I know you’d prefer ɴꜰꜱ, but for large fields, this is definitely the best way to do. https://gist.github.com/jproney/7e6cb7a40a8bf342e978a900a32e4dfc should apply to finite rings too. The point is if you know the size of your discrete logarithm result, you don’t need to apply Pohlig Hellman to all subgroups.
So once, ecm did gather enough tiny factors. Stop the factorization and apply Polhard Rho on each tiny factor while ditching the large primes or unfactored other groups in the Chinese remainder theorem.
I know you’d prefer ɴꜰꜱ, but for large fields, this is definitely the best way to do. https://gist.github.com/jproney/7e6cb7a40a8bf342e978a900a32e4dfc should apply to finite rings too. The point is if you know the size of your discrete logarithm result, you don’t need to apply Pohlig Hellman to all subgroups.
So once, ecm did gather enough tiny factors. Stop the factorization and apply Polhard Rho on each tiny factor while ditching the large primes or unfactored other groups in the Chinese remainder theorem.