Abstract
In proactive secret sharing schemes, the secret shares are periodically renewed without modifying the secret such that an adversary is unable to get any information about the secret shares unless he is able to obtain a certain number of secret shares in a short time interval. In this paper, using monotone span programs (MSP) we devise a new linear multi-secret sharing (LMSS) scheme which is also multi-stage. We also give a new general method to construct proactive and multi-use linear multi-secret sharing schemes based on MSP. An important advantage of our method compared to the others is that it does not need private channels between each pair of participants or an encryption scheme between them. Finally, we prove that our new scheme satisfies the definition of a perfect LMSS scheme.
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References
Asmuth, C., & Bloom, J. (1983). A modular approach to key safeguarding. IEEE Transactions Information Theory, 29(2), 208–210.
Cramer, R., Damg\(\dot{a}\)rd, I., & Maurer, U. (2000). General secure multi-party computation from any linear secret-sharing scheme, advances in cryptology-EUROCRYPT, pp. 316–334, 2000.
Eslami, Z., & Kabiri Rad, S. (2012). A new verifiable multi-secret sharing scheme based on bilinear maps. Wireless Personal Communications, 63(2), 459–467.
Ghasemi, R., Safi, A., & Hadian, M. (2017). You have full text access to this contentEfficient multisecret sharing scheme using new proposed computational security model, International Journal Of Communication Systems, https://doi.org/10.1002/dac.3399.
Herzberg, A., Jarecki, S., Krawczyk, H., & Yung, M. (1995). Proactive secret sharing or: How to cope with perpetual leakage. In Advances in CryptologyCRYPT0 95 (pp. 339–352). Berlin: Springer.
Hsu, C., Cheng, Q., Tang, X., & Zeng, B. (2011). An ideal multi-secret sharing scheme based on MSP. Information Sciences, 181(7), 1403–1409.
Hsu, C., Harn, L., & Cui, G. (2014). An ideal multi-secret sharing scheme based on connectivity of graphs. Wireless Personal Communications, 77(1), 383–394.
Karchmer, M., & Wigderson, A. (1993). On span programs. In Structure in complexity theory conference (pp. 102–111).
Liu, Y., Harn, L., & Chang, C.-C. (2015). A novel verifiable secret sharing mechanism using theory of numbers and a method for sharing secrets. International Journal of Communication Systems, 28, 1282–1292.
Liu, M., Xiao, L., & Zhang, Z. (2006). Linear multi-secret sharing schemes based on multi-party computation. Finite Fields and Their Applications, 12(4), 704–713.
Liu, Y. (2016). Linear (k, n) secret sharing scheme with cheating detection. Security and Communication Networks, 9(13), 2115–2121.
Mashhadi, S. (2017). Secure publicly verifiable and proactive secret sharing schemes with general access structure. Information Sciences, 378, 99–108.
Nikov, V., Nikova, S., & Preneel, B. (2007). On proactive verifiable secret sharing schemes. Serdica Journal of Computing, 1(3), 337–364.
Nikov, V., Nikova, S., Preneel, B., & Vandewalle, J. (2002). Applying general access structure to proactive secret sharing schemes. IACR Cryptology ePrint Archive, p. 141.
Nikov, V., Nikova, S., Preneel, B., & Vandewalle, J. (2002). On distributed key distribution centers and unconditionally secure proactive verifiable secret sharing schemes based on general access structure. In Progress in cryptology INDOCRYPT 2002 (pp. 422–435). Berlin: Springer.
Ostrovsky, R., & Yung, M. (1991). How to withstand mobile virus attacks. In Proceedings of the tenth annual ACM symposium on Principles of distributed computing (pp. 51–59).
Peng, Q., & Tian, Y. (2016). Publicly verifiable secret sharing scheme and its application with almost optimal information rate. Security and Communication Networks, 9(18), 6227–6238.
Peng, Q., & Tian, Y. (2016). A publicly verifiable secret sharing scheme based on multilinear Diffie–Hellman assumption. International Journal of Network Security, 18(6), 1192–1200.
Qin, H., Dai, Y., & Wang, Z. (2009). A secret sharing scheme based on (t, n) threshold and adversary structure. International Journal of Information Security, 8(5), 379–385.
Stinson, D. R., & Wei, R. (1999). Unconditionally secure proactive secret sharing scheme with combinatorial structures. In Selected areas in cryptography, (pp. 200–214). Berlin: Springer.
Xiao, L., & Liu, M. (2005). Linear multi-secret sharing schemes. Science in China Series F: Information Sciences, 48(1), 125–136.
Xiao, L., Liu, M., & Zhang, Z. (2005). Statistical multiparty computation based on random walks on graphs. IACR Cryptology ePrint Archive, p. 337.
Zarepour-Ahmadabadi, J., Shiri-Ahmadabadi, M., Miri, A., & Latif, A. (2018). A new gradual secret sharing scheme with diverse access structure. Wireless Personal Communications, 99(3), 1329–1344.
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Hadian Dehkordi, M., Mashhadi, S. & Oraei, H. A Proactive Multi Stage Secret Sharing Scheme for Any Given Access Structure. Wireless Pers Commun 104, 491–503 (2019). https://doi.org/10.1007/s11277-018-6032-7
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DOI: https://doi.org/10.1007/s11277-018-6032-7
Keywords
- Monotone span program
- Perfect multi-secret sharing scheme
- Access structure
- Multi-use scheme
- Multi-stage scheme