Science

... (AFAIK) is something called the irrational base discrete weighted {fast Fourier} transform, which replaces the integer multiply with multiple floating-point calculations. Weirdly, this sounds like the reverse of the technique in the OP. Either one of these represents a really fundamental change in the algorithm -- it's not anything like fine-tuning. This link gives a nice short intro to what's involved, as well as a further development which does not seem to be practical just yet: https://theconversation.com/weve-found-a-quicker-way-to-multiply-really-big-numbers-114923

Detailed technical discussion is found in the Wikipedia articles https://en.wikipedia.org/wiki/Fast_Fourier_transform and https://en.wikipedia.org/wiki/Multiplication_algorithm. Also briefly discussed in Knuth (vol. 2) and in more detail in Crandall and Pomerantz .

Public-key cryptographic security is often based on the assumption that factoring very large integers is so resource-intensive that it will almost never be worth the effort involved to crack a protected file. As the algorithms to find factors of large integers become faster and more powerful, larger and larger keys are required.