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FPGA acceleration of secret sharing for 3D data cubes

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Abstract

Secret sharing can protect the security of important secret information in the network environment. However, the computational complexity and processing delay increase drastically when the secret information contains large amounts of data, such as three-dimensional (3D) data cubes. To improve the efficiency of secret sharing on 3D data cubes, this paper proposes a hardware architecture to accelerate the generation of shares and reconstruction of the secret. The proposed hardware architecture parallelizes the secret sharing process and optimizes on this basis to save large amounts of circuit resources. Simulation results show that this architecture performs secret sharing more than ten times faster than the software implementation. This study enables the secret sharing of 3D data cubes, which protect large amounts of data information throughout the process and allows complete reconstruction of 3D data cubes. To be able to handle secrets without decoding them, we then extend the hardware architecture to the four basic processes of multi-party computation, demonstrating the feasibility of the structure and providing preliminary research tools for the effective implementation of multi-party computation.

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Data availability

The data used in this study are available from the corresponding author upon request.

References

  1. Beimel, A., Chor, B.: Universally ideal secret-sharing schemes. IEEE Trans. Inf. Theory 40(3), 786–794 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  2. Blakley, G.R.: Safeguarding cryptographic keys. In: International workshop on managing requirements knowledge, pp. 313–313. IEEE Computer Society (1979)

  3. Blanton, M., Kang, A., Yuan, C.: Improved building blocks for secure multi-party computation based on secret sharing with honest majority. In: International Conference on Applied Cryptography and Network Security. Springer, pp. 377–397 (2020)

  4. Chanu, O.B., Neelima, A.: A survey paper on secret image sharing schemes. Int. J. Multimed. Inf. Retriev. 8(4), 195–215 (2019). https://doi.org/10.1007/s13735-018-0161-3

    Article  Google Scholar 

  5. Halpern, J., Teague, V.: Rational secret sharing and multiparty computation. In: Proceedings of the Thirty-Sixth Annual ACM Symposium on Theory of Computing, pp. 623–632 (2004)

  6. Han, J., Susilo, W., Mu, Y., Yan, J.: Attribute-based oblivious access control. Comput. J. 55(10), 1202–1215 (2012). https://doi.org/10.1093/comjnl/bxs061

    Article  Google Scholar 

  7. Hanaoka, G., Nishioka, T., Zheng, Y., Imai, H.: A hierarchical non-interactive key-sharing scheme with low memory size and high resistance against collusion attacks. Comput. J. 45(3), 293–303 (2002). https://doi.org/10.1093/comjnl/45.3.293

    Article  MATH  Google Scholar 

  8. Hansen, J.P.: Secret sharing schemes with strong multiplication and a large number of players from toric varieties. Contemp. Math. 686, 171–185 (2017). https://doi.org/10.1090/conm/686/13783

    Article  MathSciNet  MATH  Google Scholar 

  9. Iftene, S.: General secret sharing based on the Chinese remainder theorem with applications in e-voting. Electro. Notes Theor. Comput. Sci. 186, 67–84 (2007). https://doi.org/10.1016/j.entcs.2007.01.065

    Article  MathSciNet  MATH  Google Scholar 

  10. Kabirirad, S., Eslami, Z.: Improvement of \((n, n)\)-multi-secret image sharing schemes based on Boolean operations. J. Inf. Secur. Appl. 47, 16–27 (2019). https://doi.org/10.1016/j.jisa.2019.03.018

    Article  Google Scholar 

  11. Kumar, S.: Extending boolean operations-based secret image sharing to compartmented access structure. Multimed. Tools Appl. (2022). https://doi.org/10.1007/s11042-021-11554-z

    Article  Google Scholar 

  12. Liu, J., Wu, Y., Liu, X., Zhang, Y., Xue, G., Zhou, W., Yao, S.: On the (in) security of recent group key distribution protocols. Comput. J. 60(4), 507–526 (2017). https://doi.org/10.1093/comjnl/bxw061

    Article  MathSciNet  Google Scholar 

  13. Liu, T., Yan, B., Pan, J.S.: Color visual secret sharing for QR code with perfect module reconstruction. Appl. Sci. (2019). https://doi.org/10.3390/app9214670

    Article  Google Scholar 

  14. McEliece, R.J., Sarwate, D.V.: On sharing secrets and Reed-Solomon codes. Commun. ACM 24(9), 583–584 (1981). https://doi.org/10.1145/358746.358762

