CRYPTOGRAPHIC PROTOCOL OF VERIFIABLY ENCRYPTED SIGNATURE WITH POSSIBILITY OF VERIFICATION AFTER A SPECIFIED TIME
https://doi.org/10.55452/1998-6688-2026-23-1-68-81
Abstract
One of the modern directions in the field of information security is post-quantum cryptography. Its purpose is to develop new quantum-resistant cryptographic algorithms. An important section of post-quantum cryptography is electronic digital signature algorithms. There are a number of different approaches to designing post-quantum signatures. One of the main approaches to designing post-quantum cryptographic digital signature algorithms is hash-based post-quantum digital signature schemes. Hash-based post-quantum digital signature schemes are one of the main types of post-quantum cryptographic digital signature algorithms. They are quite efficient and provably secure. Their reliable security has been established against both classical and quantum attacks. There are many types of digital signatures for solving various information security problems, such as group signatures, ring signatures, blind signatures, verifiably encrypted signatures, etc. This paper proposes a new cryptographic protocol of verifiably encrypted signature with possibility of verification after a specified time based on the post-quantum cryptographic algorithm of hash-based digital signature, TANBA-SPHINCS+. The protocol is an efficient combination of the postquantum digital signature algorithm TANBA-SPHINCS+, the cryptographic protocol providing data encryption for a specified time, ECTLC, and the verifiably encrypted signature scheme.
About the Authors
Ye. N. SeitkulovKazakhstan
Cand. Phys.-Math. Sc., Research Fellow
Astana
R. M. Ospanov
Kazakhstan
MSc (Tech.), Research Fellow
Astana
B. B. Yergaliyeva
Kazakhstan
Research Fellow
Astana
K. A. Utebayev
Kazakhstan
Master’s student, Research Fellow
Almaty
S. K., Atanov
Kazakhstan
Dr. Tech. Sc., Professor
Astana
References
1. Ospanov, R., Sejtkulov, E., Ergalieva, B., Utebaev, K., Atanov, S. TANBA-SPHINCS+ - postkvantovyj kriptograficheskij algoritm cifrovoj podpisi, osnovannoj na heshirovanii. Vestnik KazNPU imeni Abaya. Seriya: Fiziko-matematicheskie nauki, 1(89), 235–246 (2025). https://doi.org/10.51889/2959-5894.2025.89.1.020. (in Russian)
2. Asokan, N., Shoup, V., Waidner, M. Optimistic fair exchange of digital signatures. Advances in Cryptology – EUROCRYPT 1998, 1403, 591–606 (1998). https://doi.org/10.1007/BFb0054156.
3. Boneh, D., Gentry, C., Lynn, B., Shacham, H. Aggregate and verifiably encrypted signatures from bilinear maps. Advances in Cryptology – EUROCRYPT 2003, 2656, 416–432 (2003). https://doi.org/10.1007/3-540-39200-9_26.
4. Ateniese, G. Verifiable encryption of digital signatures and applications. ACM Transactions on Information and System Security, 7(1), 1–20 (2004). https://doi.org/10.1145/984334.984335
5. Lu, S., Ostrovsky, R., Sahai, A., Shacham, H., Waters, B. Sequential aggregate signatures and multisignatures without random oracles. Advances in Cryptology – EUROCRYPT 2006, 4004, 465–485 (2006). https://doi.org/10.1007/11761679_28
6. Rückert, M. Verifiably encrypted signatures from RSA without NIZKs. Progress in Cryptology – INDOCRYPT 2009, 5922, 363–377 (2009). https://doi.org/10.1007/978-3-642-10628-6_24
7. Kim, K. S., Jeong, I. R. Efficient verifiably encrypted signatures from lattices. International Journal of Information Security, 13, 305–314 (2014). https://doi.org/10.1007/s10207-014-0226-0
8. Shao, Z., Gao, Y.Certificate-based verifiably encrypted RSA signatures. Transactions on Emerging Telecommunications Technologies, 26, 276–289 (2015). https://doi.org/10.1002/ett.2607
9. Shao, Z., Gao, Y. Practical verifiably encrypted signature based on Waters signatures. IET Information Security, 9(3), 185–193 (2015). https://doi.org/10.1049/iet-ifs.2013.0385
