20061125, 22:13  #1 
Oct 2006
260_{10} Posts 
A beginners question about ECM
In regard to Alpertrons ECM applet,
Why is it that factors are found at different curves while the size of the factor remains the same? Clearer : I have found a factor P33 at curve 722, and another P33 at curve 2231. Is there any specific reason for this? Thanks, Roger 
20061126, 04:58  #2 
"Nancy"
Aug 2002
Alexandria
2467_{10} Posts 
ECM is a randomized algorithm. Whether a given factor is found with a curve depends on that curve's sigma value and the B1 and B2 values. Since we don't know which sigma values are going to be lucky in finding factors (because we don't know what the factors are!), implementations of ECM select the sigma value at random.
Alex 
20061127, 16:13  #3  
Nov 2003
2^{2}×5×373 Posts 
Quote:
it would be useful if you could tell me what you already know about the ECM algorithm and what you know about Lagrange's Theorem and elementary group theory. If you know nothing about the latter, explaining the algorithm will be impossible. 

20061129, 22:36  #4 
Oct 2006
2^{2}·5·13 Posts 
Thanks, anyway RD Silverman,
I just wanted an overview, and am quite content with Akruppa's reply. Thanks for replying, Roger PS : no, I don't have any background in those topics, though I will google them. 
Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Block Wiedemann for beginners  paul0  Factoring  7  20151116 17:09 
ECM program for beginners.  literka  GMPECM  0  20120429 23:54 
RAID for beginners  xilman  Lounge  2  20090817 17:32 
LMH for Beginners on V5  Bundu  Lone Mersenne Hunters  3  20081230 17:41 
ECM Factoring for beginners  BWetter246  GMPECM  5  20061115 13:19 