# Decrypting a small Message using RSA with a Private Key [closed]

If I have a private key of (43, 341). What would be the steps I need to take to decrypt a small message using RSA? I have looked online and everything seems very confusing. Any tips or advice would be helpful.

I have gotten this far:

1. p=31 q=11
2. p*q=341
3. O(n)=(31-1)(11-1)=300
4. e=7
5. (43*e)%300=1 e=7
6. public key (e,n) (7,341)
7. Private Key (d,n)(43,341)
8. encryption of m=2 c=2^7%341=128
9. decryption of c=128 m=128^3%341=2

What would be the next step to decrypt a message?

• Is (43,341) a 2-tuple or the number 43,341? – pg1989 Apr 17 '14 at 19:44
• Its the numbers 43 & 341 – user3542714 Apr 17 '14 at 19:45
• Ok, that's a good start. The next step is to review what you know about RSA encryption. Do you understand how you encrypt a message using an RSA public key? – pg1989 Apr 17 '14 at 19:48
• I have the algorithm to generate the public key and private keys from 2 long prime numbers but after generating the keys Im lost – user3542714 Apr 17 '14 at 19:53
• Well there's your first step :) You have to understand encryption before you understand decryption hehe. Where are you getting lost with understanding encryption? Do you understand the math behind why we can use the public key to encrypt? – pg1989 Apr 17 '14 at 20:01