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(ProQuest: ... denotes formulae omitted.)
INTRODUCTION
This paper presents a novel method of generating a strong, high entropy (pseudo-random), recoverable password based on the intersection of two functions that is approachable by students who have studied Dihedral Groups, and have had, at least, an introductory computer programming course. Although it is possible to use a small output hash function such as Adler32 [1] to generate recoverable passwords (i.e., recoverable: in the event of a lost password it can be easily reconstructed), most hash functions available will convert a seed value to a fixed character length. For a further discussion of hash functions see [2] and [3]. The intersection of two functions method is expandable to create a password of any character length. A major strength of the method outlined here ensures that passwords are recoverable in addition to high entropy, and unlike many well-known hash functions, this password method can be extended to produce a character string of any desired length.
Teachers can use this method as an example for considering why the intersection of functions might be useful and relevant to daily life. Students can use this method as a starting point for examining other functions that might generate a computer password.
This method can be used as a problem for multiple computer programming assignments: to generate discussion on what constitutes strong computer passwords, on issues of creating and forgetting computer passwords with the necessity for recoverable passwords, for questions on how to code place value, dates, and matrices, and can lead to an introduction of other types of data structures.
Consider the intersection C of an exponential function and a line determined by points A and B, where A > 1 on the v-axis and point B > 0 on the x-axis as in Figure 1, below. Then the ith character of the password is generated from the x-coordinate of C, with each value of B generated as described below.
The overall method is illustrated in Figure 2.
The password seed is generated by selecting the «th time a particular day of the week occurs in a selected month that willl always be used and not easily forgotten. The particular date of the nth occurrence of that day of the week in the...