Monthly Archives: April 2022

Optimized Montgomery Multiplication with Smaller Modulus Sizes

This is Part 2 in a planned three part series on Montgomery arithmetic. Yesterday, Part 1 showed how to use the positive inverse to improve the traditional Montgomery REDC algorithm. If you would like an excellent implementation of Montgomery arithmetic … Continue reading

Montgomery REDC using the positive inverse (mod R)

This is Part 1 in a planned three part series on Montgomery arithmetic. A few days ago, Part 0 (the prequel?) showed how best to calculate the multiplicative inverse. If you would like an excellent implementation of Montgomery arithmetic and … Continue reading

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A Faster Multiplicative Inverse (Mod A Power Of 2)

I’d originally just intended to write up a blog entry on this, but the proofs were a better fit and easier to write in the form of a paper. The paper presents what should generally be the fastest multiplicative inverse … Continue reading

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Computing the Modular Multiplicative Inverse

We’ve previously explored the Extended Euclidean algorithm, and it’s easy to use a special case of it to implement the modular multiplicative inverse. We’ll start by reproducing the final function from an older post that derived a correct and efficient … Continue reading

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