a variation of pollard rho

bhelmes · 2021-10-13, 17:28

A peaceful and pleasant night for you,

I present a variation of a pollard rho algorithm, limited to Mp, with use of a solution of the pell equation x²-2y²=-1.

Easy to understand and short for programming.
I need 3*3 multiplications for 4 gcds.

Program in C is attached.

Is this a progress compared to the pollard rho algorithm and mathematically sensefull ?

Happy5214 · 2021-11-07, 02:47

I missed the complex number unit in high school, so I won't comment on that (if anyone has good reading material for me, feel free to suggest). But the fact that you used Floyd's cycle-finding algorithm instead of Brent's, without giving justification why Brent's algorithm wouldn't work here (I think it would), implies that you haven't done enough research into modern (read: post-1980) rho implementations, which makes it a little hard to take you seriously.

BudgieJane · 2021-11-07, 22:35

Quote:

Originally Posted by Happy5214

I missed the complex number unit in high school, so I won't comment on that (if anyone has good reading material for me, feel free to suggest).

I suggest Schaum's Outline Of Complex Variables, (2nd ed. ISBN: 9780071615693). This is the book (in its earlier edition) that got me through complex analysis fifty years ago.

https://www.mhprofessional.com/97800...bles-2ed-group

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2021-11-07, 02:47	#2
Happy5214 "Alexander" Nov 2008 The Alamo City 2⁵·5² Posts	I missed the complex number unit in high school, so I won't comment on that (if anyone has good reading material for me, feel free to suggest). But the fact that you used Floyd's cycle-finding algorithm instead of Brent's, without giving justification why Brent's algorithm wouldn't work here (I think it would), implies that you haven't done enough research into modern (read: post-1980) rho implementations, which makes it a little hard to take you seriously.