Let $${\pi _A}$$ be a problem that belongs to the class NP. Then which one of the following is TRUE?

Match all items in Group 1 with correct options from those given in Group 2.

Group 1

P. Regular expression
Q. Pushdown automata
R. Dataflow analysis
S. Register allocation

Group 2

1. Syntax analysis
2. Code generation
3. Lexical analysis
4. Code optimization

While opening a TCP connection, the initial sequence number is to be derived using a time-of-day (ToD) clock that keeps running even when the host is down. The low order 32 bits of the counter of the ToD clock is to be used for the initial sequence numbers. The clock counter increments once per millisecond. The maximum packet lifetime is given to be 64s.

Which one of the choices given below is closest to the minimum permissible rate at which sequence numbers used for packets of a connection can increase?

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?