Skip to main content
Top

2016 | OriginalPaper | Chapter

Recent Advances in Non-perfect Secret Sharing Schemes

Author : Oriol Farràs

Published in: Pursuit of the Universal

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

A secret sharing scheme is non-perfect if some subsets of players that cannot recover the secret have partial information about it. This paper is a survey of the recent advances in non-perfect secret sharing schemes. We provide an overview of the techniques for constructing efficient non-perfect secret sharing schemes, bounds on the efficiency of these schemes, and results on the characterization of the ideal ones. We put special emphasis on the connections between non-perfect secret sharing schemes and polymatroids, matroids, information theory, and coding theory.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Beimel, A.: Secret-sharing schemes: a survey. In: Chee, Y.M., Guo, Z., Ling, S., Shao, F., Tang, Y., Wang, H., Xing, C. (eds.) IWCC 2011. LNCS, vol. 6639, pp. 11–46. Springer, Heidelberg (2011)CrossRef Beimel, A.: Secret-sharing schemes: a survey. In: Chee, Y.M., Guo, Z., Ling, S., Shao, F., Tang, Y., Wang, H., Xing, C. (eds.) IWCC 2011. LNCS, vol. 6639, pp. 11–46. Springer, Heidelberg (2011)CrossRef
2.
go back to reference Benaloh, J.C., Leichter, J.: Generalized secret sharing and monotone functions. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 27–35. Springer, Heidelberg (1990) Benaloh, J.C., Leichter, J.: Generalized secret sharing and monotone functions. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 27–35. Springer, Heidelberg (1990)
3.
go back to reference Blakley, G.R.: Safeguarding cryptographic keys. In: AFIPS Conference Proceedings, vol. 48, pp. 313–317 (1979) Blakley, G.R.: Safeguarding cryptographic keys. In: AFIPS Conference Proceedings, vol. 48, pp. 313–317 (1979)
4.
go back to reference 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)CrossRef 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)CrossRef
5.
go back to reference Brickell, E.F., Davenport, D.M.: On the classification of ideal secret sharing schemes. J. Cryptology 4, 123–134 (1991)MATH Brickell, E.F., Davenport, D.M.: On the classification of ideal secret sharing schemes. J. Cryptology 4, 123–134 (1991)MATH
6.
go back to reference Cascudo, I., Cramer, R., Xing, C.: Bounds on the threshold gap in secret sharing and its applications. IEEE Trans. Inf. Theory 59, 5600–5612 (2013)MathSciNetCrossRef Cascudo, I., Cramer, R., Xing, C.: Bounds on the threshold gap in secret sharing and its applications. IEEE Trans. Inf. Theory 59, 5600–5612 (2013)MathSciNetCrossRef
7.
go back to reference Chen, H., Cramer, R., Goldwasser, S., de Haan, R., Vaikuntanathan, V.: Secure computation from random error correcting codes. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 291–310. Springer, Heidelberg (2007)CrossRef Chen, H., Cramer, R., Goldwasser, S., de Haan, R., Vaikuntanathan, V.: Secure computation from random error correcting codes. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 291–310. Springer, Heidelberg (2007)CrossRef
8.
go back to reference Chen, H., Cramer, R., de Haan, R., Pueyo, I.C.: Strongly multiplicative ramp schemes from high degree rational points on curves. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 451–470. Springer, Heidelberg (2008)CrossRef Chen, H., Cramer, R., de Haan, R., Pueyo, I.C.: Strongly multiplicative ramp schemes from high degree rational points on curves. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 451–470. Springer, Heidelberg (2008)CrossRef
9.
