In an RSA cryptosystem, the value of the public modulus parameter n is 3007. If it is also known that $$\varphi $$(n) = 2880, where $$\varphi $$() denotes Euler's Totient Function, then the prime factor of n which is greater than 50 is ______.

Consider that B wants to send a message m that is digitally signed to A. Let the pair of private and public keys for A and B be denoted by $$K_x^ - $$ and $$K_x^ + $$ for x = A, B, respectively. Let K_x(m) represent the operation of encrypting m with a key K_x and H(m) represent the message digest. Which one of the following indicates the CORRECT way of sending the message m along with the digital signature to A?

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: