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Optimal Threshold Changeable Secret Sharing with New Threshold Change Range

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Provable and Practical Security (ProvSec 2020)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12505))

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Abstract

Motivated by the need of catering for changes of security policy during the deployment of distribution of trust, threshold changeable secret sharing studies the construction of secret sharing schemes that have a built-in mechanism that, when activated, transforms the scheme into one with different access structures. By combining the two main techniques frequently used in previous constructions: packing and folding, we construct optimal threshold changeable ramp schemes that cover the full threshold change range, while known constructions either achieve only reconstruction threshold change or change both privacy and reconstruction thresholds but require the two thresholds to change proportionally. We justify the claim that the full threshold change range for which optimal schemes are possible is completely covered by proving a completeness result information-theoretically. The share size of these threshold changeable ramp schemes are much bigger than the lower bounds for plain ramp schemes (without requiring threshold changeability). This suggests the natural open question of understanding the share size lower and upper bounds for ramp schemes with built-in structures.

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References

  1. Barwick, S.G., Jackson, W.-A., Martin, K.M.: Updating the parameters of a threshold scheme by minimal broadcast. IEEE Trans. Inf. Theory 51(2), 620–633 (2005)

    Article  MathSciNet  Google Scholar 

  2. Bitar, R., El Rouayheb, S.: Staircase codes for secret sharing with optimal communication and read overheads. IEEE Trans. Inf. Theory 64(2), 933–943 (2017)

    Article  MathSciNet  Google Scholar 

  3. Blakley, G.R.: Safeguarding cryptographic keys. In: Proceedings of the National Computer Conference, vol. 48 (1979)

    Google Scholar 

  4. Blundo, C., Cresti, A., De Santis, A., Vaccaro, U.: Fully dynamic secret sharing schemes. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 110–125. Springer, Heidelberg (1994). https://doi.org/10.1007/3-540-48329-2_10

    Chapter  Google Scholar 

  5. Bogdanov, A., Guo, S., Komargodski, I.: Threshold secret sharing requires a linear size alphabet. In: Hirt, M., Smith, A. (eds.) TCC 2016. LNCS, vol. 9986, pp. 471–484. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53644-5_18

    Chapter  Google Scholar 

  6. Cramer, R., Damgård, I., Nielsen, J.B.: Secure Multiparty Computation and Secret Sharing. Cambridge University Press, Cambridge (2015)

    Book  Google Scholar 

  7. Desmedt, Y.: Threshold Cryptography, pp. 1288–1293. Springer, Boston (2011)

    Google Scholar 

  8. Desmedty, Y., Jajodiay, S.: Redistributing secret shares to new access structures and its applications (1997)

    Google Scholar 

  9. Huang, W., Langberg, M., Kliewer, J., Bruck, J.: Communication efficient secret sharing. IEEE Trans. Inf. Theory 62(12), 7195–7206 (2016)

    Article  MathSciNet  Google Scholar 

  10. Jackson, W.-A., Martin, K.M.: A combinatorial interpretation of ramp schemes. Australas. J. Comb. 14, 51–60 (1996)

    MathSciNet  MATH  Google Scholar 

  11. Jia, X., Wang, D., Nie, D., Luo, X., Sun, J.Z.: A new threshold changeable secret sharing scheme based on the chinese remainder theorem. Inf. Sci. 473, 13–30 (2019)

    Article  MathSciNet  Google Scholar 

  12. Lin, F., Cheraghchi, M., Guruswami, V., Safavi-Naini, R., Wang, H.: Secret sharing with binary shares. In: 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik (2018)

    Google Scholar 

  13. Lin, F., Ling, S., Wang, H., Zeng, N.: Threshold changeable ramp secret sharing. In: Mu, Y., Deng, R.H., Huang, X. (eds.) CANS 2019. LNCS, vol. 11829, pp. 308–327. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-31578-8_17

