Advertisement

Performance evaluation of secret sharing schemes with data recovery in secured and reliable heterogeneous multi-cloud storage

  • Andrei TchernykhEmail author
  • Vanessa Miranda-López
  • Mikhail Babenko
  • Fermin Armenta-Cano
  • Gleb Radchenko
  • Alexander Yu. Drozdov
  • Arutyun Avetisyan
Article
  • 70 Downloads

Abstract

Properties of redundant residue number system (RRNS) are used for detecting and correcting errors during the data storing, processing and transmission. However, detection and correction of a single error require significant decoding time due to the iterative calculations needed to locate the error. In this paper, we provide a performance evaluation of Asmuth-Bloom and Mignotte secret sharing schemes with three different mechanisms for error detecting and correcting: Projection, Syndrome, and AR-RRNS. We consider the best scenario when no error occurs and worst-case scenario, when error detection needs the longest time. When examining the overall coding/decoding performance based on real data, we show that AR-RRNS method outperforms Projection and Syndrome by 68% and 52% in the worst-case scenario.

Keywords

Storage Reliability Residue number system 

Notes

Acknowledgments

The work is partially supported by Russian Federation President Grant SP-1215.2016, and Russian Foundation for Basic Research (RFBR) 18-07-01224.

References

  1. 1.
    Tchernykh, A., Schwiegelsohn, U., Alexandrov, V., Talbi, E.: Towards understanding uncertainty in cloud computing resource provisioning. Proc. Comput. Sci. 51, 1772–1781 (2015).  https://doi.org/10.1016/j.procs.2015.05.387 CrossRefGoogle Scholar
  2. 2.
    Tchernykh, A., Schwiegelsohn, U., Talbi, E., Babenko, M.: Towards understanding uncertainty in cloud computing with risks of confidentiality, integrity, and availability. J. Comput. Sci. (2016).  https://doi.org/10.1016/j.jocs.2016.11.011 Google Scholar
  3. 3.
    Tchernykh, A., Babenko, M., Chervyakov, N., Cortés-Mendoza, J. M., Kucherov, N., Miranda-López, V., Radchenko, G.: Towards mitigating uncertainty of data security breaches and collusion in cloud computing. In: Database and Expert Systems Applications (DEXA), 2017 28th International Workshop on, pp. 137–141. IEEE. (2017).  https://doi.org/10.1109/dexa.2017.44
  4. 4.
    Nelson, V.P.: Fault-tolerant computing: fundamental concepts. Computer 23(7), 19–25 (1990).  https://doi.org/10.1109/2.56849 CrossRefGoogle Scholar
  5. 5.
    Lin, S., Costello, D.J.: Error Control Coding, 2. Prentice Hall, Englewood Cliffs (2004)zbMATHGoogle Scholar
  6. 6.
    Barsi, F., Maestrini, P.: Error correcting properties of redundant residue number systems. IEEE Trans. Comput. 100(3), 307–315 (1973).  https://doi.org/10.1109/T-C.1973.223711 MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Mandelbaum, D.: On a class of arithmetic codes and a decoding algorithm. IEEE Trans. Inf. Theory 22(1), 85–88 (1976).  https://doi.org/10.1109/TIT.1976.1055504 MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Szabo, N.S., Tanaka, R.I.: Residue arithmetic and its applications to computer technology. McGraw-Hill, New York (1967)zbMATHGoogle Scholar
  9. 9.
    Etzel, M., Jenkins, W.: Redundant residue number systems for error detection and correction in digital filters. IEEE Trans. Acoust. Speech Signal Process. 28(5), 538–545 (1980).  https://doi.org/10.1109/TASSP.1980.1163442 MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Watson, R.W., Hastings, C.W.: Self-checked computation using residue arithmetic. Proc. IEEE 54(12), 1920–1931 (1966).  https://doi.org/10.1109/PROC.1966.5275 CrossRefGoogle Scholar
  11. 11.
    Krishna, H., Lin, K.Y., Sun, J.D.: A coding theory approach to error control in redundant residue number systems. I. Theory and single error correction. IEEE Trans. Circ. Syst. II 39(1), 8–17 (1992).  https://doi.org/10.1109/82.204106 CrossRefzbMATHGoogle Scholar
  12. 12.
