Skip to main content
SpringerLink
Log in

Multiplicative Linear Secret Sharing Without Interaction

  • Conference paper
  • First Online:
Artificial Intelligence and Security (ICAIS 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11634))

Included in the following conference series:

  • 1406 Accesses

Abstract

As an essential building block in cryptosystem, linear secret sharing is widely used to safeguard the confidentiality and reliability of outsourced data. Though addition and constant multiplication are extremely easy thanks to the linear operation over shared secrets, how to efficiently multiply multiple shares remains an open problem. In this paper, we devised a non-interactive multiplication scheme based on Shamir’s secret sharing without parameter constrain. It is proved that our scheme is unconditionally secure if no more than k participants are compromised, meaning that both the security and access structure of Shamir’s scheme are immensely retained.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. El-Sayed, H., Sankar, S., Prasad, M., et al.: Edge of things: the big picture on the integration of edge, IoT and the cloud in a distributed computing environment. IEEE Access 6(99), 1706–1717 (2018)

    Article  Google Scholar 

  2. SabatÉ, M., Costa, M.A., Kozuma, K., et al.: Survey on various data integrity attacks in cloud environment and the solutions. In: International Conference on Circuits, Power and Computing Technologies, pp. 1076–1081. IEEE (2013)

    Google Scholar 

  3. Patel, K: Secure multiparty computation using secret sharing. In: International Conference on Signal Processing, Communication, Power and Embedded System, pp. 863–866. IEEE (2017)

    Google Scholar 

  4. Liu, J., Li, W., Karame, G.O., et al.: Scalable byzantine consensus via hardware-assisted secret sharing. IEEE Trans. Comput. 1 (2016)

    Google Scholar 

  5. Xie, M.M., Liao, X.F., Zhou, Q.: Generalized oblivious transfer protocol in distributed setting based on secret sharing. Comput. Eng. 40(3), 184–187 (2014)

    Google Scholar 

  6. Attasena, V., Darmont, J., Harbi, N.: Secret sharing for cloud data security: a survey. VLDB J. 2017(2), 1–25 (2017)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  8. Blakley, G.R.: Safeguarding cryptographic keys, p. 313. IEEE Computer Society (1979)

    Google Scholar 

  9. Brickell, E.F.: Some ideal secret sharing schemes. In: Quisquater, J.-J., Vandewalle, J. (eds.) EUROCRYPT 1989. LNCS, vol. 434, pp. 468–475. Springer, Heidelberg (1990). https://doi.org/10.1007/3-540-46885-4_45

    Chapter  Google Scholar 

  10. Bertilsson, M., Ingemarsson, I.: A construction of practical secret sharing schemes using linear block codes. In: Seberry, J., Zheng, Y. (eds.) AUSCRYPT 1992. LNCS, vol. 718, pp. 67–79. Springer, Heidelberg (1993). https://doi.org/10.1007/3-540-57220-1_53

    Chapter  Google Scholar 

  11. Van Dijk, M., Kevenaar, T., Schrijen, G.J., et al.: Improved constructions of secret sharing schemes by applying (λ, w)-decompositions. In: Proceedings of the IEEE International Symposium on Information Theory, p. 282. IEEE (2003)

    Google Scholar 

  12. Beimel, A., Weinreb, E.: Monotone circuits for monotone weighted threshold functions. Elsevier North-Holland, Inc. (2006)

    Google Scholar 

  13. Li, H., Liu, H.: Multi-access structure secret sharing schemes without dealer. Nat. Sci. J. Harbin Normal Univ. (2013)

    Google Scholar 

  14. Basit, A., Kumar, N.C., Venkaiah, V.C., et al.: Multi-stage multi-secret sharing scheme for hierarchical access structure. In: International Conference on Computing, Communication and Automation. IEEE (2017)

    Google Scholar 

  15. Ito, M., Saito, A., Nishizeki, T.: Secret sharing scheme realizing general access structure. Electron. Commun. Jpn. 72(9), 56–64 (2010)

