TITLE: question based RSA Algorithm
QUESTION [4 upvotes]: The RSA system was used to encrypt the message M into the cipher-text C = 6. The
public key is given by n = p  q = 187 and e = 107. In the following, we will try to crack
the system and to determine the original message M.
(a) What parameters comprises the public key and what parameters the private key?
(b) What steps are necessary to determine the private key from the public key?
(c) Determine the private key for the given system.
(d) What is the original message M?
How would i solve this?

REPLY [1 votes]: Hint: 
(A) The public key is $(n,e)$ and the private key is $d$. We know $ed=1$  $(mod (p-1)(q-1))$. 
(B) $c:=m^e (mod (n))$ 
If you can compute the private key d, you can compute $c^d (mod \, n)$ to get m, since $c^d = (m^e)^d= m^1 (mod \, n)$ since $ed \equiv 1 (mod \,n) $.
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