10. Nishimaki, R., Xagawa, K. Verifiably encrypted signatures with short keys based on the decisional linear problem and obfuscation for encrypted VES. Cryptology ePrint Archive, Report 2015/248 (2015). URL: https://eprint.iacr.org/2015/248
11. Zhang, Y., Hu, Y. A new verifiably encrypted signature scheme from lattices. Journal of Computer Research and Development, 54, 305–312 (2017). https://doi.org/10.7544/issn1000-1239.2017.20150887
12. Wang, F., Shi, S. Lattice-based encrypted verifiably encryption signature scheme for fair and private electronic commerce. IEEE Access, 7, 147481–147489 (2019). https://doi.org/10.1109/ACCESS.2019.2946272
13. Yang, X., Lau, W. F., Ye, Q., Au, M. H., Liu, J. K., Cheng, J. Practical escrow protocol for Bitcoin. IEEE Transactions on Information Forensics and Security, 15, 3023–3034 (2020). https://doi.org/10.1109/TIFS.2020.2976607
14. Fournier, L. One-time verifiably encrypted signatures (adaptor signatures). Technical report (2019). URL: https://raw.githubusercontent.com/LLFourn/one-time-VES/master/main.pdf
15. Yang, X., Liu, M., Au, M. H., Luo, X., Ye, Q. Efficient verifiably encrypted ECDSA-like signatures and their applications. IEEE Transactions on Information Forensics and Security, 17, 1573–1582 (2022). https:// doi.org/10.1109/TIFS.2022.3165978
16. Lu, X., Yin, W., Zhang, P. Lattice-based verifiably encrypted signature scheme without Gaussian sampling for privacy protection in blockchain. Sustainability, 14(21), 14225 (2022). https://doi.org/10.3390/su142114225
17. Aumasson, J.-P., Bernstein, D. J., Beullens, W., Dobraunig, C., Eichlseder, M., Fluhrer, S., Gazdag, S.-L., Hülsing, A., Kampanakis, P., Kölbl, S. et al. SPHINCS+. Submission to the NIST Post-Quantum Cryptography Project, version 3.1 (2022). URL: https://sphincs.org/data/sphincs+-r3.1-specification.pdf
18. Bernstein, D. J., Hülsing, A., Kölbl, S., Niederhagen, R., Rijneveld, J., Schwabe, P. The SPHINCS+ signature framework. Proceedings of the ACM SIGSAC Conference on Computer and Communications Security, 2129–2146 (2019).
19. National Institute of Standards and Technology. Stateless hash-based digital signature standard. Federal Information Processing Standards Publications, FIPS 205 (2024). https://doi.org/10.6028/NIST.FIPS.205
20. Kiktenko, E., Bulychev, A., Karagodin, P., Pozhar, N., Anufriev, M., Fedorov, A. SPHINCS+ postquantum digital signature scheme with Streebog hash function. AIP Conference Proceedings, 2241, 020014 (2020).
21. Sim, M., Eum, S., Song, G., Kwon, H., Jang, K., Kim, H., Kim, H., Yang, Y., Kim, W., Lee, W. K. et al. K-XMSS and K-SPHINCS+: Hash-based signatures with Korean cryptography algorithms. Cryptology ePrint Archive, Report 2022/152 (2022). URL: https://eprint.iacr.org/2022/152
22. Tasmagambetov, O., Seitkulov, E., Ospanov, R., Yergaliyeva, B. Fault-tolerant backup storage system for confidential data in distributed servers. TELKOMNIKA, 21(5), 1030–1038 (2023). https://doi.org/10.12928/telkomnika.v21i5.25305
23. Tang, C., Chronopoulos, A. T. An efficient distributed key generation protocol for secure communications with causal ordering. Proceedings of the International Conference on Parallel and Distributed Systems, 2, 285–289 (2005).
24. Pedersen, T. P. Non-interactive and information-theoretic secure verifiable secret sharing. Lecture Notes in Computer Science, 576, 129–140 (1991).
25. Trung, M. M., Do, L. P., Tuan, D. T., Thanh, N. V., Tri, N. Q. Design a cryptosystem using elliptic curves cryptography and Vigenère symmetric key. International Journal of Electrical and Computer Engineering, 13(2), 1734–1743 (2023). https://doi.org/10.11591/ijece.v13i2.pp1734-1743
Review
For citations:
Seitkulov Ye.N., Ospanov R.M., Yergaliyeva B.B., Utebayev K.A., Atanov S.K. CRYPTOGRAPHIC PROTOCOL OF VERIFIABLY ENCRYPTED SIGNATURE WITH POSSIBILITY OF VERIFICATION AFTER A SPECIFIED TIME. Herald of the Kazakh-British Technical University. 2026;23(1):68-81. (In Russ.) https://doi.org/10.55452/1998-6688-2026-23-1-68-81
JATS XML






