Efficient group ring based post-quantum Niederreiter public key encryption and key encapsulation mechanism
Sandeep Kumarsan.kuwar@gmail.comDefence Research & Development Organisation, Near Metcalfe HouseNew Delhi, Delhi, 110054, India0009-0005-7107-3914View full profile → , *Gaurav MittalCorresponding authorgaurav.mittaltwins@gmail.comDefence Research & Development Organisation, Near Metcalfe HouseNew Delhi, Delhi, 110054, IndiaView full profile → , Sunil Sangwansunilsangwan6174@gmail.comDefence Research & Development Organisation, Near Metcalfe HouseNew Delhi, Delhi, 110054, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 02 Jun 2025
- Published Online:
- 02 Apr 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-2614
- Pages:
- 2863–2872
Abstract
In this work, we present the IND-CPA secure (quantum) dual version of group ring based McEliece public key encryption (PKE) proposed in Mittal et al. (JDMSC, 2023). We show that in comparison to the classical PKE, the dual version is much more efficient. Further, we also present IND-CCA2 secure key encapsulation mechanism and IND-CCA2 secure PKE and show that both of these are quantum secure. Furthermore, we discuss the associated parameters with all the three schemes and also discuss a toy example to showcase their practicality.
Keywords
Subject Classifications
References
[1] D. Bernstein, J. Buchmann, and E. Dahmen, Post-Quantum Cryptography. Berlin Heidelberg: Springer (2009).
[2] D. Engelbert, R. Overbeck, and A. Schmidt, “A summary of McEliece-type cryptosystems and their security,” J. Math. Cryptol., vol. 1, no. 2, pp. 151–199 (2007).
[3] E. Fujisaki and T. Okamoto, “Secure integration of asymmetric and symmetric encryption schemes,” in Advances in Cryptology – CRYPTO’99, pp. 537–554 (1999).
[4] N. Goel, I. Gupta, and M. Dubey, “Undeniable signature scheme based over group ring,” Appl. Algebra Eng. Commun. Comput., vol. 27, pp. 523–535 (2016).
[5] B. Hurley and T. Hurley, “Group ring cryptography,” Int. J. Pure Appl. Math., vol. 69, no. 1, pp. 67–86 (2011).
[6] S. Kumar, G. Mittal, and A. Yadav, “A novel and provably secure identity-based blind signature scheme for online transactions,” Sādhanā, vol. 50, no. 2, pp. 1–12 (2025).
[7] S. Kumar, G. Mittal, and S. Kumar, “Digital signature schemes based on group ring,” SN Comput. Sci., vol. 3, article 398 (2022).
[8] S. Kumar, G. Mittal, and A. Yadav, “An efficient ID-based cryptographic encryption based on group ring,” J. Discrete Math. Sci. Cryptogr., vol. 27, no. 6, pp. 1851–1866 (2024).
[9] S. Kumar, G. Mittal, and A. Yadav, “A group ring based provably secure and efficient identity-based signature scheme,” in Congress on Smart Computing Technologies. Singapore: Springer Nature, pp. 1–15 (2023).
[10] O. Küsmüs and T. Hanoymak, “A novel public-key encryption scheme based on Bass cyclic units in integral group rings,” J. Discrete Math. Sci. Cryptogr., vol. 25, no. 2, pp. 579–589 (2023).
[11] C. P. Milies and S. K. Sehgal, An Introduction to Group Rings. Dordrecht: Springer (2002).
[12] G. Mittal, S. Kumar, S. Kumar, and S. Mittal, “A novel and efficient undeniable signature scheme based on group ring,” Soft Comput., vol. 28, no. 23, pp. 13053–13070 (2024).
[13] G. Mittal, S. Kumar, and S. Kumar, “A quantum secure ID-based cryptographic encryption based on group rings,” Sādhanā, vol. 47, article 35, pp. 1–16 (2022).
[14] G. Mittal, S. Kumar, S. Narain, and S. Kumar, “Group rings based public key cryptosystems,” J. Discrete Math. Sci. Cryptogr., vol. 25, no. 6, pp. 1683–1704 (2022).
[15] G. Mittal, S. Kumar, and S. Kumar, “An efficient procedure for online/offline ID-based signature using extended chaotic maps and group ring,” Security and Privacy, vol. 6, no. 3, e279 (2023).
[16] G. Mittal, S. Kumar, and S. Kumar, “McEliece and Blum–Goldwasser group rings based probabilistic cryptosystems,” J. Discrete Math. Sci. Cryptogr., vol. 26, no. 8, pp. 2229–2242 (2023).




