In the RSA public key cryptosystem, the private and public keys are (e, n) and (d, n) respectively, where n = p$$ \times $$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'= M^e mod n
M = (M')^d mod n

II. ed ≡ 1 mod n

III. ed ≡ 1 mod $$\phi $$(n)

IV. M'= M^e mod $$\phi $$(n)
M = (M')^d mod $$\phi $$(n)

Which of the above equations correctly represent RSA cryptosystem?

The total number of keys required for a set of n individuals to be able to communicate with each other using secret key and public key crypto-systems, respectively are:

Suppose that two parties A and B wish to setup a common secret key (D - H key) between themselves using the Diffie-Hellman key exchange technique. They agree on 7 as the modulus and 3 as the primitive root. Party A chooses 2 and party B chooses 5 as their respective secrets. Their D - H key is