Sigma parameter in ecm
 

I have done a lot of web searching, including [I]MersenneWiki[/I], and I have not found anything which explains the purpose of Sigma in ECM factoring.

Anyone care to elaborate? :smile:

[QUOTE=storm5510;527596]I have done a lot of web searching, including [I]MersenneWiki[/I], and I have not found anything which explains the purpose of Sigma in ECM factoring.

Anyone care to elaborate? :smile:[/QUOTE]

It is a random number used to generate the coefficients of the elliptic curve.

[QUOTE=R.D. Silverman;527597]It is a random number used to generate the coefficients of the elliptic curve.[/QUOTE]

Understood. Thank you very much! :smile:

Here's my question about sigmas. It will expose my ignorance, but at the same time the answer might help me visualize how ECM works.

Let's say you are running curves on a composite number that has only 2 rather large prime factors, and a lucky curve found one of those factors. Is the sigma that found that factor the only sigma that could have found it, or are there a number of different sigmas that could have found that same factor?

Lots of sigmas, usually. It's possible for a large-enough factor and 32-bit limit on sigma through GMP-ECM that just one of the ~4 billion sigmas would yield the factor for a particular B1/B2 choice, but that's a rather contrived case.