Abstract
In 2012, Tim Güneysu, et al. proposed the GLP signature scheme, a practical and efficient post-quantum signature scheme. It is built on the modification of Vadim Lyubashevsky’s idea of constructing previous signature schemes. It has a significantly smaller signature and key size than prior signature scheme. The design of the GLP is a foundation to construct newer signature schemes such as Bai-Galbraith, Dilithium. However, Tim Güneysu has only given the description of the GLP signature scheme that has not yet given a detailed security proof for this scheme. Therefore, in this paper, we will present a full security proof for the GLP signature scheme. Specifically, we show that the GLP signature scheme is EU-CMA secure in the random oracle model.
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Notes
- 1.
A later scheme version is given in [GLP15]. But, it still does not contain a full security proof.
- 2.
This lemma is stated based on Lemma 3.7 in [Lyu12]. Namely, we give a reduction for the hard problems on the ideal lattices instead of the lattice in \(\mathbb {R}^n\) as in Lemma 3.7.
- 3.
This lemma is stated based on Lemma 6.1 in [Lyu08].
- 4.
This theorem is stated based on Theorem 5.1 in [Lyu12]. Namely, we provide an additional algorithms Hybrid 3 to prove the security of the GLP signature scheme.
- 5.
When it is queried, the oracle H is programmed to return a random \(\mathbf {c}\in \{ \mathbf {v}\in R_{1}^{p^n}:\sum \limits _{i=1}^{n}{\left| {{v}_{i}} \right| =32} \}\) without checking whether that value has been used before.
- 6.
This lemma is stated based on Lemma 5.2 in [Lyu12].
References
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Acknowledgements
The authors are grateful to Duong Hoang Dung and Trieu Quang Phong for helpful comments and discussions on drafts of this paper.
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Khuc, T.X., Bui, M.K., Chu, H. (2019). A Security Proof of the GLP Signature Scheme. In: Duong, T., Vo, NS., Nguyen, L., Vien, QT., Nguyen, VD. (eds) Industrial Networks and Intelligent Systems. INISCOM 2019. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 293. Springer, Cham. https://doi.org/10.1007/978-3-030-30149-1_21
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