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Faster Chinese remaindering

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Abstract

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 m_1,…,m_ℓ 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 O(log log ℓ) in the complexity of “Chinese remaindering”. For small ℓ, 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.
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Dates and versions

hal-01403810 , version 1 (27-11-2016)

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  • HAL Id : hal-01403810 , version 1

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Joris van Der Hoeven. Faster Chinese remaindering. 2016. ⟨hal-01403810⟩
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