RSA decryption exponent d (c++)

Hello all...

I am working on a small RSA encryption/decryption program in a school
project (using c++) and I'm kind of stuck because i can't figure out
how to calculate the decryption exponent d.
Keep in mind that my program doesn't use very large primes - it's sort
of a bit simplified in this respect.
My main problem revolves around how to implement a calculation of d in
my program. I can't figure out how to code this. According to various
sources i've used, d is calculated like this:

d = e^-1 (mod phi(n))

As far as I have been able to find out this means that

d mod phi(n) = e^-1 mod phi(n)

But as im not that experienced in advanced mathematics i don't really
know if this is true.

Anyway can anyone explain to me how i calculate d using c++ code or
just in plain easy-to-understand mathematics?

I have used the following numbers:

p = 37
q = 89
n = p*q = 37*89 = 3293
phi(n) = (p-1)(q-1) =3168
e = 25

thx in advance :)

TJakobsen

.

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