MIAO Fuyou, WANG Li, JI Yangyang, XIONG Yan. GOMSS: A Simple Group Oriented (t, m, n) Multi-secret Sharing Scheme[J]. Chinese Journal of Electronics, 2017, 26(3): 557-563. doi: 10.1049/cje.2016.08.014
Citation: MIAO Fuyou, WANG Li, JI Yangyang, XIONG Yan. GOMSS: A Simple Group Oriented (t, m, n) Multi-secret Sharing Scheme[J]. Chinese Journal of Electronics, 2017, 26(3): 557-563. doi: 10.1049/cje.2016.08.014

GOMSS: A Simple Group Oriented (t, m, n) Multi-secret Sharing Scheme

doi: 10.1049/cje.2016.08.014
Funds:  This work is supported in part by the National Natural Science Foundation of China (No.61572454, No.61472382, No.61572453, No.61520106007), and Open Project of Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong University.
  • Received Date: 2015-03-30
  • Rev Recd Date: 2015-07-22
  • Publish Date: 2017-05-10
  • In most (t, n)-Multi-secret sharing ((t, n)-MSS) schemes, an illegal participant, even without any valid share, may recover secrets when there are over t participants in secret reconstructions. To address this problem, the paper presents the notion of Group oriented (t, m, n)-multi-secret sharing (or (t, m, n)-GOMSS), in which recovering each secret requires all m (nmt) participants to have valid shares and actually participate in secret reconstruction. As an example, the paper then proposes a simple (t, m, n)-GOMSS scheme. In the scheme, every shareholder has only one share; to recover a secret, m shareholders construct a Polynomial-based randomized component (PRC) each with the share to form a tightly coupled group, which forces the secret to be recovered only with all m valid PRCs. As a result, the scheme can thwart the above illegal participant attack. The scheme is simple as well as flexible and does not depend on conventional hard problems or one way functions.
  • loading
  • A. Shamir, "How to share a secret", Communications of the ACM, Vol.22, No.11, pp.612-613, 1979.
    G. Blakley, "Safeguarding cryptographic keys", Proc.AFIPS 1979 Natl.Conf, pp.313-317, 1979.
    W.A. Jackson, K.M. Martin and C.M. O.Keefe, "On sharing many secrets", Asiacrypt94, pp.42-54, 1994.
    H.-Y. Chien, J.-K. Jan and Y-M. Tseng, "A practical (t,n) multi-secret sharing scheme", IEICE Transactions on Fundamentals, Vol.E83-A, No.12, pp.2792-2765, 2000.
    C.C. Yang, T.Y. Chang and M.S. Hwang, "A (t,n) multisecret sharing scheme", Applied Mathematics and Computation, Vol.151, No.2, pp.483-490, 2004.
    L.J. Pang and Y.M. Wang, "A new (t,n) multi-secret sharing scheme based on Shamirs secret sharing", Applied Mathematics and Computation, Vol.167, No.2, pp.840-848, 2005.
    J. Shao and Z. Cao, "A new efficient (t,n) Verifiable multi-secret sharing (VMSS) based on YCH scheme", Applied Mathematics and Computation, Vol.168, No.1, pp.135-140, 2005.
    Z. Eslami and S.K. Rad, "A new verifiable multi-secret sharing scheme based on bilinear maps" Wireless Personal Communications, Vol.63, No.2, pp.459-467, 2012.
    S.J. Wang, Y.R. Tsai and C.C. Shen, "Verifiable threshold scheme in multi-secret sharing distributions upon extensions of ECC", Wireless Personal Communications, Vol.56, No.1, pp.173-182, 2011.
    C. Lin and L. Harn, "Unconditionally secure multi-secret sharing scheme", IEEE International Conference on Computer Science and Automation Engineering (CSAE), Vol.1, pp.169-172, 2012.
    L. Harn, "Secure secret reconstruction and multi-secret sharing schemes with unconditional security", Security and Communication Networks, Vol.7, No.3, pp.567-573, 2014.
    J. He and E. Dawson, "Multistage secret sharing based on one way function", Electronic Letters, Vol.30, No.19, pp.1591-1592, 1994.
    L. Harn, "Efficient sharing (broadcasting) of multiple secrets", IEE Computers and Digital Techniques, Vol.142, No.3, pp.237-240, 1995.
    C. Tang and Z.-A. Yao, "A new (t,n)-threshold secret sharing scheme", Proc. of 2008 International Conference on Advanced Computer Theory and Engineering-ICACTE08, pp.920-924, 2008.
    X. Zhang, L. Zhang, Q. Zhang and C. Tang, "A secret sharing shuffling scheme based on polynomial", Proc. of 2008 IEEE International Conference on Information and Automation, pp.1746-1750, 2008.
    Ch-Q. Hu, X-F. Liao and X-ZH. Cheng, "Verifiable multi-secret sharing based on LFSR sequences", Theoretical Computer Science, Vol.445, No.11, pp.52-62, 2012.
    H. Zhao, J.Z. Sun, F. Wang, et al., "A finite equivalence of multisecret sharing based on Lagrange interpolating polynomial", Security and Communication Networks, Vol.6, No.9, pp.1169-1175, 2013.
    Y.X. Liu, L. Harn, C.N. Yang, et al., "Efficient (n,t,n) secret sharing schemes", Journal of Systems and Software, Vol.85, No.6, pp.1325-1332, 2012.
  • 加载中


    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (142) PDF downloads(343) Cited by()
    Proportional views


    DownLoad:  Full-Size Img  PowerPoint