Solution

The correct answer is option 3. 

Data:

p = 3, q = 11 and d = 7

Formula:

Φ(n)=(p-1)x(q-1)

n=p x q

Calculation:

n=3 x 11 =33

Φ(n)==(3-1)x(11-1) = 20

ex7 mod Φ(n)=1

Option 3

if e=3, 7x3 mod 20 =1

Encrypt key M^emod n= C

C=19³mod 33

C=28

∴ Hence the correct answer is (3,28)

RSA Algorithm (Rivest Shamir Adleman):

• Step 1: choose two large primes, p,q
• Step 2: Compute n=pxq , Φ(n)=(p-1)x(q-1)
• Step 3: Choose a number relatively prime to Φ(n) and call it 'd' , GCD(d, Φ(n))=1
• Find 'e' such that, exd mod Φ(n)=1
• Encrypt key M^emod n= C where C=ciper text
• Decrypt key C^dmod n= M where M=plain text