Compartmented multi-secret sharing scheme using elliptic curves
Mohan Chintamanimohansspecial@gmail.comSchool of Mathematics and StatisticsUniversity of HyderabadHyderabad, Telangana, 500046, IndiaView full profile → , Prabal Paulprabal.paul@gmail.comDepartment of MathematicsK K Birla Goa CampusBirla Institute of Technology and Science PilaniGoa, 403726, IndiaView full profile → , *Laba SaCorresponding authorlabasspecial@gmail.comSchool of Mathematics and StatisticsUniversity of HyderabadHyderabad, Telangana, 500046, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 13 Sep 2022
- Published Online:
- 03 Feb 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIOS-1362
- Pages:
- 811–831
Abstract
Keywords
Subject Classifications
References
[1] R. K. K. Ajeena and K. Hailiza, “The computational complexity of elliptic curve integer sub-decomposition (ISD) method, I,” AIP Conference Proceedings, vol. 1605, no. 1, AIP (2014).
[2] M. Backes, A. Kate, and A. Patra, “Computational verifiable secret sharing revisited,” in Advances in Cryptology – ASIACRYPT 2011, D. H. Lee and X. Wang, Eds. Lecture Notes in Computer Science, vol. 7073, Springer, Berlin, Heidelberg, pp. 7073 (2011).
[3] Q. Chen, C. Tang, and Z. Lin, “Efficient explicit constructions of compartmented secret sharing schemes,” Designs, Codes, and Cryptography, vol. 87, no. 12, pp. 2913-2940 (2019).
[4] Q. Chen, C. Tang, and Z. Lin, “Compartmented secret sharing schemes and locally repairable codes,” IEEE Transactions on Communications, vol. 68, no. 10, pp. 5976-5987 (2020).
[5] J. Coron, “Resistance against differential power analysis for elliptic curve cryptosystems,” in Proceedings of the 1st International Workshop on Cryptographic Hardware and Embedded Systems (CHES ‘99), vol. 1717 of Lecture Notes in Computer Science, Springer, pp. 292-302 (1999).
[6] P. Feldman, “A practical scheme for non-interactive verifiable secret sharing,” in 28th Annual Symposium on Foundations of Computer Science (SFCS 1987), pp. 427-438 (1987).
[7] O. Farras, J. Marti-Farre, and C. Padro, “Ideal multipartite secret sharing schemes,” Journal of Cryptology, vol. 25, no. 3, pp. 434-463 (2012).
[8] G. Frey, M. Müller, and H.-G. Rück, “The Tate pairing and the discrete logarithm applied to elliptic curve cryptosystems,” IEEE Transactions on Information Theory, vol. 45, no. 5, pp. 1717-1718 (1999).
[9] H. Ghodosi, J. Pieprzyk, and R. Safavi-Naini, “Secret sharing in multilevel and compartmented groups,” in Proc. ACISP 1998, LNCS vol. 1438, Springer Verlag, pp. 367-378 (1998).
[10] S. Iftene, “General secret sharing based on the Chinese remainder theorem with applications in E-voting,” Electronic Notes in Theoretical Computer Science, vol. 186, pp. 67-84 (2007).
[11] S. Ionica and A. Joux, “Pairing computation on elliptic curves with efficiently computable endomorphism and small embedding degree,” in Pairing-Based Cryptography - Pairing 2010, M. Joye, A. Miyaji, and A. Otsuka, Eds. Lecture Notes in Computer Science, vol. 6487, Springer, Berlin, Heidelberg (2010).
[12] A. Joux, “A one round protocol for tripartite Diffie-Hellman,” in Algorithmic Number Theory: 4th International Symposium, ANTS-IV, Lecture Notes in Computer Science, vol. 1838, Springer, 2000, pp. 385-393. Full version: Journal of Cryptology, vol. 17, pp. 263-276 (2004).
[13] K. E. Lauter and K. E. Stange, “The elliptic curve discrete logarithm problem and equivalent hard problems for elliptic divisibility sequences,” in International Workshop on Selected Areas in Cryptography, Springer: Berlin/Heidelberg, Germany, pp. 309-327 (2018).
[14] D. Liu, D. Huang, P. Luo, and Y. Dai, “New schemes for sharing points on an elliptic curve,” Computers and Mathematics with Applications, vol. 56, pp. 1556-1561 (2008).
[15] C. Mejia and J. A. Montoya, “On the information rates of homomorphic secret sharing schemes,” Journal of Information and Optimization Sciences, vol. 39, no. 7, pp. 1463-1482 (2018), https://doi.org/10.1080/02522667.2017.1367513.
[16] A. Menezes, “An introduction to pairing-based cryptography,” in Recent Trends in Cryptography, Contemp. Math., vol. 477, Amer. Math. Soc., Providence, RI, pp. 47-65 (2009).
[17] V. Miller, “The Weil pairing, and its efficient calculation,” Journal of Cryptology, vol. 17, pp. 235-261 (2004), https://doi.org/10.1007/s00145-004-0315-8.
[18] A. Mishra and A. Gupta, “Multi secret sharing scheme using iterative method,” Journal of Information and Optimization Sciences, vol. 39, no. 3, pp. 631-641 (2018), https://doi.org/10.1080/02522667.2017.1385161.
[19] E. A. Rawashdeh, “A simple method for finding the inverse matrix of Vandermonde matrix,” Matematički Vesnik, vol. 71, pp. 207-213 (2019).
[20] A. A. Selcuk and R. Yilmaz, “Joint compartmented threshold access structures,” IACR Cryptology ePrint Archive, 2013/054 (2013). [Online]. Available: https://eprint.iacr.org/2013/054.pdf.
[21] A. Shamir, “How to share a secret,” Comm. ACM, vol. 22, pp. 612-613 (1979).
[22] J. Silverman, The Arithmetic of Elliptic Curves, Springer (1986).
[23] G. Simmons, “How to (really) share a secret,” in Advances in Cryptology - Proceedings of CRYPTO ‘88, S. Goldwasser, Ed. Lecture Notes in Computer Science, vol. 403, Springer-Verlag, pp. 390-448 (1990).
[24] T. Tassa and N. Dyn, “Multipartite secret sharing by bivariate interpolation,” J. Cryptol., vol. 22, no. 2, pp. 227-258 (2009).
[25] A. N. Tentu, P. Paul, and V. Ch. Venkaiah, “Computationally perfect compartmented secret sharing schemes based on MDS codes,” Int. J. Trust Management in Computing and Communications, vol. 2, no. 4, pp. 353-378 (2014).
[26] G. Xu, J. Yuan, G. Xu, and Z. Dang, “An efficient compartmented secret sharing scheme based on linear homogeneous recurrence relations,” Security and Communication Networks, vol. 2021, Article ID 5566179 (2021). [Online]. Available: https://doi.org/10.1155/2021/5566179.
[27] Y. Yu and M. Wang, “A probabilistic secret sharing scheme for a compartmented access structure,” in Information and Communications Security, Q. S. Susilo, W. Wang, G. Liu, Eds., Lecture Notes in Computer Science, vol. 7043, Springer, Berlin, Heidelberg (2011).
