README: Pollard Rho DLP Solver Project
by:	Katherine Miller
	katherinemiller@umbc.edu
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This program uses the Pollard Rho algorithm for Discrete
Log Problems to solve a given discrete log problem. The 
interface involves large text fields for alpha, x, beta, and
N, organized in a way that reads alpha^x = beta mod N.
After inputting the parameters, click "Solve!" to run the
algorithm. The program will run the algorithm, terminating
when it finds slow a, fast A, slow b, and fast B so that
alpha^a*beta^b = alpha^A*beta^B mod N. It then looks for
a solution to the problem (B-b)x = (a-A)mod phi(N), the value
of x we are looking for. Often, especially for very large
numbers, this algorithm terminates on values of (B-b) which
are not relatively prime to phi(N). While for small problems
there may only be one or two answers to the problem, larger
problems have increasingly more answers. In order to 
make up for this problem, I have added functionality that
allows the user to check the answer given by the algorithm
which does have the possibility of being wrong. In addition,
when the user clicks solve, the program checks to see if the
text field for x is filled out. For new problems, it should 
not be. But in order to allow for other solutions of the old
problem to be generated (if they exist), my program begins 
looking for solutions after the one that is in the "x" text
area. Essentially, this allows a user to input an alpha,
beta, and N, and click solve repeatedly to generate all the
possible solutions.

EXAMPLE:I pulled this example problem off wikipedia. In
	the group of the integers mod 1019, 2 is a generator
	and 2^10 is equal to 5. Inputting alpha=2, beta=5,
	and N=1019 and clicking solve produces the first
	answer, 10. If the user is curious, he or she could
	click solve again and get 519. Because these are
	the only two solutions the algorithm generates, 
	clicking solve repeatedly will loop through these
	two answers. Then, the user can click "check answer"
	to check if any of the solutions returned are
	correct.