Advertisement

The Journal of Supercomputing

, Volume 75, Issue 11, pp 7314–7336 | Cite as

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

  • Saeideh Kabirirad
  • Mahmood Fazlali
  • Ziba EslamiEmail author
Article
  • 35 Downloads

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.

Keywords

GPU CUDA Cellular automata (n, n)-Secret sharing scheme 

Notes

References

  1. 1.
    Alvarez G, Encinas LH, Del Rey AM (2008) A multisecret sharing scheme for color images based on cellular automata. Inf Sci 178(22):4382–4395CrossRefGoogle Scholar
  2. 2.
    Blakley GR et al (1979) Safeguarding cryptographic keys. In: Proceedings of the National Computer Conference. vol 48, pp 313–317Google Scholar
  3. 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 280–300Google Scholar
  4. 4.
    Del Rey AM, Mateus JP, Sánchez GR (2005) A secret sharing scheme based on cellular automata. Appl Math Comput 170(2):1356–1364MathSciNetzbMATHGoogle Scholar
  5. 5.
    Eslami Z, Ahmadabadi JZ (2010) A verifiable multi-secret sharing scheme based on cellular automata. Inf Sci 180(15):2889–2894MathSciNetCrossRefGoogle Scholar
  6. 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):331–340MathSciNetGoogle Scholar
  7. 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 89–98Google Scholar
  8. 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 24–31Google Scholar
  9. 9.
    Ha PH, Tsigas P, Anshus OJ (2010) The synchronization power of coalesced memory accesses. IEEE Trans Parallel Distrib Syst 21(7):939–953CrossRefGoogle Scholar
  10. 10.
    He J, Dawson E (1995) Multisecret-sharing scheme based on one-way function. Electron Lett 31(2):93–95CrossRefGoogle Scholar
  11. 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 10:649–660Google Scholar
  12. 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 191–196Google Scholar
  13. 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):1291–1311CrossRefGoogle Scholar
  14. 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 1Google Scholar
  15. 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 311–320Google Scholar
  16. 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):56–64MathSciNetCrossRefGoogle Scholar
  17. 17.
    Pang LJ, Wang YM (2005) A new (t, n) multi-secret sharing scheme based on shamirs secret sharing. Appl Math Comput 167(2):840–848MathSciNetzbMATHGoogle Scholar
  18. 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 30Google Scholar
  19. 19.
    Schäfer A, Fey D (2011) High performance stencil code algorithms for GPGPUs. Procedia Comput Sci 4:2027–2036CrossRefGoogle Scholar
  20. 20.
    Schoenmakers B (1999) A simple publicly verifiable secret sharing scheme and its application to electronic voting. In: Annual International Cryptology Conference. Springer, pp 148–164Google Scholar
  21. 21.
    Shamir A (1979) How to share a secret. Commun ACM 22(11):612–613MathSciNetCrossRefGoogle Scholar
  22. 22.
    Shao J (2014) Efficient verifiable multi-secret sharing scheme based on hash function. Inf Sci 278:104–109MathSciNetCrossRefGoogle Scholar
  23. 23.
    Wang D, Zhang L, Ma N, Li X (2007) Two secret sharing schemes based on boolean operations. Pattern Recognit 40(10):2776–2785CrossRefGoogle Scholar
  24. 24.
    Wijaya S, Tan SK, Guan SU (2007) Permutation and sampling with maximum length CA or pseudorandom number generation. Appl Math Comput 185(1):312–321MathSciNetzbMATHGoogle Scholar
  25. 25.
    Wolfram S (2018) Cellular automata and complexity: collected papers. CRC Press, Boca RatonCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Data and Computer SciencesShahid Beheshti University, G.C.TehranIran

Personalised recommendations