UGC-NET | UGC NET CS 2017 Jan – III | Question 29

In RSA public key cryptosystem suppose n = p ∗ q where p and q are primes. (e, n) and (d, n) are public and private keys respectively. Let M be an integer such that o < M < n and φ(n) = (p – 1)(q – 1). Which of the following equations represent RSA public key cryptosystem ?

     I. C ≡ Me(mod n)         
        M ≡ (C)d(mod n) 
    II.ed ≡ 1(mod n)
   III.ed ≡ 1(mod φ(n))           
    IV. C ≡ Me(mod φ(n))
        M ≡ Cd(mod φ(n))

Codes :
(A) I and II
(B) I and III
(C) II and III
(D) I and IV


Answer: (B)

Explanation: I is true because

Encrypted-Text = (Plain-Text)e mod n
    Plain-Text = (Encrypted-Text)d mod n 

III is true because

   d-1 = e mod ϕ(n)
Or ed = 1 mod ϕ(n)

II and IV is wrong.
So, option (B) is correct.

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