Hybrid Protocol of Quantum-Classical Digital Signatures QDS-Hybrid
EDN: FUTNKW
Abstract
This research aims to develop and analyze a hybrid digital signature protocol, QDS-Hybrid, which combines quantum verification and the post-quantum Dilithium algorithm. The objectives of the research include ensuring resistance to quantum attacks and classical threats, optimizing the speed of signature generation and verification while maintaining unconditional security based on quantum mechanics, and identifying solutions to the problems of quantum memory, decoherence, and scalability of existing QDS protocols. The research proposes a hybrid approach based on quantum-classical synthesis. The paper also provides a proof of security using the qCMA (Quantum Chosen Message Attack) model and universal compositional security (UC). The protocol provides protection against state substitution and man-in-the-middle (MITM) attacks through QZKP (Quantum Zero-Knowledge Proof). It is proven that a hack requires simultaneously breaking Dilithium and QKD. The paper proposes solutions for eliminating dependence on quantum memory through dynamic state generation and one-time keys. The paper demonstrates paths to decentralization through blockchain and quantum Byzantine agreements. The key innovation obtained in the study is a hybrid architecture that integrates Dilithium with quantum verification via phase encoding. Implemented QZKP verification helps for signature authenticity confirmation without revealing the secret key, using the properties of quantum entanglement and the no-cloning theorem. QDS-Hybrid demonstrates a practical compromise between security and efficiency, addressing the key shortcomings of purely quantum protocols.
About the Author
S. B. Kuznetsov
University “Sirius”, Federal Territory “Sirius”
Russian Federation
Russian Federation
Sergey B. Kuznetsov — Candidate of Physical and Mathematical Sciences, Associate Professor, Leading Research Engineer, Scientific Center for Information Technology and Artificial Intelligence
Sochi
References
1. Gottesman D., Chuang I. Quantum Digital Signatures, arXiv:quant-ph/0105032v2, 2001. DOI: 10.48550/arXiv.quant-ph/0105032 (accessed: 25.04.2025).
2. Cao Z. A Note On Gottesman-Chuang Quantum Signature Scheme. Penn State University, 2010. Available at: https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=8f1ef45fe04efd373346ac4b9 dca75b078399680 (accessed: 25.04.2025).
3. Ablayev F.M., Ablayev M.F., Vasilyev A.V. Universalnoye kvantovoye kheshirovaniye [Universal quantum hashing], Uchenyye zapiski Kazanskogo universiteta. Seriya: Fiziko-matematicheskiye nauki [Scientific Notes of Kazan University. Series: Physical and Mathematical Sciences], 2014, vol. 156, no. 3, pp. 7–18.
4. Childs A.M. Secure assisted quantum computation, arXiv:quant-ph/0111046v1, 2001. DOI: 10.48550/arXiv.quant-ph/0111046 (accessed: 25.04.2025).
5. Smirnova A.A., Tiskin A.F. Analiz kriptograficheskikh svoystv otechestvennykh khesh-algoritmov [Analysis of cryptographic properties of domestic hash algorithms], Vestnik Novosibirskogo gosudarstvennogo universiteta. Seriya: Informatsionnyye tekhnologii [Bulletin of Novosibirsk State University. Series: Information Technology ], 2014, vol. 12, no. 2, pp. 102–111. DOI: 10.25205/1684-599X-2014-12-2-102-111
6. Batenko K.E., Prokudin A.N. Post-kvantovyy algoritm elektronno-tsifrovoy podpisi na osnove dereva Merkla i GOST RF 34.11‒12 “Stribog” [Post-quantum digital signature algorithm based on the Merkle tree and GOST RF 34.11-12 “Stribog”], Molodoy uchenyy [Young Scientist], 2017, no. 23 (157), pp. 100–103. Available at: https://moluch.ru/archive/157/44376/ (accessed: 25.04.2025).
7. Merkle R.C. Secure communications over insecure channels, Communications of the ACM, 1978, vol. 21, no. 4, pp. 294–299. DOI: 10.1145/359460.359473
8. Bennett C.H., Brassard G. Quantum Cryptography: Public Key Distribution and Coin Tossing, Proceedings of International Conference on Computers, Systems & Signal Processing (Bangalore, India, December 9–12, 1984). IEEE, 1984, p. 175.
9. Monz T. et al. Realization of a scalable Shor algorithm, Science, 2016, vol. 351, is. 6277, pp. 1068–1070. DOI: 10.1126/science.aad9480
10. Ben-Or M. et al. The universal composable security of quantum key distribution, arXiv:quant-ph/ 0409078v2, 2005. Available at: https://arxiv.org/abs/quant-ph/0409078 (accessed: 25.04.2025).
11. Kitaev A.Yu. Quantum computations: algorithms and error correction, Russian Mathematical Surveys, 1997, vol. 52, no. 6, pp. 1191–1249. DOI: 10.1070/RM1997v052n06ABEH002155
12. Shor Peter W., Preskill John. Simple Proof of Security of the BB84 Quantum Key Distribution Protocol, Physical Review Letter, 2000, vol. 85, no. 1, p. 441. DOI: 10.1103/PhysRevLett.85.441
13. Harry Buhrman et al. Quantum Fingerprinting, Physical Review Letters, 2001, vol. 87, no. 16. Article 167902. DOI: 10.1103/PhysRevLett.87.167902. Available at: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.87.167902 (accessed: 25.04.2025).