    Article  MathSciNet  Google Scholar 

  16. Benaloh, J., Leichter, J.: Generalized secret sharing and monotone functions. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 27–35. Springer, New York (1990). https://doi.org/10.1007/0-387-34799-2_3

    Chapter  Google Scholar 

  17. Karchmer, M., Wigderson, A.: On span programs. In: IEEE Conference on Structure in Complexity Theory, pp. 102–111. IEEE Computer Society (1993)

    Google Scholar 

  18. Csirmaz, L.: The size of a share must be large. J. Cryptol. 10(4), 223–231 (1997)

    Article  MathSciNet  Google Scholar 

  19. Jhanwar, M.P., Safavi-Naini, R.: Unconditionally-secure robust secret sharing with minimum share size. In: Sadeghi, A.-R. (ed.) FC 2013. LNCS, vol. 7859, pp. 96–110. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39884-1_9

    Chapter  Google Scholar 

  20. Tran, T., Rahman, M., Bhuiyan, M.Z.A., et al.: Optimizing share size in efficient and robust secret sharing scheme for big data. IEEE Trans. Big Data PP(99), 1 (2017)

    Article  Google Scholar 

  21. Boyle, E., Couteau, G., Gilboa, N., et al.: Homomorphic secret sharing: optimizations and applications. In: ACM SIGSAC Conference on Computer and Communications Security, pp. 2105–2122. ACM (2017)

    Google Scholar 

  22. Damgård, I., Fitzi, M., Kiltz, E., Nielsen, J.B., Toft, T.: Unconditionally secure constant-rounds multi-party computation for equality, comparison, bits and exponentiation. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 285–304. Springer, Heidelberg (2006). https://doi.org/10.1007/11681878_15

    Chapter  Google Scholar 

  23. Nishide, T., Ohta, K.: Multiparty computation for interval, equality, and comparison without bit-decomposition protocol. In: Okamoto, T., Wang, X. (eds.) PKC 2007. LNCS, vol. 4450, pp. 343–360. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-71677-8_23

    Chapter  Google Scholar 

  24. Boyle, E., Gilboa, N., Ishai, Y., et al.: Foundations of homomorphic secret sharing. In: 9th Innovations in Theoretical Computer Science Conference, vol. 21, pp. 1–20 (2018)

    Google Scholar 

  25. Gennaro, R., Rabin, M.O., Rabin, T.: Simplified VSS and fast-track multiparty computations with applications to threshold cryptography. In: Proceedings of the ACM Symposium on Principles of Distributed Computing, pp. 101–111. ACM Press (1998)

    Google Scholar 

  26. Ishai, Y., Kushilevitz, E.: Randomizing polynomials: a new representation with applications to round-efficient secure computation. In: Proceedings of the Symposium on Foundations of Computer Science, pp. 294–304. IEEE (2000)

    Google Scholar 

  27. Ishai, Y., Kushilevitz, E., Meldgaard, S., Orlandi, C., Paskin-Cherniavsky, A.: On the power of correlated randomness in secure computation. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 600–620. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36594-2_34

    Chapter  MATH  Google Scholar 

  28. Barkol, O., Ishai, Y., Weinreb, E.: On d-multiplicative secret sharing. J. Cryptol. 23(4), 580–593 (2010)

    Article  MathSciNet  Google Scholar 

  29. Yoshida, M., Obana, S.: Verifiably multiplicative secret sharing. In: International Conference on Information Theoretic Security, pp. 73–82 (2017)

    Google Scholar 

  30. Watanabe, T., Iwamura, K., Kaneda, K.: Secrecy multiplication based on a (k, n)-threshold secret-sharing scheme using only k servers. In: Park, J., Stojmenovic, I., Jeong, H., Yi, G. (eds.) Computer Science and its Applications. LNEE, vol. 330, pp. 107–112. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-45402-2_16

