Question

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 ofr values, then the number of source elements is r^k and the number of target elements is the smaller number r^p. A particular sourceelement x_i 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, yj, could beproduced by an adversary?

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

Answer 1

a) Since there are r^k source elements, then an adversary has 1/r^k probability to guess the correct source element in one try.

b) Each element in the r^p target elements is mapped to by r^k/r^p = r^k-p target elements. There arer^k-p target elements, so there are r^k-p-1 DIFFERENT source elements. The probability of selecting on of these is(r^k-p-1)/r^k.

c) Since there are r^p target elements, then the adversary has 1/r^p probability to guess the correct target element.

Answer 2

Length of source elements=k<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />

Length of target elements=p

Number of source elements is r^k

Number of target elements is r^p

a)      Probability that the correct source element can be selected by an adversary on one try is 1/r^k

b)      Each element in the r^p target elements can be mapped to by r^k/r^p = r^k-p target elements.

       Number of target elements is r^k-p

       Number of source elements is r^k-p-1

       Probability of selecting on of these is (r^k-p-1)/r^k.

c)      Probability that the correct target element can be produced by an adversary on one try is 1/r^p