14. Shor Peter W. Scheme for reducing decoherence in quantum computer memory, Physical Review A, 1995, vol. 52, is. 4, pp. R2493–R2496. DOI: 10.1103/PhysRevA.52.R2493
15. Canetti Ran, Krawczyk Hugo. Analysis of Key-Exchange Protocols and Their Use for Building Secure Channels, Advances in Cryptology – EUROCRYPT 2001. Lecture Notes in Computer Science, vol. 2045, 2001, Springer. Berlin, Heidelberg, 2001. DOI: 10.1007/3-540-44987-6_8
16. Iyer Pavithran et al. Efficient diagnostics for quantum error correction, Physical Review Research, 2022, vol. 4, article 043218. DOI: 10.1103/PhysRevResearch.4.043218
17. Bibikov S.A. Kvantovaya teleportatsiya i zaputannyye sostoyaniya [Quantum teleportation and entangled states], Vestnik Novosibirskogo gosudarstvennogo universiteta. Seriya: Fizika [Bulletin of Novosibirsk State University. Series: Physics], 2021, vol. 16, no. 3, pp. 45–52. DOI: 10.25205/1818-4373-2021-16-3-45-52
18. Milekhin Alexey. Quantum error correction and large N, SciPost Physics, 2021, vol. 11, no. 5. Article 094. DOI: 10.21468/SciPostPhys.11.5.094
19. Crépeau Claude, Gottesman Daniel, Smith Adam. Secure Multi-Party Quantum Computation, Proceedings of the Thirty-Fourth Annual ACM Symposium on Theory of Computing. STOC '02. Association for Computing Machinery. New York, USA, pp. 643–652. DOI: 10.1145/509907.509992
20. Petrenko A.S., Petrenko S.A. Metod otsenivaniya kvantovoy ustoychivosti blokcheyn-platform [A Method for Assessing the Quantum Resilience of Blockchain Platforms], Voprosy kiberbezopasnosti [Cybersecurity Issues], 2022, no. 3 (49). Available at: https://cyberrus.info/wp-content/uploads/2022/07/2-22-349-22_1.- Petrenko.pdf (accessed: 25.04.2025).
21. Ekert Artur K. Quantum cryptography based on Bell’s theorem, Physical Review Letter, 1991, vol. 67, no. 6, p. 661. DOI: 10.1103/PhysRevLett.67.661
22. Sahai Amit, Waters Brent. Fuzzy Identity-Based Encryption, EUROCRYPT, 2005. LNCS, vol. 3494, Springer. Berlin, Heidelberg, pp. 457–473. DOI: 10.1007/11426639_27
23. Shamir Adi. How to Share a Big Secret, Proceedings of the 11th ACM International Systems and Storage Conference (SYSTOR ’18). Haifa, Israel. ACM, New York, USA, pp. 76–88. DOI: 10.1145/3211890.3211896
24. Il’in N.S., Aristova A.V., Lychkovskiy O. Adiabatic theorem for closed quantum systems initialized at finite temperature, Physical Review A, 2021, vol. 104. Article L030202. DOI: 10.1103/PhysRevA.104.L030202 (accessed: 25.04.2025).
25. Printsipy proyektirovaniya protokolov raspredeleniya klyuchey dlya kvantovykh setey s doverennymi uzlami [Design Principles of Key Distribution Protocols for Quantum Networks with Trusted Nodes]. Available at: https://article/n/printsipy-proektirovaniya-setevyh-protokolov-raspredeleniya-klyuchey-dlya-kvantovyh-setey (accessed: 25.04.2025).
26. Beresneva A.V., Yepishkina A.V. O primenenii kriptograficheskikh primitivov, realizuyushchikh porogovuyu podpis [On the application of cryptographic primitives implementing a threshold signature], Bezopasnost informatsionnykh tekhnologiy [Information Technology Security], 2015, vol. 22, no. 3.
27. Razbor struktury i printsipov raboty sovremennykh potokovykh shifrov, vklyuchaya dinamicheskoye taktirovaniye registrov sdviga (primer A5 v GSM) [An analysis of the structure and operating principles of modern stream ciphers, including dynamic clocking of shift registers (example A5 in GSM)]. Available at: https://studfile.net/preview/6022635/1 (accessed: 25.04.2025).
28. Bellare M., Rogaway P. Entity Authentication and Key Distribution, Advances in Cryptology – EUROCRYPT’93, LNCS, vol. 765. Berlin, Heidelberg. DOI: 10.1007/3-540-48285-7_24
29. Goldwasser S., Micali S., Rackoff C. The Knowledge Complexity of Interactive Proof-Systems, SIAM Journal on Computing, 1989, vol. 18, no. 1, pp. 186–208. DOI: 10.1137/0218012
30. Page Don N., Wootters William K. Evolution without evolution: Dynamics described by stationary observables, Physical Review D, 1983, vol. 27, no. 12, p. 2885. DOI: 10.1103/PhysRevD.27.2885
31. Bennett Charles H., Brassard Gilles. Quantum cryptography: Public key distribution and coin tossing, Proceedings of IEEE International Conference on Computers, Systems & Signal Processing (Bangalore, India, December 9–12, 1984). IEEE, 1984, p. 175.
32. Shor Peter W., Preskill John. Simple Proof of Security of the BB84 Quantum Key Distribution Protocol, Physical Review Letter, 2000, vol. 85, no. 1, p. 441. DOI: 10.1103/PhysRevLett.85.441
33. Zhang Y. et al. Long-distance continuous-variable quantum digital signatures over 120-km fiber, Optics Express, 2021, vol. 29, is. 23, pp. 37614–37627. DOI: 10.1364/OE.438605. Available at: https://opg.optica.org/oe/fulltext.cfm?uri=oe-29-23-37614&id=462809 (accessed: 25.04.2025).
Review
For citations:
Kuznetsov S.B. Hybrid Protocol of Quantum-Classical Digital Signatures QDS-Hybrid. Territory Development. 2025;(4 (42)):86-106. (In Russ.) EDN: FUTNKW
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