A (t, n) Threshold Signature Scheme Based on Factorial Decompose Theorem of Polynomial

Abstract:

The traditional threshold signature scheme is a combination of the digital signature scheme and the secret sharing scheme. Any group of t (threshold value) or more players can reconstruct the secret together but no group of fewer than t players can in secret sharing scheme. Because of this property of secret sharing scheme, the current threshold signature scheme has a natural weakness in the anti-collusion attack. A new threshold signature scheme based on the factorial decompose theorem is designed successfully without the secret sharing scheme in order to get the ability of anti-collusion attacks. It not only has the property of group signature and threshold signature, but also has some good features including traceability，robustness and resisting forgery attacks.

• Periodical: Applied Mechanics and Materials (Volumes 50-51)
• Pages: 49-53
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.50-51.49
• Online since: February 2011
• Authors: Yong Quan Cai, Fu Lai Cheng
• Keywords: Conspiracy Attack, Factorial Decompose Theorem, Threshold Signature, Traceability

References

[1] Y. DESMEDT and Y. FRANKEL: Shared generation of authenticators and signatures. In：Proceedings of Crypto'91, Santa Barbara, California, USA, 1991. pp.457-469.

DOI: 10.1007/3-540-46766-1_37

[2] C.M. LI, T. HWANG and N.Y. LEE: Remark on the threshold RSA signature scheme. In: Advances in Cryptology-Crypto'93 Proceedings, Berlin. 1994, LNCS773: pp.413-420.

DOI: 10.1007/3-540-48329-2_35

[3] C.T. Wang, C.H. Lin and C.C. Chang: Threshold signature schemes with traceable signers in group communications. Computer Communications, 21(8), 1998, p.771.

DOI: 10.1016/s0140-3664(98)00142-x

[4] Q.L. XU: A modified threshold RSA digital signature scheme. Chinese Journal of Computers, 23(5), 2000, p.449.

[5] B. WANG, J.H. LI: (t, n) threshold signature scheme without a trusted party. Chinese Journal of Computers, 26(11), 2003, p.1581.

[6] Q. XIE and X.Y. Yu: A new (t, n) threshold signature scheme withstanding the conspiracy attack. Wuhan University Journal of Natural Sciences, 10(1), 2005, p.107.

DOI: 10.1007/bf02828628

[7] L.F. GUO, X.G. CHENG: Security analysis of a (t, n) threshold signature scheme without a trusted party. Chinese Journal of Computers, 29(11), 2006, p. (2031).

[8] W.F. ZHANG, X.M. WANG, D.K. HE: Security analysis of the (t, n) threshold signature scheme without a trusted party and its improvement. Journal of the China Railway Society, 30(3), 2008, p.40.

[9] X.L. ZHANG: An efficient group signature scheme based on factorial decompose theorem of polynomial with factors in finite field. Microelectronics & Computer, 27(3), 2010, p.163.

[10] G.L. WANG, S.H. QING: Weaknesses of some threshold group signature schemes. Journal of Software, 11(10), 2000, p.1326.