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Identity-based Linkable Ring Signcryption on NTRU Lattice

Xiaofang Huang

Published Sep 1, 2025• 0 citations
Publisher

Abstract

Although the current lattice-based ring signcryption scheme resists quantum attacks,it has large key storage and high encryption/decryption time.The linkable lattice ring signcryption scheme not only can protect signer anonymity,but also can determine whether two signatures are generated by the same signer.Thus,based on the compact Gaussian sampling algorithm and rejection sampling technique,the identity-based linkable ring signcryption scheme is constructed on the NTRU lattice.Firstly,the system master key is generated using the trapdoor generation algorithm on the NTRU lattice.Then private keys of ring members are obtained based on the compact Gaussian sampling algorithm.Finally,the user signature is generated using rejection sampling,and the key encapsulation mechanism encrypts the signature.Security proof in the random oracle model (ROM) that DRLWE and NTRU small integer solutions are difficult to solve ensures confidentiality,unforgeability,unconditional anonymity,and linkability.Performance analysis shows that compared to the lattice-based ring signcryption and linkable ring signature schemes on NTRU,the proposed scheme has a smaller public key and lower encryption/decryption cost,greatly improving efficiency.

DOI
10.11896/jsjkx.240700126

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Although the current lattice-based ring signcryption scheme resists quantum attacks,it has large key storage and high encryption/decryption time.The linkable lattice ring signcryption scheme not only can protect signer anonymity,but also can determine whether two signatures are generated by the same signer.Thus,based on the compact Gaussian sampling algorithm and rejection sampling technique,the identity-based linkable ring signcryption scheme is constructed on the NTRU lattice.Firstly,the system master key is generated using the trapdoor generation algorithm on the NTRU lattice.Then private keys of ring members are obtained based on the compact Gaussian sampling algorithm.Finally,the user signature is generated using rejection sampling,and the key encapsulation mechanism encrypts the signature.Security proof in the random oracle model (ROM) that DRLWE and NTRU small integer solutions are difficult to solve ensures confidentiality,unforgeability,unconditional anonymity,and linkability.Performance analysis shows that compared to the lattice-based ring signcryption and linkable ring signature schemes on NTRU,the proposed scheme has a smaller public key and lower encryption/decryption cost,greatly improving efficiency.
Although most existing linkable ring signature schemes on lattice can effectively resist quantum attacks, they still have the disadvantages of excessive time and storage overhead. This paper constructs an identity-based linkable ring signature (LRS) scheme over NTRU lattice by employing the technologies of trapdoor generation and rejection sampling. The security of this scheme relies on the small integer solution (SIS) problem on NTRU lattice. We prove that this scheme has unconditional anonymity, unforgeability, and linkability under the random oracle model (ROM). Through the performance analysis, this scheme has a shorter size of public/private keys, and when the number of ring members is small (such as N ≤ 8 ), this scheme has a shorter signature size compared with other existing latest lattice-based LRS schemes. The computational efficiency of signature has also been further improved since it only involves multiplication in the polynomial ring and modular operations of small integers. Finally, we implemented our scheme and other similar schemes, and it is shown that the time for the signature generation and verification of this scheme decreases roughly by 44.951% and 33.503%, respectively.
With the rapid expansion of consumer electronics and the Internet of Things (IoT) ecosystem, ensuring secure communication in resource-constrained edge devices has become a critical challenge, especially under the threat of quantum attacks. Although lattice-based cryptographic schemes provide post-quantum security, they often suffer from large key storage and high computational overhead, limiting their applicability in edge environments. To address these challenges, we propose an identity-based linkable ring signcryption scheme constructed on the post quantum Lattice cryptography, tailored for edge-enabled IoT systems. The scheme employs a trapdoor generation algorithm to establish the master keys, utilizes compact Gaussian sampling to derive private keys for ring members, and integrates rejection sampling to generate user signatures with strong anonymity. Furthermore, a key encapsulation mechanism ensures identity protection during encryption. Security analysis under the Random Oracle Model (ROM) demonstrates the scheme's resistance to forgery and its linkability property. Performance evaluation shows that the proposed approach achieves smaller public keys, reduced encryption/decryption costs, and enhanced efficiency, making it well-suited for lightweight IoT and consumer electronics applications in the post-quantum era.
A signcryption scheme provides both the function of digital signature and encryption scheme at the same time. Additionally, it has lower cost than traditional sign-then-encrypt or encrypt-then-sign approaches. Many useful applications have been found where confidentiality and non-repudiation are both required. On the other hand, with the current development of rapid quantum computing, currently schemes based on traditional numerical assumptions (e.g., decisional Diffie-Hellman assumption) are more likely to be attacked by quantum computers. Therefore, lattice-based signcryption schemes have been extensively studied in recent years. However, most of them are either inefficient or secure-proved under the assumptions of random oracles. Although some of them are proved in the standard model, they are not practical in low-cost devices. Since the security is based on "Learning with Errors" (LWE) or "Short Integer Solution" problems, it will result in extremely large size of keys. In this paper, we propose an efficient NTRU-based signcryption scheme, which is inspired from Pion et al.'s key encapsulation mechanism. We provide rigorous security proofs for the confidentiality and unforgeability under NTRU-based assumptions in the standard model. Compared with other schemes, we conclude that our scheme is more efficient and secure.
This work proposes a Fiat-Shamir linkable ring lattice-based signature scheme, building on Yuen et al. ‘s generic ring signature. It converts the MLWE-based Σ-protocol into a linkable ring signature through the Fiat-Shamir transformation, employing rejection sampling to avoid private key leakage. Linkability is achieved by attaching a public key structure label, avoiding complex zero-knowledge proofs and pseudorandom function calculations. Compared to other lattice-based schemes, our approach improves signature length. Security analysis under the random oracle model confirms correctness, anonymity, unforgeability, linkability, and non-slanderability.
Signcryption is a cryptographic primitive that can provide valid solution for authentication and confidentiality.In this paper, an efficient identity-based signcryption scheme from lattice was proposed.Our scheme based on Macciancio and Piekert's trapdoor generation method and delegate algorithm for lattice.Our main idea is that establish the identity-based system master key via trapdoor generation method for lattice, and extract user's key by trapdoor delegate algorithm.With the aid of random oracle, we prove that the proposed scheme has CCA security under the learning with errors (LWE) assumption and unforgeability against adaptive chosen messages attacks under the small integer solution (SIS) assumption.Comparison with signature-then-encryption approach shows that our scheme is efficient.
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.