Optimum secret sharing scheme secure against cheating

被引:53
作者
Ogata, W
Kurosawa, K
Stinson, DR
机构
[1] Tokyo Inst Technol, Grad Sch Innovat Management, Meguro Ku, Tokyo 1528552, Japan
[2] Ibaraki Univ, Dept Comp & Informat Sci, Ibaraki 3168511, Japan
[3] Univ Waterloo, Sch Comp Sci, Waterloo, ON N2L 3G1, Canada
关键词
cryptography; secret sharing schemes; cheaters; balanced incomplete block design; difference sets;
D O I
10.1137/S0895480100378689
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Tompa and Woll introduced a problem of cheating in (k, n) threshold secret sharing schemes. In this problem k - 1 malicious participants aim to cheat an honest one by opening forged shares and causing the honest participant to reconstruct the wrong secret. We first derive a tight lower bound on the size of shares \V-i\ for secret sharing schemes that protect against this type of attack: \V-i\ >= (\S\ - 1)/delta + 1, where V-i denotes the set of shares of participant P-i, S denotes the set of secrets, and delta denotes the cheating probability. We next present an optimum scheme, which meets the equality of our bound, by using "difference sets." A partial converse and some extensions are also shown.
引用
收藏
页码:79 / 95
页数:17
相关论文
共 50 条
  • [1] A Simple and Efficient Secret Sharing Scheme Secure against Cheating
    Araki, Toshinori
    Ogata, Wakaha
    IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, 2011, E94A (06) : 1338 - 1345
  • [2] Almost Optimum Secret Sharing with Cheating Detection
    Jhanwar, Mahabir Prasad
    Safavi-Naini, Reihaneh
    SECURITY, PRIVACY, AND APPLIED CRYPTOGRAPHY ENGINEERING (SPACE 2015), 2015, 9354 : 359 - 372
  • [3] MDS secret-sharing scheme secure against cheaters
    Okada, K
    Kurosawa, K
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2000, 46 (03) : 1078 - 1081
  • [4] Cheating Detectable Secret Sharing Scheme Suitable for Implementation
    Hoshino, Hidetaka
    Obana, Satoshi
    2016 FOURTH INTERNATIONAL SYMPOSIUM ON COMPUTING AND NETWORKING (CANDAR), 2016, : 623 - 628
  • [5] Linear (k,n) secret sharing scheme with cheating detection
    Liu, Yanxiao
    SECURITY AND COMMUNICATION NETWORKS, 2016, 9 (13) : 2115 - 2121
  • [6] Cheating on a Visual Secret Sharing Scheme under a Realistic Scenario
    Lumyong, Pichanee
    Iwamoto, Mitsugu
    Ohta, Kazuo
    2014 INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY AND ITS APPLICATIONS (ISITA), 2014, : 575 - 579
  • [7] Almost Optimum Secret Sharing Schemes with Cheating Detection for Random Bit Strings
    Hoshino, Hidetaka
    Obana, Satoshi
    ADVANCES IN INFORMATION AND COMPUTER SECURITY (IWSEC 2015), 2015, 9241 : 213 - 222
  • [8] Toward a secure protection scheme for visual secret sharing
    Lee, C. -C.
    Lee, C. -C.
    Liu, H. -T.
    Tsai, C. -S.
    IMAGING SCIENCE JOURNAL, 2014, 62 (06) : 342 - 352
  • [9] Cheating prevention in linear secret sharing
    Pieprzyk, J
    Zhang, XM
    INFORMATION SECURITY AND PRIVACY, 2002, 2384 : 121 - 135
  • [10] On Converting Secret Sharing Scheme to Visual Secret Sharing Scheme
    Wang, Daoshun
    Yi, Feng
    EURASIP JOURNAL ON ADVANCES IN SIGNAL PROCESSING, 2010,