What is the practical value of algorithms for fast multiplication of long numbers?

Question

Algorithms

I was asked to write a short report on fast multiplication algorithms. Among other things, in this report I need to express my point of view on the importance of studying this topic and its practical significance, i.e. where and why are fast multiplication algorithms used these days, especially algorithms for multiplying large numbers. And also, for which numbers and under what circumstances these algorithms work faster, and when they work slower, i.e. When is it best to use something else?
PS Since a cursory search in Google did not give any results, I'm asking here.

Answer 1

those. where and why are fast multiplication algorithms used these days, especially algorithms for multiplying large numbers.

Cryptography. As a textbook example, RSA. Here is a work on the topic , see section 7.1. More work .

Answer 2

Well, it's nice to multiply your large numbers quickly, and not slowly, this is probably their whole practical meaning.