應用於叢集運算之RSA系統

The Application of the RSA System on the Cluster Computing

張德仁、邱迺軒、陳清音、黃俊豫
T. J. Chang, N. H. Chiu, C. Y. Chen and C. Y. Huang

國防大學　電機電子工程學系
Department of Electrical and Electronic Engineering, Chung Cheng Institute of Technology, National Defense University

　　為了RSA系統的安全性，其公開金鑰必須達到1,024位元以上，本篇研究改進C語言整數類別變數，其儲存空間不足的缺點，透過陣列方式儲存並計算，達到「大數運算」之功能。 除C語言之外，本篇研究還會使用到MPICH2軟體，將實驗室電腦組成叢集電腦，由滑動視窗法、加法鏈法兩種演算法，延伸出兩套適合平行處理的模指數法，大幅減少高位數模指數的計算時間，並有效利用每節點的計算能力，有助於未來雲端運算的資訊安全。

關鍵字：RSA系統、公開金鑰、大數運算


ABSTRACT

　　For the security of the RSA system, the public key needs 1,024 bits. In this paper, we improve the size of the variables in C language. The computer can store and compute the high bits through the array. We call this method as “a large number calculation”. Apart from C language, this study will use MPICH2 software. The cluster is composed of laboratory computers by MPICH2. Extending two modes suits the parallel processes of the modular exponentiation by combining the sliding method and the addition chain method. It will significantly reduce the computing time of the modular exponentiation which more digits, effectively use computing power per node. It will contribute to the security of the cloud computing.

Keywords: RSA system; public key; a large number calculation