Hash functions and sensing In message authentication codes, a family of hash functions hk, where k is the secret key, are employed. The properties of good families are:

(1) Ease of computation of hk(x), given k.

(2) Compression of an input x of arbitrary length into a sequence of fixed length, n.

(3) Even given many text–message-authentication-code pairs (xi, hk(xi)) it is computationally infeasible to compute any text–message-authenticationcode pair (x, hk(x)) for a new input x not equal to xi.

(a) What brute force attacks could result in the determination of the hash function, and what is a simple counter-measure?

(b) How is hash function compression similar to and different from the mapping of data from the physical world into a decision by a sensor node?