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Old 2020-09-15, 16:23   #1
Deuterium's Avatar
Sep 2020

48 Posts
Default On Pollard Rho Cycle

Dear all,
I am new to this forum, I have decided to subscribe because there are lot of intelligent and good people (CRGreathouse is one of them), lot of dreamers (my connational Alberico Lepore) and lot of ideas.
Last premise : I am ready to be "dissed" by Silverman, but if he is real Mr Silverman, then he really knows math. So I will accept that.

Back to the question then.

I have read a lot about Rho Pollard Cycle and I have not understood all, even if it is considered an "easy" factorization method.
What I cannot understand is this : after a certain amount of iterations, the alghorhytm spontaneously evolves in a cycle, providing that there will be a certain amount of terms that will repeat in an infinite sequence.

First question : if a cycle is detected, is it correct to say that the alghorithm is "failing" and needs to be reinitialized or it's a good thing and it leads to one of the factors ? I think first statement is correct, but please tell me if I am wrong.

Second question : In case the answer to first question is that "cycles must be avoided", is there a trick to reinitialize the new sequence in order to obtain good values to get the first factor ? Or it's like "just reinitialize the sequence and cross your fingers ?"
Is there a way to "learn" from the first detected cycle and

A) Avoid a new cycle
B) Get better numbers that leads straightforward to factorization ?
Or maybe if you reinitialize it, sooner or later, the iterations will spontaneously fallback in another cycle ?

Excuse me for the naive questions, I hope to find here a place for discussion and not finding big headed id10ts like in stackexchange


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