The rapid development of technology, business, the Chief of informationization, making password technology-based disciplines such mathematical techniques to a wide range of applications. For example, represented by RSA,ElGarmal and ECC digital signatures technology, but which has emerged in recent years NTRU public key cryptographic system, by virtue of its rapid increase declassified, high efficiency and high security has become a hot research codes. And the threshold of modern cryptography as a dynamic branch of cryptography, in real life a very important role. This major study is the threshold and NTRU public key cryptography system. In the first chapter of this simple introduction to the development of public key cryptography background, the development of history. Further highlights NTRU public key cryptography algorithms and threshold development process, and the vector space on Brickell passwords [10] sharing programme. Chapter II will be closed Mei polynomial Central NTRU in the presentation and analysis of the decryption work. And in the back with a simple example to test the feasibility of NTRU public key algorithms, in the final two chapters, we will declassification correctness of the parameters and key generation options analysis and discussion. Chapter III will be based on the NTRU public key algorithm is based on Brickell against polynomial vector space programme password sharing adjustments, and then given a new threshold NTRU public key encryption programme, and then use an example to test the programme, Finally this new programme will make a simple point safety analysis.
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