Assume that source elements of length k are mapped in some uniform fashion into a target elements of length p. If each digit can take on one of r values, then the number of source elements is r k and...

Assume that source elements of length k are mapped in some uniform fashion into a target elements of length p. If each digit can take on one of r values, then the number of source elements is r
^k
and the number of target elements is the smaller number r p . A particular source element xi is mapped to a particular target element y_j.

a. What is the probability that the correct source element can be selected by an adversary on one try?

b. What is the probability that a different source element x_k(x_i
≠ x_k) that results in the same target element, y_j
, could be produced by an adversary?

c. What is the probability that the correct target element can be produced by an adversary on one try?