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Unconditionally secure non-malleable secret sharing and circular external difference families

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Abstract

Various notions of non-malleable secret sharing schemes have been considered. In this paper, we review the existing work on non-malleable secret sharing and suggest a novel game-based definition. We provide a new construction of an unconditionally secure non-malleable threshold scheme with respect to a specified relation. To do so, we introduce a new type of algebraic manipulation detection code and construct examples of new variations of external difference families, which are of independent combinatorial interest.

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Notes

  1. This is an extended version of [23].

References

  1. Aggarwal D., Damgård I., Nielsen J.B., Obremski M., Purwanto E., Ribeiro J., Simkin M.: Stronger leakage-resilient and non-malleable secret sharing schemes for general access structures. In: Advances in Cryptology—CRYPTO 2019. Lect. Notes Comput. Sci., vol. 11693, pp. 510–539 (2019).

  2. Albab K.D., Issa R., Varia M., Graffi K.: Batched differentially private information retrieval. In: 31st USENIX Security Symposium (USENIX Security 22), pp. 3327–3344 (2022).

  3. Badrinarayanan S., Srinivasan A.: Revisiting non-malleable secret sharing. In: Advances in Cryptology—EUROCRYPT 2019. Lect. Notes Comput. Sci., vol. 11476, pp. 593–622 (2019).

  4. Bentov I., Kumaresan R.: How to use bitcoin to design fair protocols. In: Advances in Cryptology—CRYPTO 2014. Lect. Notes Comput. Sci., vol. 8617, pp. 421–439 (2014).

  5. Blakley G. R.: Safeguarding cryptographic keys. In: International Workshop on Managing Requirements Knowledge, pp. 313–318 (1979)

  6. Brian G., Faonio A., Venturi D.: Continuously non-malleable secret sharing for general access structures. In: TCC 2019: Theory of Cryptography. Lect. Notes Comput. Sci., vol. 11892, pp. 211–232 (2019).

  7. Cohen S.D., Sharma H., Sharma R.: Primitive values of rational functions at primitive elements of a finite field. J. Number Theory 219, 237–246 (2021).

    Article  MathSciNet  Google Scholar 

  8. Cramer R., Dodis Y., Fehr S., Padró C., Wichs D.: Detection of algebraic manipulation with applications to robust secret sharing and fuzzy extractors. In: Advances in Cryptology—EUROCRYPT 2008. Lect. Notes Comput. Sci., vol. 4965, pp. 471–488 (2008).

  9. Cramer R., Fehr S., Padró C.: Algebraic manipulation detection codes. Sci. China Math. 56, 1349–1358 (2013).

    Article  MathSciNet  Google Scholar 

  10. Cramer R., Padró C., Xing C.: Optimal algebraic manipulation detection codes in the constant-error model. In: TCC 2015. Lecture Notes in Computer Science, vol. 9014, pp. 481–501 (2015).

  11. Damgård I., Groth J.: Non-interactive and reusable non-malleable commitment schemes. In: STOC ’03: Proceedings of the Thirty-fifth Annual ACM Symposium on Theory of Computing, pp. 426–437 (2003).

  12. Dolev D., Dwork C., Naor M.: Non-malleable cryptography. SIAM J. Comput. 30, 391–437 (2000).

    Article  MathSciNet  Google Scholar 

  13. Dwork C., Kenthapadi K., McSherry F., Mironov I., Naor M.: Our data, ourselves: privacy via distributed noise generation. In: Advances in Cryptology—EUROCRYPT 2006. Lect. Notes Comput. Sci., vol. 4004, pp. 486–503 (2006).

  14. Dziembowski S., Pietrzak K., Wichs D.: Non-malleable codes. In: Innovations in Computer Science, pp. 434–452 (2010).

  15. Dziembowski S., Pietrzak K., Wichs D.: Non-malleable codes. J. ACM 65, 1–32 (2018).

    Article  MathSciNet  Google Scholar 

  16. Faonio A., Venturi D.: Non-malleable secret sharing in the computational setting: Adaptive tampering, noisy-leakage resilience, and improved rate. In: Advances in Cryptology - CRYPTO 2019. Lect. Notes Comput. Sci., vol. 11693, pp. 448–479 (2019).

  17. Fischlin M., Fischlin R.: Efficient non-malleable commitment schemes. J. Cryptol. 24, 203–244 (2011).

    Article  MathSciNet  Google Scholar 

  18. Gordon S.D.: On fairness in secure computation. PhD thesis, University of Maryland, College Park (2010).

  19. Gordon S.D., Ishai Y., Moran T., Ostrovsky R., Sahai A.: On complete primitives for fairness. In: TCC 2010: Theory of Cryptography. Lect. Notes Comput. Sci., vol. 5978, pp. 91–108 (2010).

  20. Goyal V., Kumar A.: Non-malleable secret sharing. In: STOC 2018: Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, pp. 685–698 (2018).

  21. Goyal V., Kumar A.: Non-malleable secret sharing for general access structures. In: Advances in Cryptology - CRYPTO 2018 Lect. Notes Comput. Sci., vol. 5157, pp. 501–530 (2018).

  22. Huczynska S., Jefferson C., Nepšinská S.: Strong external difference families in abelian and non-abelian groups. Cryptogr. Commun. 13, 331–341 (2021).

    Article  MathSciNet  Google Scholar 

  23. Ishai Y., Prabhakaran M., Sahai A.: Founding cryptography on oblivious transfer–efficiently. In: Advances in Cryptology - CRYPTO 2008. Lect. Notes Comput. Sci., vol. 5157, pp. 572–591 (2008).

  24. Ishai Y., Prabhakaran M., Sahai A.: Founding cryptography on oblivious transfer—efficiently. https://www.cse.iitb.ac.in/~mp/pub/mpc-ot.pdf.

  25. Kenthapadi K.: Models and algorithms for data privacy. PhD thesis, Stanford University (2006).

  26. Paterson M.B., Stinson D.R.: Combinatorial characterizations of algebraic manipulation detection codes involving generalized difference families. Discret. Math. 339, 2891–2906 (2016).

    Article  MathSciNet  Google Scholar 

  27. Rosulek M.: Universal composability from essentially any trusted setup. In: Advances in Cryptology—CRYPTO 2012. Lect. Notes Comput. Sci., vol. 7417, pp. 406–423 (2012).

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

    Article  MathSciNet  Google Scholar 

  29. Tompa M., Woll H.: How to share a secret with cheaters. J. Cryptol. 1, 133–138 (1989).

    Article  MathSciNet  Google Scholar 

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Acknowledgements

We thank Steven Wang for bringing the results of [7] to our attention.

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Authors and Affiliations

  1. Department of Computer Science, ETH Zurich, Zurich, Switzerland

    Shannon Veitch

  2. School of Mathematics and Statistics, Carleton University, Ottawa, ON, K1S 5B6, Canada

    Douglas R. Stinson

  3. David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Douglas R. Stinson

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  1. Shannon Veitch
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Correspondence to Douglas R. Stinson.

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Communicated by Y. Zhou.

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D.R. Stinson’s research is supported by NSERC discovery Grant RGPIN-03882.

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Veitch, S., Stinson, D.R. Unconditionally secure non-malleable secret sharing and circular external difference families. Des. Codes Cryptogr. 92, 941–956 (2024). https://doi.org/10.1007/s10623-023-01322-5

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  • DOI: https://doi.org/10.1007/s10623-023-01322-5

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