go back to reference Chen, Q., Yeung, R.W.: Two-partition-symmetrical entropy function regions. In: ITW, pp. 1–5 (2013) Chen, Q., Yeung, R.W.: Two-partition-symmetrical entropy function regions. In: ITW, pp. 1–5 (2013)
10.
go back to reference Cramer, R., Damgård, I.B., Döttling, N., Fehr, S., Spini, G.: Linear secret sharing schemes from error correcting codes and universal hash functions. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9057, pp. 313–336. Springer, Heidelberg (2015) Cramer, R., Damgård, I.B., Döttling, N., Fehr, S., Spini, G.: Linear secret sharing schemes from error correcting codes and universal hash functions. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9057, pp. 313–336. Springer, Heidelberg (2015)
11.
go back to reference Cramer, R., Damgård, I.B., de Haan, R.: Atomic secure multi-party multiplication with low communication. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 329–346. Springer, Heidelberg (2007)CrossRef Cramer, R., Damgård, I.B., de Haan, R.: Atomic secure multi-party multiplication with low communication. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 329–346. Springer, Heidelberg (2007)CrossRef
12.
go back to reference Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley, New York (1991) Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley, New York (1991)
14.
go back to reference Druk, E., Ishai, Y.: Linear-time encodable codes meeting the Gilbert-Varshamov bound and their cryptographic applications. In: ITCS, pp. 169–182 (2014) Druk, E., Ishai, Y.: Linear-time encodable codes meeting the Gilbert-Varshamov bound and their cryptographic applications. In: ITCS, pp. 169–182 (2014)
15.
go back to reference Farràs, O., Hansen, T., Kaced, T., Padró, C.: Optimal non-perfect uniform secret sharing schemes. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part II. LNCS, vol. 8617, pp. 217–234. Springer, Heidelberg (2014)CrossRef Farràs, O., Hansen, T., Kaced, T., Padró, C.: Optimal non-perfect uniform secret sharing schemes. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part II. LNCS, vol. 8617, pp. 217–234. Springer, Heidelberg (2014)CrossRef
16.
go back to reference Farràs, O., Hansen, T., Kaced, T., Padró, C.: On the information ratio of non-perfect uniform secret sharing schemes. Cryptology ePrint Archive 2014/124 (2014) Farràs, O., Hansen, T., Kaced, T., Padró, C.: On the information ratio of non-perfect uniform secret sharing schemes. Cryptology ePrint Archive 2014/124 (2014)
17.
go back to reference Farràs, O., Martín, S., Padró, C.: A note on ideal non-perfect secret sharing schemes. Cryptology ePrint Archive 2016/348 (2016) Farràs, O., Martín, S., Padró, C.: A note on ideal non-perfect secret sharing schemes. Cryptology ePrint Archive 2016/348 (2016)
18.
go back to reference Farràs, O., Padró, C.: Extending Brickell-Davenport theorem to non-perfect secret sharing schemes. Des. Codes Cryptogr. 74(2), 495–510 (2015)MathSciNetCrossRefMATH Farràs, O., Padró, C.: Extending Brickell-Davenport theorem to non-perfect secret sharing schemes. Des. Codes Cryptogr. 74(2), 495–510 (2015)MathSciNetCrossRefMATH
19.
go back to reference Franklin, M., Yung, M.: Communication complexity of secure computation. In: STOC, pp. 699–710 (1992) Franklin, M., Yung, M.: Communication complexity of secure computation. In: STOC, pp. 699–710 (1992)
21.
go back to reference Fujishige, S.: Entropy functions and polymatroids–combinatorial structures in information theory. Electron. Comm. Japan 61, 14–18 (1978)MathSciNet Fujishige, S.: Entropy functions and polymatroids–combinatorial structures in information theory. Electron. Comm. Japan 61, 14–18 (1978)MathSciNet
