NTRU Threshold Signature Theory And Algorithm Research

Threshold signature is one of the significant parts of threshold cryptography. It has an extensive application in electronic commerce activity.The main idea of threshold digital signature is to divide the secret key into several participants. Each participant has a share of the secret,only the specific numbers of participants can reconstruct the secret. So it cannot breach the system security even some participants expose their shares. The use of secret sharing and threshold digital signature reduce the probability of the exposure of secret key. The current threshold signature scheme which based on RSA or ECC algorithm has shortcomings of large amount of calculation during signature generation and certification process; adjust the threshold value required dealer to participate in etc.Lattice is a typical linear algebra structure; using NP-hard problem based on lattice to construct a new cryptosystem is widely concerned by the scholars in the field of cryptography. The public key cryptosystems which based on lattice NP-hard problem including AD, GGH and NTRU etc. But AD and GGH cryptosystems have been cracked due to some defects. Nevertheless, NTRU is a promising public key cryptosystem which security is based on lattice Shortest Vector Problem. When compared with other typical encryption algorithms such as RSA and ECC, the NTRU algorithm has obvious advantages in security and speed.In this thesis, firstly discusses the mathematical foundation,detail description about NTRU and NTRUSign algorithm. Then detailed discusses some classic threshold sharing schemes and analyzs NTRU system application schemes in threshold sharing. In the last, we present a changeable threshold signature scheme which is based on the changeable threshold Shamir secret sharing scheme and NTRUSign algorithm. The scheme has the properties as follow:(1) The proposed scheme mainly based on polynomial multiplication and integer coefficient modular arithmetic and needn't introduce exponential operation; it needn't to introduce exponential operation and has a faster pace of signature and certification without compromising the security, quite applicable for the field of compute, storage and bandwidth ability be restricted.(2) The signature can be safely generated with different threshold and needn't to modify the group public key and redistribute the subsecrets when changing the threshold, make full use of these advantage of the NTRUSign algorithm such as fast calculation speed, few requirements of resource and good security.