The Improved RSA Algorithm And Application In Digital Signatures

As a special modular exponentiation arithmetic in cryptosystem, RSA algorithm, which is the most comprehensible among the various public key cryptosystem, is the best choice in both theory and application. In this algorithm both encryption key and algorithm can be published and the key of decipher is possessed by the individual user. From its birth on, the RSA algorithm has received much attention and has been used widely because of its capability of high security and easy operation. The digital signature technique is one of the kernel techniques of network business security, and it has widespread application in electronic commerce especially in the authentication.The mathematical basis, encryption algorithm, signature algorithm, the security and parameter selection of the public key cryptosystem were studied deeply in this thesis. On the one hand, the security of RSA public key cryptosystem was analyzed, many methods used to attack RSA were discussed, and how the corresponding processing was made in the correlation algorithm to resist these attacks was put forth; On the other hand, detailed analysis was made about several factors which affected the speed of the algorithm and the time-consuming modulo exponentiation computation was found, which has always been the bottle-neck of RSA. Simultaneously, the defects of RSA in digital signature application were found. Based on these, some improved RSA algorithms were proposed.RSA algorithm can be used in digital signature and identification system. The purpose on the application of RSA algorithm to the digital signature is not only to make the receiver prove the message sender's identify and the correctness of the message, but, most importantly, is to provide data integrity and non-repudiation. According to the defects of RSA in digital signature, some improved algorithms were proposed.When the information which needs to be encrypted is English, the thought of pretreatment table was also proposed in the thesis, which can produce a data sheet in advance, which places all the cryptographs of the possibly letters. Then in the following transformation from definite orders to cryptograph, the information can be directly looked up from the table, which can save the calculating time extremely. The time that pretreatment table algorithm saves is related with how many definite orders the indefinite information have. More definite orders, more saved time.