Abstract
In this work, we construct a non-threshold secret sharing scheme that realizes a non-threshold access structure by using linear codes, in which any element of the non-threshold access structure can reconstruct the secret key. We prove that our scheme is a multiprover zero-knowledge proof system in the random oracle model, which shows that a passive adversary gains no information about the secret key. Our scheme is also a leakage-resilient secret sharing scheme (LRSS) in the bounded-leakage model, and it is \((\varepsilon ,l)\)-secure as long as the overall amount of information about the secret key learned by a malicious adversary is bounded by l bits. As an application, we propose a new group identification protocol (GID-scheme) from our LRSS, and we prove that it is a leakage-resilient GID-scheme. In our leakage-resilient GID-scheme, the verifier believes the validity of qualified group members and tolerates l bits of adversarial leakage in the distribution protocol, whereas for unqualified group members, the verifier cannot believe their valid identifications in the proof protocol.
This work was supported by National Natural Science Foundation of China (No. 61702126).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ajtai, M.: Secure computation with information leaking to an adversary. In: Proceedings of the Forty-Third Annual ACM Symposium on Theory of Computing, pp. 715–724. ACM (2011)
Blakley, G.R., et al.: Safeguarding cryptographic keys. In: Proceedings of the National Computer Conference, vol. 48, pp. 313–317 (1979)
Dziembowski, S., Pietrzak, K.: Leakage-resilient cryptography. In: 2008 IEEE 49th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2008, pp. 293–302. IEEE (2008)
Galbraith, S.D., Petit, C., Silva, J.: Identification protocols and signature schemes based on supersingular isogeny problems. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017. LNCS, vol. 10624, pp. 3–33. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70694-8_1
Goldreich, O.: Foundations of cryptography (fragments of a book) (1995)
Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof systems. SIAM J. Comput. 18(1), 186–208 (1989)
Goldwasser, S., Rothblum, G.N.: Securing computation against continuous leakage. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 59–79. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14623-7_4
Goyal, V., Kumar, A.: Non-malleable secret sharing for general access structures. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10991, pp. 501–530. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96884-1_17
Hazay, C., López-Alt, A., Wee, H., Wichs, D.: Leakage-resilient cryptography from minimal assumptions. J. Cryptol. 29(3), 514–551 (2016)
Karchmer, M., Wigderson, A.: On span programs. In: Proceeding of the 8th IEEE Structure in Complexity Theory, pp. 102–111 (1993)
Kiltz, E., Pietrzak, K.: Leakage resilient elgamal encryption. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 595–612. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17373-8_34
Komargodski, I., Paskin-Cherniavsky, A.: Evolving secret sharing: dynamic thresholds and robustness. In: Kalai, Y., Reyzin, L. (eds.) TCC 2017. LNCS, vol. 10678, pp. 379–393. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70503-3_12
Okada, K., Kurosawa, K.: MDS secret-sharing scheme secure against cheaters. IEEE Trans. Inf. Theory 46(3), 1078–1081 (2000)
Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Li, P., Li, J., Hassan, A. (2019). Group Identification via Non-threshold Leakage-Resilient Secret Sharing Scheme. In: Vaidya, J., Zhang, X., Li, J. (eds) Cyberspace Safety and Security. CSS 2019. Lecture Notes in Computer Science(), vol 11983. Springer, Cham. https://doi.org/10.1007/978-3-030-37352-8_20
Download citation
DOI: https://doi.org/10.1007/978-3-030-37352-8_20
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-37351-1
Online ISBN: 978-3-030-37352-8
eBook Packages: Computer ScienceComputer Science (R0)