With 3 as the input numer, ecm gets stuck in infinite loop

With echo 3 | ./ecm -param 1 1000 1000 it gets stuck in an infinite loop in get_curve_from_random_parameter().

closed with commit 8c927a17

thank you for the bug report. This should be fixed by commit 8c927a17. Ok?

Yes, this seems to avoid the infinite loop. How likely is a random curve parameter to produce an invalid curve? Is there any plausible risk of ECM exiting with error because it randomly chose 10 bad parameters?

for param=1, since d = sigma^2/2^64 and we want d different from 0 and 1 (mod n), I would say there are at most 3 bad values of sigma. For n=4 this gives a probability of 5% for 10 tries. Anyway this is better than an infinite loop. Maybe we could store the sigma values already tried (mod n) and only try "new" values. With only 4 tries this would ensure we find a valid value.

I did a quick test; n = 4 always instantly finds the factor 2, which is not a problem. n = 5 fails to find a valid sigma with 10 tries in about 1 in 150 runs.

I know nothing about the new parametrizations. Would it be possible, in case of an invalid sigma value, to try sigma_new = ceil(sqrt(2^64*(d+1))), so that the new value of d is 1 greater than the old one? Then we could reliably step over the bad values 0 and 1 (mod n) and find a good sigma with at most 3 tries.

nice idea, I did implement that. With n=5 we get no failure any more. Is the new version ok?

I tried 10000 runs with each of n = 3, 5, 7 and -param 1, 2, 3. All worked fine.

mentioned in commit 8c927a17