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doi: 10.17586/2226-1494-2025-25-3-446-456

Analysis of the applicability of existing secret separation schemes in the post-quaternary era

E. F. Kustov, S. V. Bezzateev


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Article in Russian

For citation:
Kustov E.F., Bezzateev S.V. Analysis of the applicability of existing secret separation schemes in the post-quaternary era. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2025, vol. 25, no. 3, pp. 446–456 (in Russian). doi: 10.17586/2226-1494-2025-25-3-446-456


Abstract
Modern approaches to secret sharing have been examined, encompassing both classical and post-quantum cryptographic schemes. The study explores methods for distributing secret information among multiple participants using various mathematical primitives, such as Lagrange and Newton polynomials, the Chinese remainder theorem, error-correcting codes, lattice theory, elliptic curve isogenies, multivariate equations, and hash functions. A comparative analysis of different schemes is provided in terms of their resistance to quantum attacks, efficiency, and compliance with Shamir’s criteria. Special attention is given to assessing the schemes resilience against attacks using quantum computers, which is particularly relevant given the advancement of quantum technologies. The advantages and disadvantages of each scheme are discussed, including their computational complexity, flexibility, and adaptability to various conditions. It is shown that classical schemes, such as those by Shamir and Newton, remain efficient and easy to implement but are vulnerable to quantum attacks. Meanwhile, post-quantum schemes based on lattice theory demonstrate a high level of security but require more complex computations.


 


Keywords: post-quantum cryptography, secret sharing scheme, threshold scheme, public-key cryptography, lattice theory, elliptic curves, multivariate equations, error-correcting codes, hash functions

Acknowledgements. The work was carried out within the framework of the State Assignment (project No. FSER-2025-0003).

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