Efficient Word Size Modular Arithmetic

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Abstract
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.

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