    Tay, T. F., & Chang, C. H.: A new algorithm for single residue digit error correction in Redundant Residue Number System. In: Circuits and Systems (ISCAS), 2014 IEEE International Symposium on, pp. 1748–1751. IEEE. (2014).  https://doi.org/10.1109/iscas.2014.6865493
  13. 13.
    Asmuth, C., Bloom, J.: A modular approach to key safeguarding. IEEE Trans. Inf. Theory 29, 208–210 (1983).  https://doi.org/10.1109/TIT.1983.1056651 MathSciNetCrossRefGoogle Scholar
  14. 14.
    Mignotte, M.: How to Share a Secret. In: Beth, T. (ed.) Cryptography. EUROCRYPT 1982. Lecture Notes in Computer Science, col 149. Springer, Berlin. pp. 371–375 (1982). doi:  https://doi.org/10.1007/3-540-39466-4_27
  15. 15.
    Ţiplea, F., Drăgan, C.: A necessary and sufficient condition for the asymptotic idealness of the GRS threshold secret sharing scheme. Inf. Process. Lett. 114(6), 299–303 (2014).  https://doi.org/10.1016/j.ipl.2014.01.008 MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Celesti, A., Fazio, M., Villari, M., Puliafito, A.: Adding long-term availability, obfuscation, and encryption to multi-cloud storage systems. J. Netw. Comput. Appl. 59, 208–218 (2016).  https://doi.org/10.1016/j.jnca.2014.09.021 CrossRefGoogle Scholar
  17. 17.
    Chessa, S., Maestrini, P.: Dependable and Secure data storage and retrieval in mobile, wireless networks. In: 2003 International Conference on Dependable Systems and Networks. Proceedings. pp. 207–216 (2003)Google Scholar
  18. 18.
    Chervyakov, N., Babenko, M., Tchernykh, A., Kucherov, N., Miranda-López, V., Cortés-Mendoza, J.M.: AR-RRNS: configurable, scalable and reliable systems for internet of things to ensure security. Futur. Gener. Comput. Syst. (2017).  https://doi.org/10.1016/j.future.2017.09.061 Google Scholar
  19. 19.
    Dworkin M.: SHA-3 standard: permutation-based hash and extendable-output functions. (2015). doi: https://dx.doi.org/10.6028/NIST.FIPS.202
  20. 20.
    Tay, T.F., Chang, C.H.: A non-iterative multiple residue digit error detection and correction algorithm in RRNS. IEEE Trans. Comput. 65(2), 396–408 (2016).  https://doi.org/10.1109/TC.2015.2435773 MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Chervyakov, N.I., Lyakhov, P.A., Babenko, M.G., Garyanina, A.I., Lavrinenko, I.N., Lavrinenko, A.V., Deryabin, M.A.: An efficient method of error correction in fault-tolerant modular neurocomputers. Neurocomputing. 205, 32–44 (2016).  https://doi.org/10.1016/j.neucom.2016.03.041 CrossRefGoogle Scholar
  22. 22.
    Babenko, M., Kucherov, N., Tchernykh, A., Chervyakov, N., Nepretimova, E., & Vashchenko, I.: Development of a control system for computations in BOINC with homomorphic encryption in residue number system. In: BOINC:FAST 2017: Third International Conference BOINC-based High Performance Computing: Fundamental Research and Development. CEUR-WS. 1973, pp. 78–84 (2017)Google Scholar
  23. 23.
    Chervyakov, N.I., Lyakhov, P.A., Babenko, M.G., Lavrinenko, I.N., Lavrinenko, A.V., Nazarov, A.S.: The architecture of a fault-tolerant modular neurocomputer based on modular number projections. Neurocomputing 272, 96–107 (2018)CrossRefGoogle Scholar
  24. 24.
    Su, C.C., Lo, H.Y.: An algorithm for scaling and single residue error correction in residue number systems. IEEE Trans. Comput. 39(8), 1053–1064 (1990).  https://doi.org/10.1109/12.57044 CrossRefGoogle Scholar
  25. 25.
    Dimauro, G., Impedovo, S., Pirlo, G.: A new technique for fast number comparison in the residue number system. IEEE Trans. Comput. 42(5), 608–612 (1993).  https://doi.org/10.1109/12.223680 MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Wang, Y., Song, X., & Aboulhamid, M.: A new algorithm for RNS magnitude comparison based on new Chinese remainder theorem II. In: Proceedings. Ninth Great Lakes Symposium on VLSI. IEEE. pp. 362–365 (1999).  https://doi.org/10.1109/glsv.1999.757457
  27. 27.
    Goh, V.T., Siddiqi, M.U.: Multiple error detection and correction based on redundant residue number systems. IEEE Trans. Commun. 56(3), 325–330 (2008).  https://doi.org/10.1109/TCOMM.2008.050401 CrossRefGoogle Scholar