    Chapter  Google Scholar 

  14. Maeda, A., Miyaji, A., Tada, M.: Efficient and unconditionally secure verifiable threshold changeable scheme. In: Varadharajan, V., Mu, Y. (eds.) ACISP 2001. LNCS, vol. 2119, pp. 403–416. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-47719-5_32

    Chapter  MATH  Google Scholar 

  15. Martin, K.M., Pieprzyk, J., Safavi-Naini, R., Wang, H.: Changing thresholds in the absence of secure channels. In: Pieprzyk, J., Safavi-Naini, R., Seberry, J. (eds.) ACISP 1999. LNCS, vol. 1587, pp. 177–191. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48970-3_15

    Chapter  Google Scholar 

  16. Martínez-Peñas, U.: Communication efficient and strongly secure secret sharing schemes based on algebraic geometry codes. IEEE Trans. Inf. Theory 64(6), 4191–4206 (2018)

    Article  MathSciNet  Google Scholar 

  17. Nielsen, J.B., Simkin, M.: Lower bounds for leakage-resilient secret sharing. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020. LNCS, vol. 12105, pp. 556–577. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45721-1_20

    Chapter  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  19. Steinfeld, R., Pieprzyk, J., Wang, H.: Lattice-based threshold-changeability for standard CRT secret-sharing schemes. Finite Fields Appl. 12(4), 653–680 (2006)

    Article  MathSciNet  Google Scholar 

  20. Steinfeld, R., Pieprzyk, J., Wang, H.: Lattice-based threshold changeability for standard shamir secret-sharing schemes. IEEE Trans. Inf. Theory 53(7), 2542–2559 (2007)

    Article  MathSciNet  Google Scholar 

  21. Wang, H., Wong, D.S.: On secret reconstruction in secret sharing schemes. IEEE Trans. Inf. Theory 54(1), 473–480 (2008)

    Article  MathSciNet  Google Scholar 

  22. Zhang, Z., Chee, Y.M., Ling, S., Liu, M., Wang, H.: Threshold changeable secret sharing schemes revisited. Theory Comput. Sci. 418, 106–115 (2012)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The authors would like to thank the anonymous reviewers for their helpful and valuable suggestions. Especially, Remark 1 was inspired by a question from one of the reviewers. The work of Jian Ding and Changlu Lin was supported partly by National Natural Science Foundation of China (U1705264 and 61572132), Natural Science Foundation of Fujian Province (2019J01275), and Anhui Province Natural Science Research (KJ2018A0584). The work of Fuchun Lin was supported by EPSRC grant EP/S021043/1.

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Authors and Affiliations

  1. College of Mathematics and Informatics, Fujian Normal University, Fujian, China

    Jian Ding & Changlu Lin

  2. Fujian Provincial Key Lab of Network Security and Cryptology, Fujian Normal University, Fujian, China

    Jian Ding & Changlu Lin

  3. Department of Electrical and Electronic Engineering, Imperial College London, London, UK

    Fuchun Lin

Authors
  1. Jian Ding
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  2. Changlu Lin
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  3. Fuchun Lin
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Corresponding author

Correspondence to Fuchun Lin .

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Editors and Affiliations

  1. Nanyang Technological University, Singapore, Singapore

    Khoa Nguyen

  2. Chinese Academy of Sciences, Beijing, China

    Wenling Wu

  3. Nanyang Technological University, Singapore, Singapore

    Kwok Yan Lam

  4. Nanyang Technological University, Singapore, Singapore

    Huaxiong Wang

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Ding, J., Lin, C., Lin, F. (2020). Optimal Threshold Changeable Secret Sharing with New Threshold Change Range. In: Nguyen, K., Wu, W., Lam, K.Y., Wang, H. (eds) Provable and Practical Security. ProvSec 2020. Lecture Notes in Computer Science(), vol 12505. Springer, Cham. https://doi.org/10.1007/978-3-030-62576-4_18

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  • DOI: https://doi.org/10.1007/978-3-030-62576-4_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-62575-7

  • Online ISBN: 978-3-030-62576-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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