# GATE Papers >> CSE >> 2009 >> Question No 46

Question No. 46

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 Φ(n) = (p-1)(q-1). Now consider the following equations.

I.   M' = Me mod n
M = (M')d mod n
II.  ed $\equiv$ 1 mod n
III. ed $\equiv$ 1 mod Φ(n)
IV. M' = Me mod Φ(n)
M = (M')d mod Φ(n)

Which of the above equations correctly represent RSA cryptosystem?