A (t, n) Threshold Signature Scheme Based on Factorial Decompose Theorem of Polynomial
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.
Shaobo Zhong, Yimin Cheng and Xilong Qu
Y. Q. Cai and F. L. Cheng, "A (t, n) Threshold Signature Scheme Based on Factorial Decompose Theorem of Polynomial", Applied Mechanics and Materials, Vols. 50-51, pp. 49-53, 2011