The Chinese remainder theorem is a key tool for the design of efficient multi-modular algorithms. In this paper, we study the case when the moduli are fixed and can even be chosen by the user. Through an appropriate use of the technique of FFT-trading, we will show that this assumption allows for the gain of an asymptotic factor in the complexity of “Chinese remaindering”. For small , we will also show how to choose “gentle moduli” that allow for further gains at the other end. The multiplication of integer matrices is one typical application where we expect practical gains for various common matrix dimensions and integer bitsizes.

Keywords: Chinese remainder theorem, algorithm, complexity, integer matrix multiplication

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Note: this paper has partly been published at the MACIS 2017 conference under the title “Fast Chinese remaindering in practice”