  28. 28.
    Haron, N.Z., Hamdioui, S.: Redundant residue number system code for fault-tolerant hybrid memories. ACM J. Emerg.Technol. Comput. Syst. (JETC) 7(1), 4 (2011).  https://doi.org/10.1145/1899390.1899394 Google Scholar
  29. 29.
    Yau, S.S., Liu, Y.C.: Error correction in redundant residue number systems. IEEE Trans. Comput. 22(1), 5–11 (1973).  https://doi.org/10.1109/T-C.1973.223594 MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Chang, C.H., Molahosseini, A.S., Zarandi, A.A.E., Tay, T.F.: Residue number systems: a new paradigm to datapath optimization for low-power and high-performance digital signal processing applications. IEEE Circuits Syst. Mag. 15, 26–44 (2015).  https://doi.org/10.1109/MCAS.2015.2484118 CrossRefGoogle Scholar
  31. 31.
    Gomathisankaran, M., Tyagi, A., Namuduri, K.: HORNS: A homomorphic encryption scheme for Cloud Computing using Residue Number System. In: 2011 45th Annual Conference on Information Sciences and Systems (CISS). pp. 1–5 (2011).  https://doi.org/10.1109/ciss.2011.5766176
  32. 32.
    Miranda-López, V., Tchernykh, A., Cortés-Mendoza, J. M., Babenko, M., Radchenko, G., Nesmachnow, S., & Du, Z.: Experimental Analysis of Secret Sharing Schemes for Cloud Storage Based on RNS. In: Latin American High Performance Computing Conference. Springer, Cham. pp. 370–383 (2017)Google Scholar
  33. 33.
    Quisquater, M., Preneel, B., & Vandewalle, J.: On the security of the threshold scheme based on the Chinese remainder theorem. In: Public Key Cryptography. pp. 199–210 (2002).  https://doi.org/10.1007/3-540-45664-3_14
  34. 34.
    Tentu, A.N., Venkaiah, V.C., Prasad, V.K.: CRT based multi-secret sharing schemes: revisited. Int. J. Secur. Netw. 13(1), 1–9 (2018).  https://doi.org/10.1504/IJSN.2018.090637 CrossRefGoogle Scholar
  35. 35.
    Kaya, K., Selçuk, A.A.: Threshold cryptography based on Asmuth-Bloom secret sharing. Inf. Sci. 177, 4148–4160 (2007).  https://doi.org/10.1016/j.ins.2007.04.008 MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Drăgan, C.C., Ţiplea, F.L.: Distributive weighted threshold secret sharing schemes. Inf. Sci. 339, 85–97 (2016).  https://doi.org/10.1016/j.ins.2016.01.019 MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Barzu, M., Ţiplea, F.L., Drăgan, C.C.: Compact sequences of co-primes and their applications to the security of CRT-based threshold schemes. Inf. Sci. 240, 161–172 (2013).  https://doi.org/10.1016/j.ins.2013.03.062 MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    Tchernykh, A., Babenko, M., Chervyakov, N., Miranda-López, V., Kuchukov, V., Cortés-Mendoza, J.-M., Deryabin, M., Kucherov, N., Radchenko, G., Avetisyan, A.: AC-RRNS: Anti-Collusion Secured Data Sharing Scheme for Cloud Storage. Int. J. Approx. Reason. 102, 60–73 (2018).  https://doi.org/10.1016/j.ijar.2018.07.010 MathSciNetCrossRefGoogle Scholar
  39. 39.
    thinkBoradband (2018). Retrieved from https://www.thinkbroadband.com
  40. 40.
    Drăgan, C.C., Tiplea, F.L.: On the asymptotic idealness of the Asmuth-Bloom threshold secret sharing scheme. Inf. Sci. (2018).  https://doi.org/10.1016/j.ins.2018.06.046 MathSciNetGoogle Scholar
  41. 41.
    Muhammad, Y.I., Kaiiali, M., Habbal, A., Wazan, A.S., Sani Ilyasu, A.: A secure data outsourcing scheme based on Asmuth-Bloom secret sharing. Enterpr. Inf. Syst. 10(9), 1001–1023 (2016).  https://doi.org/10.1080/17517575.2015.1120347 CrossRefGoogle Scholar
  42. 42.
    Harn, L., Hsu, C., Zhang, M., He, T., Zhang, M.: Realizing secret sharing with general access structure. Inf. Sci. 367, 209–220 (2016).  https://doi.org/10.1016/j.ins.2016.06.006 CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.CICESE Research CenterEnsenadaMexico
  2. 2.North-Caucasus Federal UniversityStavropolRussia
  3. 3.South Ural State UniversityChelyabinskRussia
  4. 4.Moscow Institute of Physics and TechnologyMoscowRussia
  5. 5.Institute for System ProgrammingMoscowRussia

Personalised recommendations