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?

Let G(x) be the generator polynomial used for CRC checking. What is the condition that should be satisfied by G(x) to detect odd number of bits in error?

Frames of 1000 bits are sent over a 10⁶ bps duplex link between two hosts. The propagation time is 25 ms. Frames are to be transmitted into this link to maximally pack them in transit (within the link).

Suppose that the sliding window protocol is used with the sender window size of 2^l, where l is the number of bits identified in the earlier part and acknowledgements are always piggy backed. After sending 2^l frames, what is the minimum time the sender will have to wait before starting transmission of the next frame? (Identify the closest choice ignoring the frame processing time.)

Frames of 1000 bits are sent over a 10⁶ bps duplex link between two hosts. The propagation time is 25 ms. Frames are to be transmitted into this link to maximally pack them in transit (within the link).
What is the minimum number of bits (I) that will be required to represent the sequence numbers distinctly? Assume that no time gap needs to be given between transmission of two frames.