To slove the problems that Chinese Remainder Theorem (CRT) based threshold RSA signature scheme can not be used to sign some messages and the amount of computation in partial signatures combining phase is large, an improving method is proposed, in which a virtual group member is introduced, making the scheme can be used to sign all messages and significantly reducing the amount of computation in partial signatures combining phase, e.g. when the threshold value is 10, the amount of computation in partial signatures combining phase can be reduced to 1/6 of the original. The security and practicability of the improved scheme are analyzed. Results show that it is non-forgeable against an adaptive chosen message attack and more efficient than other threshold RSA signatures.
徐甫,马静谨. 基于中国剩余定理的门限RSA签名方案的改进[J]. 电子与信息学报, 2015, 37(10): 2495-2500.
Xu Fu, Ma Jing-jin. Improvement of Threshold RSA Signature Scheme Based on Chinese Remainder Theorem. JEIT, 2015, 37(10): 2495-2500.
Ma Chun-guang, Shi Lan, Zhou Chang-li, et al.. Threshold attribute-based signature and its security[J]. Acta Electronica Sinica, 2013, 41(5): 1012-1015.
Yang Xiao-dong, Li Chun-mei, Xu Ting, et al.. ID-based on-line/off-line threshold signature scheme without bilinear pairing[J]. Journal on Communications, 2013, 34(8): 185-190.
Cui Tao, Liu Pei-yu, and Wang Zhen. Forward secure (t,n) threshold proxy signature scheme with designated verifier[J]. Journal of Chinese Computer Systems, 2014, 35(5): 1061-1064.
Zhang Wen-fang, Wang Xiao-min, Guo Wei, et al.. An efficient inter-enterprise authentication scheme for VE based on the elliptic curve cryptosystem[J]. Acta Electronica Sinica, 2014, 42(6): 1095-1102.
[5]
Shoup V. Practical threshold signatures[C]. Proceedings of EUROCRYPT 2000, Bruges, Belgium, 2000: 207-220.
Zhang Wen-fang, He Da-ke, Wang Xiao-min, et al.. A new RSA threshold group signature scheme based on modified Shamir’s secret sharing solution[J]. Journal of Electronic & Information Technology, 2005, 27(11): 1745-1749.
[8]
Aboud S J, Yousef S, and Cole M. Undeniable threshold proxy signature scheme[C]. Proceedings of 5th International Conference on Computer Science and Information Technology, Amman, Jordan, 2013: 150-153.
[9]
Gennaro R, Jarecki S, Krawczyk H, et al.. Robust threshold DSS signatures[J]. Information and Computation, 2001, 164(1): 54-84.
[10]
Kim S, Kim J, Cheon J H, et al.. Threshold signature schemes for ElGamal variants[J]. Computer Standards & Interfaces, 2011, 33(4): 432-437.
[11]
Shamir A. How to share a secret?[J]. Communications of the ACM, 1979, 22(11): 612-613.
[12]
Asmuth C and Bloom J. A modular approach to key safeguarding[J]. IEEE Transactions on Information Theory, 1983, 29(2): 208-210.
[13]
Kaya K and Sel?uk A A. Threshold cryptography based on Asmuth-Bloom secret sharing[J]. Information Sciences, 2007, 177(19): 4148-4160.
Jin Chen-hui, Zheng Hao-ran, Zhang Shao-wu, et al.. Cryptography[M]. Beijing: Higher Education Press, 2009: 244-367.
[15]
Iftene S and Grindei M. Weighted threshold RSA based on the Chinese remainder theorem[C]. Proceedings of Ninth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, Timisoara, Romania, 2007: 175-181.
Wang Gui-lin, Qing Si-han, and Wang Ming-sheng. Improvement of Shoup’s threshold RSA signature scheme[J]. Journal of Computer Research and Development, 2002, 39(9): 1046-1050.
