I'll keep it simple.
When factoring with ECM, you run the algorithm on the numer using multiple different curves of the same "size", each of which can yield a factor (or not). It is known how many (different) curves you need at each factor size to get a certain probability to find a factor (of that size). The sigma parameter is a number, from which the parameters (like coefficients) of the curve are derived. Testing with the same number with the same sigma, b1 and b2 would yield absolutely the same result. Running 100 curves means randomly chosing 100 sigmas.
You might also notice that sigmas start with "0:" or "1:" – those are different parametizations. Basically, also just different ways to get curves.
Last fiddled with by DukeBG on 20190226 at 11:26
