Study On Chaotic Sequence In The Applications Of Digital Signature

The digital signature can not only prevent the sender of the transaction from denying transaction content, but also can prevent the recipient from forging, tampering with the transaction content, and even can defend itself against the network hacker attack on the transaction content. In order to ensure that the messages will not be pretended, intercepted in the transmission process,content signature is needed. Due to the password characteristics of chaos, this paper tries to apply chaotic sequence to digital signature, design and realize a system of signature validation for e-mail on Windows XP system. The designed message signature can be passed and verified between the PC machines, and it achieves the expectant results. In this paper, the research content is mainly divided into the following three parts:(1) A new log-function chaotic system is constructed. For the design of the complex chaotic system, a mathematical model of the log-function chaotic system is designed based on the Chen system design, and its dynamic characteristics are analyzed in theory and simulation, random property of the chaotic sequence was also studied by NIST test. The analysis and experimental results show that when compared to the Chen system, the log-function chaotic system expands the parameters of the key space, and the digital chaotic sequence has more randomness.Logarithmic operational circuit and logarithmic chaotic circuit are designed and realized, circuit experiment proved the feasibility in log-function chaotic system for the practical application.(2) A chaotic Hash function is designed. The foundation of the chaotic Hash function concept is that the Hash digest with fixed length will be worked out, when iterating the contents of arbitrary length with chaotic equation. The discrete log-function chaos equation will be achieved after adopting Euler method quantification to the log-function chaotic system. Using another chaos iterative equation to do the math calculation for the content, and the results will be an initial value of the discrete logarithm equation for further iterations to obtain the digest. After operation on all the contents, message content is diffused through the log-function chaotic system, thus increasing the sensitivity to the content. The key space of Hash operation contains both iterative initial value and the corresponding parameters of chaotic system. The experimental results show that the chaotic Hash algorithm is very strong in terms of secrecy capacity, and also sensitive to the message content.(3)A digital signature system based on chaos is designed. Combined with the log-function chaotic systems, Hash function of chaos and RSA encryption, this paper designs and implements a digital signature system, which is used to sign and verify the emails. Sender calculates the contentsthrough Hash function and gets a Hash digest which has fixed length, and then encrypts the Hash digest and the parameters of log-function chaos in RSA encryption to get a signature, and sends them with emails’ contents to the receiver eventually. After receiving the email, receiver gets a new digest through calculating the contents with chaos’ parameter, and verifies the new digest with the decryption Hash digest. This system builds the email interface with MFC, writes the signature behavior with VC++ program. The digital signature of secure email keeps the original speed of RSA encryption, further increases the key space and improves the security. The experiments prove that the digital signature system can be used normally in the email signature and achieves the expectant results.