Modular multiplication is used in a wide range of applications. Most of the existing modular multiplication algorithms in the literature often focus on large size moduli. However, those large moduli oriented modular multiplication solutions are also used to implement modular arithmetic for applications requiring modular arithmetic on moduli of size inferior to a word size i.e., 32/64bits. As it happens, a large majority of applications are using word size modular arithmetic. In this work, we propose a new modular multiplication designed to be computed on one word size only. For word size moduli, in a large majority of instances, our solution outperforms other existing solutions including generalist solutions like Montgomery's and Barrett's modular multiplication as well as classes of moduli like Mersenne, Pseudo-Mersenne, Montgomery-Friendly and Generalized Mersenne.

中文翻译：

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高效字长模运算


模乘法有着广泛的应用。文献中大多数现有的模乘算法通常关注大尺寸模。然而，那些面向大模的模乘解决方案也用于为需要对大小小于字大小(即32/64位)的模进行模运算的应用实现模运算。碰巧的是，绝大多数应用程序都使用字长模运算。在这项工作中，我们提出了一种新的模乘法，设计为仅在一个字长上进行计算。对于字长模数，在大多数情况下，我们的解决方案优于其他现有解决方案，包括蒙哥马利和巴雷特模乘法等通用解决方案以及梅森、伪梅森、蒙哥马利友好和广义梅森等模类。