Skip to main content

SW-SSS: Slepian-Wolf Coding-Based Secret Sharing Scheme

  • Conference paper
  • First Online:
International Joint Conference (CISIS 2015)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 369))

  • 801 Accesses

Abstract

A secret sharing scheme is a method for protecting distributed file systems against data leakage and for securing key management systems. The secret is distributed among a group of participants where each participant holds a share of the secret. The secret can be only reconstructed when a sufficient number of shares are reconstituted. Although many secret sharing schemes have been proposed, these schemes have not achieved an optimal share size and have not supported the share repair feature. This paper proposes a secret sharing scheme based on the Slepian-Wolf coding, named the SW-SSS, to obtain an optimal share size and to provide the share repair without recovering the secret. Furthermore, the share in the SW-SSS is constructed using the exclusive-OR (XOR) operation for fast computation. Unlimited parameters are also supported in the SW-SSS. To the best of our knowledge, we are the first applying the Slepian-Wolf coding to a secret sharing scheme.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
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. Pedersen, T.B, Saygin, Y., Savas, E.: Secret Sharing vs. Encryption-based techniques for privacy preserving data mining, pp. 17–19. Sciences, New York (2007)

    Google Scholar 

  2. Nirali, R.N., Devesh, C.J.: A game theory based repeated rational secret sharing scheme for privacy preserving distributed data mining. SECRYPT, pp. 512–517 (2013)

    Google Scholar 

  3. Kaya, S.V., Pedersen, T.B., Savaş, E., Saygıýn, Y.: Efficient privacy preserving distributed clustering based on secret sharing. In: Washio, T., Zhou, Z.-H., Huang, J.Z., Hu, X., Li, J., Xie, C., He, J., Zou, D., Li, K.-C., Freire, M. (eds.) PAKDD 2007. LNCS (LNAI), vol. 4819, pp. 280–291. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  5. Blakley, G.R.: Safeguarding cryptographic keys. AFIPS National Comput. Conf. 48, 313–317 (1979)

    Google Scholar 

  6. Karnin, E., Greene, J.W., Hellman, M.E.: On secret sharing systems. IEEE Trans. Inform. Theory 29(1), 3541 (1983)

    MathSciNet  Google Scholar 

  7. Capocelli, R.M., Santis, A.D., Gargano, L., Vaccaro, U.: On the size of shares for secret sharing schemes. J. Cryptology 6, 157167 (1993)

    Article  Google Scholar 

  8. Blakley, G.R., Meadows, C.: Security of ramp schemes. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 242–268. Springer, Heidelberg (1985)

    Chapter  Google Scholar 

  9. Yamamoto, H.: On secret sharing systems using \((k, L, n)\) threshold scheme. IEICE Trans. Fundam. 68(9), 945–952 (1985) (Japanese Edition)

    Google Scholar 

  10. Kurosawa, K., Okada, K., Sakano, K., Ogata, W., Tsujii, T.: Non perfect secret sharing schemes and matroids. In: Workshop on the Theory and Application of Cryptographic Techniques (EUROCRYPT). LNCS 765, Springer, pp. 126–141 (1993)

    Google Scholar 

  11. Ogata, W., Kurosawa, K.: Some basic properties of general nonperfect secret sharing schemes. J. Univ. Comput. Sci. 4(8), 690–704 (1998)

    MATH  MathSciNet  Google Scholar 

  12. Okada, K., Kurosawa, K.: Lower bound on the size of shares of nonperfect secret sharing schemes. In: Conference on the Theory and Applications of Cryptology (ASIACRYPT). LNCS 917, p. 3441. Springer (1994)

    Google Scholar 

  13. Wang, Y.: Efficient LDPC Code Based Secret Sharing Schemes and Private Data Storage in Cloud without Encryption. Technical report, UNC Charlotte (2012)

    Google Scholar 

  14. Ishizu, H., Ogihara, T.: A study on long-term storage of electronic data. IEICE Gen. Conf. 125(1), 9–10 (2004)

    Google Scholar 

  15. Hosaka, N., Tochikubo, K., Fujii, Y., Tada, M., Kato, T.: \((2, n)\)-threshold secret sharing systems based on binary matrices. In: Symposium on SCIS, pp. 2D1-4 (2007) (in Japanese)

    Google Scholar 

  16. Kurihara, J., Kiyomoto, S., Fukushima, K., Tanaka, T.: A fast (3, n)-threshold secret sharing scheme using exclusive-OR operations. IEICE Trans. E91-A(1), 127–138 (2008)

    Google Scholar 

  17. Shiina, N., Okamoto, T., Okamoto, E.: How to convert 1-out-of-n proof into k-out-of-n proof. In: Symposium on SCIS (in Japanese), pp. 1435–1440 (2004)

