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Having not a super high-level background in math, I can't understand several parts of RSA.

I know that you select a number n, and two numbers e and d.

Then you have ed= mod(φ(n)), which looking it up means that ed is equal to the number you get when you count in a "modular way" in a rotation of φ(n), like a clock, except instead of 12 hours, you have φ(n) hours.

Looking up φ(n), it seems to count the number of relatively prime numbers to n.

Then you tell everyone e and n.

Then to send a message, you make sure the message number and n are relatively prime to each other, and that it's smaller than n (also greater than 1).

Then you do R = M^e mod n, and I am not really sure what is going on at this point.

And then you decode the message with R^d mod n, which again I don't know what is going on.

And I am now lost.

Throwaway34
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    I’d probably suggest just learning a bit about modular arithmetic first, rather than insisting on figuring out RSA without the basic background. – Kevin Carlson Jan 13 '22 at 21:09
  • Do you have a good source for that? – Throwaway34 Jan 13 '22 at 21:10
  • It’s difficult to say without knowing anything about your background, but this is taught in any book on number theory or discrete math. – Kevin Carlson Jan 13 '22 at 21:11
  • @Moo not really. I mean, I could probably understand how to do all those computations, but the underlying proofs and why it all works in a bigger picture, I don't understand. – Throwaway34 Jan 13 '22 at 22:25
  • Take a look at http://www.math-cs.gordon.edu/~kcrisman/mat338/NTIC.html Chapters 4 to 12 cover most of what you need to know to understand RSA, but it's a good idea to start at the beginning of the course. (Many of the pages in that course have examples using Sage. Some of them no longer work since Sage upgraded from Python 2 to Python 3, but if you know a little Python they're mostly easy to fix). – PM 2Ring Jan 13 '22 at 22:31

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