Skip to main content
Log in

High-speed GPU implementation of a secret sharing scheme based on cellular automata

  • Published:
The Journal of Supercomputing Aims and scope Submit manuscript

Abstract

Parallel implementation provides a solution for the problem of accelerating cellular automata (CA)-based secret sharing schemes and make them appropriate for bulk data sharing and real-time applications. By presenting new platforms, we need new implementation techniques to run algorithms as fast as possible on the platform. In this paper, we present a new implementation of a CA-based secret sharing scheme using the Graphic Processing Unit (GPU). We propose a new data arrangement that reduces the total number of accesses to the memories in GPU. Our algorithm further reduces the amount of data required by each thread and at the same time achieves a high cache hit rate. Also, it can achieve coalesced memory accesses to optimal use of the global memory bandwidth. The proposed method obtains speedup up to four times faster than the best previous GPU implemented CA-based multi-secret sharing schemes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Alvarez G, Encinas LH, Del Rey AM (2008) A multisecret sharing scheme for color images based on cellular automata. Inf Sci 178(22):4382–4395

    Article  Google Scholar 

  2. Blakley GR et al (1979) Safeguarding cryptographic keys. In: Proceedings of the National Computer Conference. vol 48, pp 313–317

  3. Cramer R, Damgård I, Nielsen JB (2001) Multiparty computation from threshold homomorphic encryption. In: International Conference on the Theory and Applications of Cryptographic Techniques. Springer, pp 280–300

  4. Del Rey AM, Mateus JP, Sánchez GR (2005) A secret sharing scheme based on cellular automata. Appl Math Comput 170(2):1356–1364

    MathSciNet  MATH  Google Scholar 

  5. Eslami Z, Ahmadabadi JZ (2010) A verifiable multi-secret sharing scheme based on cellular automata. Inf Sci 180(15):2889–2894

    Article  MathSciNet  Google Scholar 

  6. Faraoun KM (2014) A novel fast and provably secure (t, n)-threshold secret sharing construction for digital images. J Inf Secur Appl 19(6):331–340

    MathSciNet  Google Scholar 

  7. Goyal V, Pandey O, Sahai A, Waters B (2006) Attribute-based encryption for fine-grained access control of encrypted data. In: Proceedings of the 13th ACM Conference on Computer and Communications Security. ACM, pp 89–98

  8. Grosser T, Cohen A, Kelly P.H, Ramanujam J, Sadayappan P, Verdoolaege S (2013) Split tiling for GPUs: automatic parallelization using trapezoidal tiles. In: Proceedings of the 6th Workshop on General Purpose Processor Using Graphics Processing Units. ACM, pp 24–31

  9. Ha PH, Tsigas P, Anshus OJ (2010) The synchronization power of coalesced memory accesses. IEEE Trans Parallel Distrib Syst 21(7):939–953

    Article  Google Scholar 

  10. He J, Dawson E (1995) Multisecret-sharing scheme based on one-way function. Electron Lett 31(2):93–95

    Article  Google Scholar 

  11. Hernandez-Becerril A, Nakano-Miyatake M, Ramirez-Tachiquin M, Perez-Meana H (2013) Parallel implementation of multiple secret image sharing based on cellular automata. J Commun Comput 10:649–660

    Google Scholar 

  12. Hernandez-Becerril A, Nakano-Miyatake M, Ramirez-Tachiquin M, Perez-Meana H (2013) A parallel implementation of multiple secrete image sharing based on cellular automata with LSB steganography. In: Intelligent Software Methodologies, Tools and Techniques (SoMeT), 2013 IEEE 12th International Conference on. IEEE, pp 191–196

  13. Hernandez-Becerril RA, Bucio-Ramirez AG, Nakano-Miyatake M, Perez-Meana H, Ramirez-Tachiquin MP (2016) A GPU implementation of secret sharing scheme based on cellular automata. J Supercomput 72(4):1291–1311

    Article  Google Scholar 

  14. Hernandez-Becerrjl A, Nakano-Miyatake M, Perez-Meana H.M, Bucio A, Ramirez-Tachiquin M (2014) A parallel authenticated encryption sharing scheme based on cellular automata. In: Proceedings of the World Congress on Engineering and Computer Science. vol 1

  15. Holewinski J, Pouchet L.N, Sadayappan P (2012) High-performance code generation for stencil computations on GPU architectures. In: Proceedings of the 26th ACM International Conference on Supercomputing. ACM, pp 311–320

  16. Ito M, Saito A, Nishizeki T (1989) Secret sharing scheme realizing general access structure. Electron Commun Jpn (Part III Fundam Electron Sci) 72(9):56–64

    Article  MathSciNet  Google Scholar 

  17. Pang LJ, Wang YM (2005) A new (t, n) multi-secret sharing scheme based on shamirs secret sharing. Appl Math Comput 167(2):840–848

    MathSciNet  MATH  Google Scholar 

  18. Rahman S.M.F, Yi Q, Qasem A (2011) Understanding stencil code performance on multicore architectures. In: Proceedings of the 8th ACM International Conference on Computing Frontiers. ACM, p 30

  19. Schäfer A, Fey D (2011) High performance stencil code algorithms for GPGPUs. Procedia Comput Sci 4:2027–2036

    Article  Google Scholar 

  20. Schoenmakers B (1999) A simple publicly verifiable secret sharing scheme and its application to electronic voting. In: Annual International Cryptology Conference. Springer, pp 148–164

  21. Shamir A (1979) How to share a secret. Commun ACM 22(11):612–613

    Article  MathSciNet  Google Scholar 

  22. Shao J (2014) Efficient verifiable multi-secret sharing scheme based on hash function. Inf Sci 278:104–109

    Article  MathSciNet  Google Scholar 

  23. Wang D, Zhang L, Ma N, Li X (2007) Two secret sharing schemes based on boolean operations. Pattern Recognit 40(10):2776–2785

    Article  Google Scholar 

  24. Wijaya S, Tan SK, Guan SU (2007) Permutation and sampling with maximum length CA or pseudorandom number generation. Appl Math Comput 185(1):312–321

    MathSciNet  MATH  Google Scholar 

  25. Wolfram S (2018) Cellular automata and complexity: collected papers. CRC Press, Boca Raton

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ziba Eslami.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kabirirad, S., Fazlali, M. & Eslami, Z. High-speed GPU implementation of a secret sharing scheme based on cellular automata. J Supercomput 75, 7314–7336 (2019). https://doi.org/10.1007/s11227-019-02910-w

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11227-019-02910-w

Keywords

Navigation