parameter settings are given, and the experimental results show that the new scheme has higher encryption and decryption efficiency and shorter ciphertext length than the typical lattice IBE scheme.

DOI
10.1504/ijics.2025.10072460

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The identity-based encryption (IBE) scheme takes the user's identity as the public key, which avoids the disadvantages of digital certificate management. Lattice-based IBE scheme has the advantages of resistant to quantum attack, high efficiency and simple structure, and has become a research hotspot in the field of post-quantum information security. In this paper, an IBE scheme is designed based on NTRU lattice, and the hybrid sampling algorithm proposed by Ducas and Prest is used in the private key extraction algorithm of the scheme, which improves the implementation efficiency of the key generation algorithm while ensuring the security of the private key. The encryption and decryption algorithm of the IBE scheme is designed by using the framework structure of the encryption algorithm based on the LWE problem. Under the condition that the NTRU difficulty hypothesis and the LWE difficulty hypothesis hold simultaneously, the scheme is proved to have indistinguishability under chosen plaintext attack with identity-based encryption (IND-ID-CPA). The software implementation of the scheme and the efficiency under the specific parameter settings are given, and the experimental results show that the new scheme has higher encryption and decryption efficiency and shorter ciphertext length than the typical lattice IBE scheme.
The identity-based encryption (IBE) scheme takes the user's identity as the public key, which avoids the disadvantages of digital certificate management. Lattice-based IBE scheme has the advantages of resistant to quantum attack, high efficiency and simple structure, and has become a research hotspot in the field of post-quantum information security. In this paper, an IBE scheme is designed based on NTRU lattice, and the hybrid sampling algorithm proposed by Ducas and Prest is used in the private key extraction algorithm of the scheme, which improves the implementation efficiency of the key generation algorithm while ensuring the security of the private key. The encryption and decryption algorithm of the IBE scheme is designed by using the framework structure of the encryption algorithm based on the LWE problem. Under the condition that the NTRU difficulty hypothesis and the LWE difficulty hypothesis hold simultaneously, the scheme is proved to have indistinguishability under chosen plaintext attack with identity-based encryption (IND-ID-CPA). The software implementation of the scheme and the efficiency under the specific parameter settings are given, and the experimental results show that the new scheme has higher encryption and decryption efficiency and shorter ciphertext length than the typical lattice IBE scheme.
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.
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.
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.