are you sure it's not:
and
...?
I am trying to understand how this method for simplifying the decryption process works. I understand that if I have the message c raised to the public exponent modulo the modulus, then to decrypt it, I need to raise the encrypted message to the private exponent modulo the modulus.
Say I have a public key (13, 673627) and a private key (103381, 673627) and I want to read the message 174277, I understand that I can do this by raising and taking mod 673627 to get it. However, I have a guided question that goes through a method that doesn't require as much computation and I don't quite understand it.
It says "find the other information in (103381, 673627), is chosen so that , chosen so that and chosen so that .
I factored the modulus to get 673627 = 919*733 =
I found that:
and
and
How do I use them to decrypt 174277?
If it helps, here is a walk-through that parallels the guided question. I completed all the steps but couldn't get the answer 10000 - perhaps I am misunderstanding part of it. I can't be sure which variables are which in my question. I found all the values that satisfied the equations successfully but completing the final computation gave me something different to .
Compute:
Compute:
Find:
and
Compute:
Finally compute:
Method is from notes, question is from a handout.
So, in that case,
But a doesn't seem to be used :S
How would you find the message with your method and maybe I can extract what I need to do from that.