Oblivious signature based on the theory of elliptic curve isogeny

Altana F. Khutsaeva

2026 , VOLUME 26, NUMBER 2 ( march-april )

ISSN 2226-1494 (print), ISSN 2500-0373 (online)

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Nikiforov
Vladimir O.
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doi: 10.17586/2226-1494-2026-26-2-442-445

Oblivious signature based on the theory of elliptic curve isogeny

A. F. Khutsaeva

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Article in Russian

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Khutsaeva A.F. Oblivious signature based on the theory of elliptic curve isogeny. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2026, vol. 26, no. 2, pp. 442–445 (in Russian). doi: 10.17586/2226-1494-2026-26-2-442-445

Abstract

This paper presents a novel 1-out-of-n post-quantum oblivious signature scheme based on supersingular elliptic curve isogenies. The proposed scheme is built upon the Commutative Supersingular Isogeny based Fiat-Shamir scheme whose security relies on the hardness assumption of the multiple-target group action inverse problem. This approach ensures resistance against attacks using Shor’s algorithm. The key generation algorithm, the interactive signing protocol, and the verification algorithm are formalized. Experimental evaluation in SageMath demonstrates more than a threefold reduction in communication overhead compared to a lattice-based counterpart.

Keywords: oblivious signature, post-quantum cryptography, isogenies of elliptic curves, digital signature, MT-GAIP, CSI-FiSh

Acknowledgements. This research was funded by the State Assignment grant number FSER-2025-0003. The author is grateful to S.V. Bezzateev for scientific supervision and valuable advice. The author also wishes to thank the anonymous reviewer and the editor for their constructive criticism which helped improve this paper.

References

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