Study On Niederreiter Public-key Cryptosystem Based On Error-correcting Code

With the rapid development of computer and communication technology,information security is needed in the communication process. Encryption becomes more and more important. However,there are a variety of signal interferences in the communication channel,which make the received messages have errors. Thus error-correcting coding technique is required. If quantum computer was made,information security would have been greatly challenged. So combining cryptography with error-correcting code is the inevitable trend of modern communication.Public key cryptography based on error-correcting codes is the product of combining cryptography with error-correcting codes,such as McEliece public-key cryptosystem and Niederreiter public-key cryptosystem. After McEliece public-key cryptosystem was proposed,the public-key cryptosystems based on error-correcting codes have been widely studied and improved by many scholars. Generally,there are two ways to construct code-based public-key cryptosystems. First,the cryptosystem is reformed and its parameters are optimized. Second,the high-performance error-correcting code is found to construct public-key cryptosystem. In this paper,public-key cryptosystems are constructed based on the two methods. The main achievements and innovation are as follows.Firstly,Niederreiter public-key cryptography is mainly researched. On the basis of the original Niederreiter public-key cryptosystem,new public-key cryptosystem based on Goppa code is constructed by using dual public-key H1′and H2′.The complexity of decryption is enhanced by using dual public-key. Then through analyzing existing methods of attacking Niederreiter public-key cryptosystem,the security of the cryptosystem is confirmed to be improved. As the public key,after some elementary transformations on the rows,the check matrix can be transformed into systematic form. After that,the public key sizes of the cryptosystem is reduced. It is shown that error-correcting capability is improved.Secondly,because QC-LDPC code has very low linear encoding complexity,which is a great discovery in the field of error-correcting code,it is considered as a good code with high practicality in modern communication,we use the check matrix of QC-LDPC for constructing new scheme. In this paper,a new Niederreiter public-key cryptosystem based on QC-LDPC codes is proposed. As the check matrix of QC-LDPC codes is spare,who has the structure of circulative blocks and high error correction capability, compared with other public-key cryptosystem,the key sizes of the new cryptosystem is reduced and transmission rate is improved. The parity-check matrix was changed by multiplying it with a invertible transformation matrix Q with diagonal form in its right side. The sparse characteristic of H′is countervailed. Through analyzing existing attacking methods , the security of the cryptosystem is confirmed to be improved.