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RSA加密算法加密强度高、易于使用,但其现有实现算法时间复杂度高、运行效率低,主要是由于大数模幂乘运算之时间复杂度高引起的,这是影响其实际应用的关键因素。因而有必要研究算法中的大数模幂乘运算方法,使其时间复杂度降低,提高其运行效率。本文对RSA算法中的大数模幂乘计算方法做了较为深入的研究,对窗口算法做了理论分析和模拟测试,计算出了窗口的长度k,为其在实际中的应用提供了依据。分析表明,实际数据测试之结果与理论分析吻合。
The RSA encryption algorithm has high encryption strength and is easy to use. However, the existing algorithm has high time complexity and low operation efficiency, which is mainly caused by the high time complexity of the arithmetic operation of large numbers and modules, which is the key factor affecting its practical application factor. Therefore, it is necessary to study the large modular exponentiation algorithm in the algorithm to reduce the time complexity and improve its operating efficiency. This paper makes a deep research on the arithmetic of exponentiation of large numbers and modular exponentials in the RSA algorithm. The theoretical analysis and simulation testing of the windowing algorithm are done, and the length k of the window is calculated, which provides the basis for its application in practice. The analysis shows that the actual data test results are in good agreement with the theoretical analysis.