    Chapter  Google Scholar 

  31. Blackburn, S.R., Burmester, M., Desmedt, Y., Wild, P.R.: Efficient multiplicative sharing schemes. In: Maurer, U. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 107–118. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-68339-9_10

    Chapter  Google Scholar 

  32. Wang, H., Lam, K.Y., Xiao, G.-Z., Zhao, H.: On multiplicative secret sharing schemes. In: Dawson, E.P., Clark, A., Boyd, C. (eds.) ACISP 2000. LNCS, vol. 1841, pp. 342–351. Springer, Heidelberg (2000). https://doi.org/10.1007/10718964_28

    Chapter  Google Scholar 

  33. Jackson, W.A., Martin, K.M., O’Keefe, C.M.: Mutually trusted authority-free secret sharing schemes. J. Cryptol. 10(4), 261–289 (1997)

    Article  MathSciNet  Google Scholar 

  34. Boyle, E., Gilboa, N., Ishai, Y.: Group-based secure computation: optimizing rounds, communication, and computation. In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017. LNCS, vol. 10211, pp. 163–193. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-56614-6_6

    Chapter  Google Scholar 

  35. Pilaram, H., Eghlidos, T.: An efficient lattice based multi-stage secret sharing scheme. IEEE Trans. Dependable Secure Comput. 14(1), 2–8 (2017)

    Google Scholar 

  36. Shi, M., Guan, Y., Solé, P.: Two new families of two-weight codes. IEEE Trans. Inf. Theory PP(99), 1 (2017)

    MathSciNet  MATH  Google Scholar 

  37. Gopinath, V., Bhuvaneswaran, R.S.: Design of ECC based secured cloud storage mechanism for transaction rich applications. CMC: Comput. Mater. Continua 57(2), 341–352 (2018)

    Google Scholar 

  38. Zhong, J., Liu, Z., Xu, J.: Analysis and improvement of an efficient controlled quantum secure direct communication and authentication protocol. CMC: Comput. Mater. Continua 57(3), 621–633 (2018)

    Google Scholar 

Download references

Acknowledgments

This work is supported by the National Science Foundation of China P. R. (NSFC) under Grants 61703063, 61573076, 61663008; Chongqing Research Program of Basic Research and Frontier Technology under Grant CSTC2017jcyjAX0411; the Scientific Research Foundation for the Returned Overseas Chinese Scholars under Grant 2015-49; the Program for Excellent Talents of Chongqing Higher School under Grant 2014-18; Science and Technology Research Project of Chongqing Municipal Education Commission of China P. R. under Grants KJ1705139, KJ1600518, KJ1705121 and KJ1605002; Chongqing Municipal Social Livelihood Science and Technology Innovation Project under Grant CSTC2016shmszx30026; Urumqi Science and Technology Plan Project under Grant Y161320008.

Author information

Authors and Affiliations

  1. Institute of Information Science and Engineering, Chongqing Jiaotong University, Chongqing, 400074, China

    Bo Mi, Darong Huang, Jianqiu Cao, Ping Long & Hongyang Pan

Authors
  1. Bo Mi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Darong Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jianqiu Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ping Long
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Hongyang Pan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Darong Huang .

Editor information

Editors and Affiliations

  1. Nanjing University of Information Science and Technology, Nanjing, China

    Xingming Sun

  2. Nanjing University of Information Science and Technology, Nanjing, China

    Zhaoqing Pan

  3. Purdue University, West Lafayette, IN, USA

    Elisa Bertino

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Mi, B., Huang, D., Cao, J., Long, P., Pan, H. (2019). Multiplicative Linear Secret Sharing Without Interaction. In: Sun, X., Pan, Z., Bertino, E. (eds) Artificial Intelligence and Security. ICAIS 2019. Lecture Notes in Computer Science(), vol 11634. Springer, Cham. https://doi.org/10.1007/978-3-030-24271-8_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-24271-8_16

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-24270-1

  • Online ISBN: 978-3-030-24271-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation