# Subexponential algorithms that apply only one of factoring and discrete logarithm?

Shor (quantum polynomial), Number Field Sieve (subexponential), Pollard rho (square root) all have both factoring and discrete logarithm over $$\mathbb F_p^*$$ variants.

What are the subexponential techniques that only applies to

1. balanced semiprime integer factoring but not to discrete logarithm over some cryptographically important structures including $$\mathbb F_p^*$$ and Elliptic Curve Discrete Logarithm?

2. balanced semiprime integer factoring but not to discrete logarithm over all cryptographically important structures including $$\mathbb F_p^*$$ and Elliptic Curve Discrete Logarithm?

3. discrete logarithm over some cryptographically important structure including $$\mathbb F_p^*$$ but not to balanced semiprime integer factoring?

• What about the algebraic factoring algorithms such as the Pollard $p-1$ and Williams $p+1$ (which are efficient when the underlying primes are smooth)? I am not aware of their counterparts in the discrete-log setting. – Occams_Trimmer Jul 23 at 8:48