Question

Derive a suitable RSA key pair (in,e) and (n,d) by hand. Pick p and q to be at least three digits each. Supply an e that is not prime.

Answer 1

Select two prime no's. Suppose P = 131 and Q = 101. Now First part of the Public key : n = P*Q = 13231.

We also need a small exponent say e : But e Must be

An integer.

Not be a factor of n.

1 < e < Φ(n) [Φ(n) is discussed below], Let us now consider it to be equal to 4.

Our Public Key is made of n and e

We need to calculate Φ(n) : Such that Φ(n) = (P-1)(Q-1) so, Φ(n) = 13000

Now calculate Private Key, d : d = (k*Φ(n) + 1) / e for some integer k For k = 2, value of d is 6500.

Lets us encrypt the word "HI"

Convert letters to numbers : H = 8 and I = 9

Thus Encrypted Data c = 89^e mod n. Thus our Encrypted Data comes out to be 839

Now we will decrypt 839 :

Decrypted Data = c^d mod n. Thus our Encrypted Data comes out to be 89

8 = H and I = 9 i.e. "HI".