    Google Scholar 

  18. Kurihara, J., Kiyomoto, S., Fukushima, K., Tanaka, T.: A new (k,n)-threshold secret sharing scheme and its extension. In: Wu, T.-C., Lei, C.-L., Rijmen, V., Lee, D.-T. (eds.) ISC 2008. LNCS, vol. 5222, pp. 455–470. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  19. Chunli, L., Jia, X., Tian, L., Jing, J., Sun, M.: Efficient ideal threshold secret sharing schemes based on EXCLUSIVE-OR operations. In: 4th Conference on Network and System Security (NSS), pp. 136–143 (2010)

    Google Scholar 

  20. Wang, Y., Desmedt, Y.: Efficient Secret Sharing Schemes Achieving Optimal Information Rate. In: Information Theory Workshop (ITW) (2014)

    Google Scholar 

  21. Kurihara, J., Kiyomoto, S., Fukushima, K., Tanaka, T.: A fast (k-L-N)-threshold Ramp secret sharing scheme. IEICE Trans. Fundam. (2009). doi:10.1587/transfun.E92.A.1808

  22. Kurihara, M., Kuwakado, H.: Secret sharing schemes based on minimum bandwidth regenerating codes. In: Symposium on Information Theory and its Applications (ISITA), pp. 255–259 (2012)

    Google Scholar 

  23. Liu, J., Wang, H., Xian, M., Huang, K.: A secure and efficient scheme for cloud storage against eavesdropper. In: Qing, S., Zhou, J., Liu, D. (eds.) ICICS 2013. LNCS, vol. 8233, pp. 75–89. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  24. Cai, N., Raymond, W.Y.: Secure network coding. In: IEEE International Symposium on Information Theory (2002)

    Google Scholar 

  25. Katti, S., Rahul, H., Hu, W., Katabi, D., Medard, M., Crowcroft, J.: XORs in the air: practical wireless network coding. Trans. Netw. 16(3), 497–510 (2008)

    Article  Google Scholar 

  26. Yu, Z., Wei, Y., Ramkumar, B., Guan, Y.: An efficient scheme for securing XOR network coding against pollution attacks. In: 28th Conference on Computer Communication (INFOCOM), pp. 406–414 (2009)

    Google Scholar 

  27. Slepian, D., Wolf, J.K.: Noiseless coding of correlated information sources. IEE Trans. Inf. Theory 19(4), 471–480 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  28. Cheng, S.: Slepian-Wolf Code Designs. http://tulsagrad.ou.edu/samuel_cheng/information_theory_2010/swcd.pdf (2010)

  29. Ahlswede, R., Cai, N., Li, S.Y.R., Yeung, R.W.: Network information flow. IEEE Trans. Inf. Theory 46(4), 1204–1216 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  30. Ho, T., Medard, M., Koetter, R., Karger, D.R., Effros, M., Shi, J., Leong, B.: A random linear network coding approach to multicast. IEEE Trans. Inf. Theory 52(10), 4413–4430 (2006)

    Article  MathSciNet  Google Scholar 

  31. Li, S.-Y.R., Raymond, W.Y., Cai, N.: Linear network coding. IEEE Trans. Inf. Theory 49(2), 371–381 (2003)

    Article  MATH  Google Scholar 

  32. Agrawal, S., Boneh, D.: Homomorphic MACs: MAC-based integrity for network coding. In: Abdalla, M., Pointcheval, D., Fouque, P.-A., Vergnaud, D. (eds.) ACNS 2009. LNCS, vol. 5536, pp. 292–305. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  33. Stankovic, V., Liveris, A.D., Xiong, Z., Georghiades, C.N.: On code design for the Slepian-Wolf problem and lossless multiterminal networks. IEEE Trans. Inf. Theory 52(4), 1495–1507 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  34. Stankovi, V., Liveris, A.D., Xiong, Z., Georghiades, C.N: Design of Slepian-Wolf codes by channel code partitioning. In: Data Compression Conference (DCC), pp. 302–311 (2004)

    Google Scholar 

  35. Cheng, C., Jiang, T.: An efficient homomorphic MAC with small key size for authentication in network coding. IEEE Trans. Comput. 62(10), 2096–2100 (2012)

    Article  MathSciNet  Google Scholar 

  36. Johnson, R., Molnar, D., Song, D., Wagner, D.: Homomorphic Signature Schemes. In: Preneel, B. (ed.). CT-RSA 2002. LNCS, vol. 2271, pp. 244–262. Springer, Heidelberg (2002)

    Google Scholar 

  37. Freeman, D.M.: Improved security for linearly homomorphic signatures: a generic framework. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol. 7293, pp. 697–714. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Tran Phuong Thao .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Omote, K., Thao, T.P. (2015). SW-SSS: Slepian-Wolf Coding-Based Secret Sharing Scheme. In: Herrero, Á., Baruque, B., Sedano, J., Quintián, H., Corchado, E. (eds) International Joint Conference. CISIS 2015. Advances in Intelligent Systems and Computing, vol 369. Springer, Cham. https://doi.org/10.1007/978-3-319-19713-5_30

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-19713-5_30

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19712-8

  • Online ISBN: 978-3-319-19713-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics