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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