    Article  MathSciNet  Google Scholar 

  15. Pan, J.S., Sun, X.X., Chu, S.C., Abraham, A., Yan, B.: Digital watermarking with improved SMS applied for QR code. Eng. Appl. Artif. Intell. 97, 104049 (2021). https://doi.org/10.1016/j.engappai.2020.104049

    Article  Google Scholar 

  16. Pan, J.S., Liu, T., Yang, H.M., Yan, B., Chu, S.C., Zhu, T.: Visual cryptography scheme for secret color images with color QR codes. J. Vis. Commun. Image Represent. 82, 103405 (2022)

    Article  Google Scholar 

  17. Patel, R., Wolfe, P.F., Munafo, R., Varia, M., Herbordt, M.: Arithmetic and Boolean secret sharing MPC on FPGAs in the data center. In: 2020 IEEE High Performance Extreme Computing Conference (HPEC), pp. 1–8. IEEE (2020)

  18. Pilaram, H., Eghlidos, T., Toluee, R.: An efficient lattice-based threshold signature scheme using multi-stage secret sharing. IET Inf. Secur. 15(1), 98–106 (2021). https://doi.org/10.1049/ise2.12007

    Article  Google Scholar 

  19. Prasetyo, H., Simatupang, J.W.: XOR-ed based friendly-progressive secret sharing. In: 2019 International Symposium on Intelligent Signal Processing and Communication Systems (ISPACS), pp. 1–2. IEEE (2019)

  20. Qin, C., Jiang, C., Mo, Q., Yao, H., Chang, C.C.: Reversible data hiding in encrypted image via secret sharing based on GF (p) and GF (\(2^{8}\)). IEEE Trans. Circ. Syst. Video Technol. 32(4), 1928–1941 (2021). https://doi.org/10.1109/TCSVT.2021.3091319

    Article  Google Scholar 

  21. Rolf, O.: Contemporary cryptography. Ph.D. thesis, Artech House, Inc. (2011)

  22. Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979). https://doi.org/10.1145/359168.359176

    Article  MathSciNet  MATH  Google Scholar 

  23. Stangl, J., Lorünser, T., Dinakarrao, S.M.P.: A fast and resource efficient FPGA implementation of secret sharing for storage applications. In: 2018 Design, Automation & Test in Europe Conference & Exhibition (DATE), pp. 654–659. IEEE (2018)

  24. Thien, C.C., Lin, J.C.: Secret image sharing. Comput. Graph. 26(5), 765–770 (2002). https://doi.org/10.1016/S0097-8493(02)00131-0

    Article  Google Scholar 

  25. Wang, R.Z., Su, C.H.: Secret image sharing with smaller shadow images. Pattern Recogn. Lett. 27(6), 551–555 (2006). https://doi.org/10.1016/j.patrec.2005.09.021

    Article  Google Scholar 

  26. Wang, F., Chang, C.C., Harn, L.: Simulatable and secure certificate-based threshold signature without pairings. Secur. Commun. Netw. 7(11), 2094–2103 (2014). https://doi.org/10.1002/SEC.921

    Article  Google Scholar 

  27. Xing, F., Yan, X., Yu, L., Sun, Y.: Information hiding in the sharing domain. J. Vis. Commun. Image Represent. 86, 103520 (2022). https://doi.org/10.1016/j.jvcir.2022.103520

    Article  Google Scholar 

  28. Xiong, L., Han, X., Yang, C.N.: CP-PSIS: CRT and polynomial-based progressive secret image sharing. Signal Process. 185, 108064 (2021). https://doi.org/10.1016/j.sigpro.2021.108064

    Article  Google Scholar 

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Acknowledgements

This work was funded by the Shandong Provincial Natural Science Foundation (No. ZR2021MF050), the Ministry of Education in China (MOE) Project of Humanities and Social Sciences (Project No. 18YJAZH110), and the National Statistics Science Project (2021LY082).

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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by TL, BY, J-SP and H-MY. The first draft of the manuscript was written by Z-MW and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Bin Yan.

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Wu, ZM., Liu, T., Yan, B. et al. FPGA acceleration of secret sharing for 3D data cubes. J Real-Time Image Proc 20, 82 (2023). https://doi.org/10.1007/s11554-023-01337-0

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