Finding d given everything else in RSA

Question

I've got everything else (e, p, q, phi(n), n), but cannot see a way to figure out what d should be. P and q are both 300 digits, so phi(n) and n are about 600 digits, but e is only 5 digits. I do already understand that ed is congruent to 1 mod phi(n). Thanks for any suggestions.

score 2 · Answer 1 · answered Mar 20 '16 at 06:26

2

Usually you can calculate D with

$ D = (phi(N)*K + 1) / e$

Where

$K =$ Any small value, try 2

This video will help you, a lot: https://www.youtube.com/watch?v=e_auEoqetec

answered Mar 20 '16 at 06:26

AppIns

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score 1 · Accepted Answer · answered Mar 20 '16 at 06:34

Well, $d$ is just the inverse of $d$ modulo $\phi(n)$, as you state. So (if you don't want to write a program) go to a site like Wolfram and type the query (with the correct numbers, not 3 and 35 as I did as an example).

Some googling will give you simple python programs that will do it (python has built-in bignums so it's easy to do in that language).

Finding d given everything else in RSA

2 Answers2