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Old 2012-08-26, 16:11   #7
Dec 2011

11·13 Posts

Originally Posted by Walter Nissen View Post
... what parts of what papers do I need to read ...?
Walter: I think the journal article you seek is "A Practical Analysis of the Elliptic Curve Factoring Algorithm", by Robert D. Silverman and Samuel S. Wagstaff, Jr., Mathematics of Computation, v61, n203, July 1993, pp 445-462.

According to Table 3, a round B1 value for 40 digits might have been better chosen as about 4000000. As the paper points out, the curves are very flat where we are working. "Changes of +/- 10% in B1 can result in less than a 1% change in the global response surface..." So, at 40 digits, B1 is a little lower than perhaps it should be. But we do more curves to compensate.

Disclaimer: The above referenced paper is, I believe, the primary basis by which curve choices are made. I don't necessarily agree with those choices. My own (unpublished) analysis, using some different assumptions, shows that we may be doing too many curves at each level. But that's a topic for another day.
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