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International Journal of Ad Hoc and Ubiquitous Computing

An Efficient and Secure Undeniable Signature Scheme based on Ring Learning with Error

Akanksha Singh, Harish Chandra, Saurabh Rana

Published Jan 1, 2026• 0 citations
Publisher
DOI
10.1504/ijahuc.2026.10076212

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An efficient and secure undeniable signature scheme based on ring learning with error

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This paper, proposes a novel undeniable signature scheme based on the ring learning with errors (RLWE) problem, a complex lattice problem. In our scheme, authentic signatures can be validated via an interactive protocol, which guarantees that adversaries cannot forge signatures. Moreover, it ensures that honest participants consistently finish the verification procedure. Thus, the scheme is a strong and effective quantum-resistant undeniable signature scheme. Our security analysis, demonstrates resilience against both classical and quantum adversaries, based on the RLWE problem's hardness assumptions. Additionally, the random Oracle model is utilised to evaluate our protocol's security, showing that our scheme satisfies important cryptographic properties like completeness, soundness, and unforgeability. Our work advances the feasibility of post-quantum undeniable signature schemes for real-world cryptographic applications.

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In order to solve the problem of large key size and low efficiency in the linkable ring signature scheme on lattice, this paper reconstructs the linkable ring signature scheme from lattice based on the ring learning with errors (RLWE) problem, according to the technical route of “homomorphic commitment→∑-protocol→Fiat-Shamir transformation”. This paper first constructs a homomorphic commitment scheme over a polynomial ring based on the RLWE problem, and then designs a ∑-protocol based on the commitment scheme, and transforms the ∑-protocol into a linkable ring signature scheme using the Fiat-Shamir transformation methods. Finally, this paper proposes a simple digital currency model based on the linkable ring signature scheme. Security analysis shows since the proposed scheme is constructed based on the problem of RLWE, its security can reduce to the lattice-based difficult problem and resist the quantum computer attack. Efficiency analysis shows compared with the previous linkable ring signature schemes on lattice, since the ring elements in the scheme are taken from small polynomials, the proposed scheme has shorter key size and higher computational efficiency, and the description of the scheme is simpler.

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Compared to the classical cryptography, lattice-based cryptography is more secure, flexible and simple, and it is believed to be secure against quantum computers.In this paper, an efficient signature scheme is proposed from the ring learning with errors (R-LWE), which avoids sampling from discrete Gaussians and has the characteristics of the much simpler description etc.Then, the scheme is implemented in C/C++ and makes a comparison with the RSA signature scheme in detail.Additionally, a linearly homomorphic signature scheme without trapdoor is proposed from the R-LWE assumption.The security of the above two schemes are reducible to the worst-case hardness of shortest vectors on ideal lattices.The security analyses indicate the proposed schemes are unforgeable under chosen message attack model, and the efficiency analyses also show that the above schemes are much more efficient than other correlative signature schemes.

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This paper, proposes a novel undeniable signature scheme based on the ring learning with errors (RLWE) problem, a complex lattice problem. In our scheme, authentic signatures can be validated via an interactive protocol, which guarantees that adversaries cannot forge signatures. Moreover, it ensures that honest participants consistently finish the verification procedure. Thus, the scheme is a strong and effective quantum-resistant undeniable signature scheme. Our security analysis, demonstrates resilience against both classical and quantum adversaries, based on the RLWE problem's hardness assumptions. Additionally, the random Oracle model is utilised to evaluate our protocol's security, showing that our scheme satisfies important cryptographic properties like completeness, soundness, and unforgeability. Our work advances the feasibility of post-quantum undeniable signature schemes for real-world cryptographic applications.
In order to solve the problem of large key size and low efficiency in the linkable ring signature scheme on lattice, this paper reconstructs the linkable ring signature scheme from lattice based on the ring learning with errors (RLWE) problem, according to the technical route of “homomorphic commitment→∑-protocol→Fiat-Shamir transformation”. This paper first constructs a homomorphic commitment scheme over a polynomial ring based on the RLWE problem, and then designs a ∑-protocol based on the commitment scheme, and transforms the ∑-protocol into a linkable ring signature scheme using the Fiat-Shamir transformation methods. Finally, this paper proposes a simple digital currency model based on the linkable ring signature scheme. Security analysis shows since the proposed scheme is constructed based on the problem of RLWE, its security can reduce to the lattice-based difficult problem and resist the quantum computer attack. Efficiency analysis shows compared with the previous linkable ring signature schemes on lattice, since the ring elements in the scheme are taken from small polynomials, the proposed scheme has shorter key size and higher computational efficiency, and the description of the scheme is simpler.
Compared to the classical cryptography, lattice-based cryptography is more secure, flexible and simple, and it is believed to be secure against quantum computers.In this paper, an efficient signature scheme is proposed from the ring learning with errors (R-LWE), which avoids sampling from discrete Gaussians and has the characteristics of the much simpler description etc.Then, the scheme is implemented in C/C++ and makes a comparison with the RSA signature scheme in detail.Additionally, a linearly homomorphic signature scheme without trapdoor is proposed from the R-LWE assumption.The security of the above two schemes are reducible to the worst-case hardness of shortest vectors on ideal lattices.The security analyses indicate the proposed schemes are unforgeable under chosen message attack model, and the efficiency analyses also show that the above schemes are much more efficient than other correlative signature schemes.