GATE | GATE-CS-2009 | Question 60

In the RSA public key cryptosystem, the private and public keys are (e, n) and (d, n) respectively, where n = p*q and p and q are large primes. Besides, n is public and p and q are private. Let M be an integer such that 0 < M < n and f(n) = (p- 1)(q-1). Now consider the following equations.

 
I.  M’= Me mod n
    M = (M’)d mod n 

II.  ed ≡ 1 mod n 

III. ed ≡ 1 mod f(n)

IV. M’= Me mod f(n)
    M = (M’)d mod f(n) 

Which of the above equations correctly represent RSA cryptosystem?

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


Answer: (B)

Explanation: I is true because below is true in RSA-Cryptosystem.



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

III is true because below is true

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


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