Please help me understand RSA mathematics

[brajesh]

TL;DR Summary

Understanding the RSA mathematics

Please help me understand the RSA encryption.
I understand part of it, then I don't understand.

Definitions:

M=plain text message
C=encrypted message
N=public key
E=encoding key
D=decoding key
P,Q are prime factors on N

I get that
P x Q = N (where P and Q are primes).

I get that

Φ(N) = (P-1) x (Q-1)

I get that

M^EmodN = C

I get that

C^DmodN = M

But after this I don't understand the relevance of this equation to solve D and E

D x E mod Φ(N) = 1

Seems to be some step or something obvious I'm missing?

 

[fresh_42]

Have you read what Wikipedia has about it?
https://en.wikipedia.org/wiki/RSA_(cryptosystem)#Encryption

I find it a good explanation. And here are some RSA calculators:
https://www.physicsforums.com/threa...h-physics-earth-and-other-curiosities.970262/