| Summary: | 碩士 === 國立中山大學 === 資訊工程學系研究所 === 103 === With the rapid development of the Internet, human can not live without the Internet today.Moreover,the trading behavior through the Internet is more frequently. Therefore,much attention has been paid to the field of information security.RSA encryption and decryption system mentioned in this thesis is a well-known system developed for a long time. It uses a simple modulus to ensure that the information in the transmission process is safe.
But with the development of science and technology, this system is possible to be broken through the violent method.To ensure adequate security,RSA encryption system usually requires the key length more than 1024 or 2048. But executing this system by software is time-consuming. In order to improve this problem, we use hardware design to implement this system. RSA encryption system is mainly composed of the modular exponentiation , and the modular exponentiation is composed of modular multiplication . And in order to reduce the difficulties in the hardware design,the Montgomery algorithm has been proposed. The algorithm can use the addition and shift to implement modular multiplication.
However, the traditional Montgomery algorithm has security problems,we need to use a large size of modulus for long-term security. But it causes the potential problem of high fan-out signals, we use word-based Montgomery architecture to improve the problem. To execute Montgomery multiplication more quickly, we combines the high-radix technique. Moreover ,we propose High-Radix Word-based generalized design method and regulation . We use hybrid-radix technique to reduce the numbers of partial product and Montgomery multiplication hardware delay and area.So that the design can use fewer execution cycles to complete the operation.
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