23.
go back to reference Geil, O., Martin, S., Matsumoto, R., Ruano, D., Luo, Y.: Relative generalized hamming weights of one-point algebraic geometric codes. IEEE Trans. Inform. Theory 60, 5938–5949 (2014)MathSciNetCrossRef Geil, O., Martin, S., Matsumoto, R., Ruano, D., Luo, Y.: Relative generalized hamming weights of one-point algebraic geometric codes. IEEE Trans. Inform. Theory 60, 5938–5949 (2014)MathSciNetCrossRef
24.
go back to reference Ishai, Y., Kushilevitz, E., Strulovich, O.: Lossy chains and fractional secret sharing. In: STACS 2013. LIPICS, vol. 20, pp. 160–171 (2013) Ishai, Y., Kushilevitz, E., Strulovich, O.: Lossy chains and fractional secret sharing. In: STACS 2013. LIPICS, vol. 20, pp. 160–171 (2013)
25.
go back to reference Kurosawa, K., Okada, K., Sakano, K., Ogata, W., Tsujii, S.: Nonperfect secret sharing schemes and matroids. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 126–141. Springer, Heidelberg (1994)CrossRef Kurosawa, K., Okada, K., Sakano, K., Ogata, W., Tsujii, S.: Nonperfect secret sharing schemes and matroids. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 126–141. Springer, Heidelberg (1994)CrossRef
27.
go back to reference Okada, K., Kurosawa, K.: Lower bound on the size of shares of nonperfect secret sharing schemes. In: Safavi-Naini, R., Pieprzyk, J.P. (eds.) ASIACRYPT 1994. LNCS, vol. 917, pp. 33–41. Springer, Heidelberg (1995)CrossRef Okada, K., Kurosawa, K.: Lower bound on the size of shares of nonperfect secret sharing schemes. In: Safavi-Naini, R., Pieprzyk, J.P. (eds.) ASIACRYPT 1994. LNCS, vol. 917, pp. 33–41. Springer, Heidelberg (1995)CrossRef
28.
go back to reference Ogata, W., Kurosawa, K., Tsujii, S.: Nonperfect secret sharing schemes. In: Zheng, Y., Seberry, J. (eds.) AUSCRYPT 1992. LNCS, vol. 718, pp. 56–66. Springer, Heidelberg (1993)CrossRef Ogata, W., Kurosawa, K., Tsujii, S.: Nonperfect secret sharing schemes. In: Zheng, Y., Seberry, J. (eds.) AUSCRYPT 1992. LNCS, vol. 718, pp. 56–66. Springer, Heidelberg (1993)CrossRef
29.
go back to reference Padró, C.: Lecture Notes in Secret Sharing. Cryptology ePrint Archive 2012/674 Padró, C.: Lecture Notes in Secret Sharing. Cryptology ePrint Archive 2012/674
30.
go back to reference Paillier, A.: On ideal non-perfect secret sharing schemes. In: Christianson, B., Crispo, B., Lomas, M., Roe, M. (eds.) Security Protocols 1997. LNCS, vol. 1361, pp. 207–216. Springer, Heidelberg (1998)CrossRef Paillier, A.: On ideal non-perfect secret sharing schemes. In: Christianson, B., Crispo, B., Lomas, M., Roe, M. (eds.) Security Protocols 1997. LNCS, vol. 1361, pp. 207–216. Springer, Heidelberg (1998)CrossRef
32.
go back to reference Yoshida, M., Fujiwara, T.: Secure construction for nonlinear function threshold ramp secret sharing. In: IEEE International Symposium on Information Theory, ISIT 2007, pp. 1041–1045 (2007) Yoshida, M., Fujiwara, T.: Secure construction for nonlinear function threshold ramp secret sharing. In: IEEE International Symposium on Information Theory, ISIT 2007, pp. 1041–1045 (2007)
33.
go back to reference Yoshida, M., Fujiwara, T., Fossorier, M.: Optimum general threshold secret sharing. In: Smith, A. (ed.) ICITS 2012. LNCS, vol. 7412, pp. 187–204. Springer, Heidelberg (2012)CrossRef Yoshida, M., Fujiwara, T., Fossorier, M.: Optimum general threshold secret sharing. In: Smith, A. (ed.) ICITS 2012. LNCS, vol. 7412, pp. 187–204. Springer, Heidelberg (2012)CrossRef
Metadata
Title
Recent Advances in Non-perfect Secret Sharing Schemes
Author
Oriol Farràs
Copyright Year
2016
DOI
https://doi.org/10.1007/978-3-319-40189-8_9

Premium Partner