- 學位論文
以特定型態公鑰加速RSA運算
Efficient Computing with Specified RSA Public Modulus
摘要
在RSA密碼系統中，模指數運算為其核心運算可由重複的模乘法運算組成。因為安全性的考量，會選擇較長位元的整數做公鑰，但是大整數會造成模乘法運算在計算較花費時間。為了減少運算時間，一般普遍認為蒙哥馬利乘法(Montgomery multiplication)是讓運算變得更有效率的最好方法。因為在蒙哥馬利乘法中，去除了模乘法運算中的試除法運算。本研究提出在RSA公鑰中嵌入特定資訊的概念，藉以再提升蒙哥馬利乘法的效能，並針對一般模乘法、蒙哥馬利乘法以及本研究所提出之方法等三種演算法中，使用的單精確度乘法和單精確度除法的次數，探討彼此間效能之提升。
並列摘要
In RSA cryptosystem, modular exponentiation is the most time-consuming operation, it can be composed of repetition of modular multiplications. In order to improve the performance of modular exponentiation, it is usually using Montgomery multiplication. Montgomery multiplication reduces the computation time by omitting the trial division. In this thesis, we use the idea of embedding specified information in RSA public keys; it makes the Montgomery multiplication more efficiently. We also discuss the performance of general modular multiplication, original Montgomery multiplication, and Montgomery multiplications with predetermined portion in comparison with the number of single-precision multiplications and single-precision divisions.
參考文獻
延伸閱讀
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