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Old 2019-10-09, 13:49   #1
storm5510
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Default Sigma parameter in ecm

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

Anyone care to elaborate?
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Old 2019-10-09, 13:50   #2
R.D. Silverman
 
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Quote:
Originally Posted by storm5510 View Post
I have done a lot of web searching, including MersenneWiki, and I have not found anything which explains the purpose of Sigma in ECM factoring.

Anyone care to elaborate?
It is a random number used to generate the coefficients of the elliptic curve.
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Old 2019-10-09, 16:22   #3
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Quote:
Originally Posted by R.D. Silverman View Post
It is a random number used to generate the coefficients of the elliptic curve.
Understood. Thank you very much!
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Old 2019-11-30, 20:36   #4
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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?
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Old 2019-11-30, 21:32   #5
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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.
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