Value of s in ECM

2011-09-03, 19:52

I have a question (only a curiosity). What does the value of s in ECM rappresent?
ECM on Mxxxx: curve #1 with s=?
Thanks

fivemack · 2011-09-03, 20:00

The value of 's' tells you which elliptic curve is being used for the elliptic curve method; ECM works if it can find an elliptic curve whose order over the field defined modulo a prime factor of the number you're factorising is smooth, it runs by trying lots of curves until one works, and the value of 's' tells you which one it's looking at.

rogue · 2011-09-03, 21:19

Quote:

Originally Posted by Unregistered

I have a question (only a curiosity). What does the value of s in ECM rappresent?
ECM on Mxxxx: curve #1 with s=?
Thanks

sigma

2011-09-03, 19:52	#1
Unregistered 5·1,021 Posts	Value of s in ECM I have a question (only a curiosity). What does the value of s in ECM rappresent? ECM on Mxxxx: curve #1 with s=? Thanks

2011-09-03, 20:00	#2
fivemack (loop (#_fork)) Feb 2006 Cambridge, England 2³×11×73 Posts	The value of 's' tells you which elliptic curve is being used for the elliptic curve method; ECM works if it can find an elliptic curve whose order over the field defined modulo a prime factor of the number you're factorising is smooth, it runs by trying lots of curves until one works, and the value of 's' tells you which one it's looking at.