The cryptographic relevance of this problem will become evident when we cover hash functions in class. For each question below, provide a brief explanation and a compact formula for your answer. Let n be a positive integer. Consider an experiment involving a group of participants, where we assign each participant a number that is randomly chosen from the set {1,2,...,n} (so all these assignments are independent events). Note that we allow for the possibility of assigning the same number to two different participants. Now pick your favourite number N between 1 and n. When any one of the participants is assigned the number N, we refer to this as a weak collision (with N). In this problem, we determine how to ensure at least a 50% chance of a weak collision in our experiment. a. What is the probability that a given participant is assigned your favourite number N? b. What is the probability that a given participant is not assigned the number N? c. Suppose k people participate in the experiment (for some positive integer k). What is the probability that none of them is assigned the number N, i.e. that there is no weak collision?
The cryptographic relevance of this problem will become evident when we cover hash functions in class. For each question below, provide a brief explanation and a compact formula for your answer. Let n be a positive integer. Consider an experiment involving a group of participants, where we assign each participant a number that is randomly chosen from the set {1,2,...,n} (so all these assignments are independent events). Note that we allow for the possibility of assigning the same number to two different participants. Now pick your favourite number N between 1 and n. When any one of the participants is assigned the number N, we refer to this as a weak collision (with N). In this problem, we determine how to ensure at least a 50% chance of a weak collision in our experiment. a. What is the probability that a given participant is assigned your favourite number N? b. What is the probability that a given participant is not assigned the number N? c. Suppose k people participate in the experiment (for some positive integer k). What is the probability that none of them is assigned the number N, i.e. that there is no weak collision?
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.7: Introduction To Coding Theory (optional)
Problem 12E: Suppose that the check digit is computed as described in Example . Prove that transposition errors...
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