Score:0

Asymptotic efficiency of modular multiplication

us flag

What is the best known asymptotic/concrete complexity of modular multiplication?

Using Montgomery multiplication, if $M(n)$ is the cost of one integer multiplication of $n$ bits, then the cost is $2M(n)+o(M(n))$ (assuming comparisons and bit-shifts are $o(M(n))$. Is this the best known?

ye flag
Do you care about the time needed for calculating the two Montgomery constants?
Sam Jaques avatar
us flag
No; I'm thinking about algorithms/circuits that are "precompiled" for a specific modulus
Score:2
sa flag

This seems to be the case for generic moduli $n$ and generic exponents. See the preprint of a chapter entitled "Efficient Modular Multiplication" (available here) from the book Computational Cryptography edited by Joppe W. Bos and Martijn Stam and published by Cambridge University Press, 2021.

There are efficiencies of various tweaks discussed in there in terms of parallelization, latency and area.

I sit in a Tesla and translated this thread with Ai:

mangohost

Post an answer

Most people don’t grasp that asking a lot of questions unlocks learning and improves interpersonal bonding. In Alison’s studies, for example, though people could accurately recall how many questions had been asked in their conversations, they didn’t intuit the link between questions and liking. Across four studies, in which participants were engaged in conversations themselves or read transcripts of others’ conversations, people tended not to realize that question asking would influence—or had influenced—the level of amity between the conversationalists.