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Cybernetics and Systems Analysis

Beyond Post-Quantum Cryptography: Cryptosystems that are Secure in Certain Computation Models

V. K. Zadiraka, Антон Михайлович Кудін, I. A. Kudin, Інна Віталіївна Швідченко

Published Nov 1, 2025• 1 citation
Publisher
DOI
10.1007/s10559-025-00821-8

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The security of current public-key cryptosystems relies on the hardness of factoring large integers or solving discrete logarithm problems. However, these mathematical problems can be solved in polynomial time using a quantum computer. This vulnerability has prompted research into post-quantum cryptography using alternative mathematical problems that are secure in the era of quantum computers. In this regard, the National Institute of Standards and Technology (NIST) began to standardize post-quantum cryptography in 2016. In this expository article, we give an overview of recent research on post-quantum cryptography. In particular, we describe the construction and security of multivariate polynomial cryptosystems and lattice-based cryptosystems, which are the main candidates of post-quantum cryptography.
Abstract Due to the development of quantum computing, there is a need for the development and analysis of cryptosystems resistant to attacks using a quantum computer (post-quantum cryptography algorithms). The security of many well-known post-quantum cryptosystems based on lattice theory depends on the complexity of solving the shortest vector problem (SVP). In this paper, a model of quantum oracle developed from Grover’s algorithm is described to implement a hybrid quantum–classical algorithm based on GaussSieve. This algorithm can be used for attacks on cryptosystems whose security depends on solving the SVP. Upper bounds for the number of qubits and the depth of the circuit were obtained for two implementations of the proposed quantum oracle model: minimizing the number of qubits and minimizing the circuit depth. The complexity of implementing the proposed quantum oracle model to attack post-quantum lattice-based cryptosystems that are finalists of the NIST post-quantum cryptography competition is analyzed.