# 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 known cryptographically important structures including $$\mathbb F_p^*$$ and Elliptic Curve Discrete Logarithm?

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

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

Lenstra's ECM method is, in the worst case ($$N = pq$$ with $$p < q$$ both primes of the same size), $$L_p(1/2)$$ (see H. W. Lenstra, Jr., Factoring integers with elliptic curves, Ann. of Math. (2) vol. 126 no. 3 (1987): 649-37). ECM cannot be used to solve discrete logs in elliptic curves or finite fields, so I think this answers 1. and 2.

For 3., there are subexponential finite-field-discrete-log-specific algorithms (like Adleman's Function Field Sieve, for example, or more recently the Barbulescu-Gaudry-Joux-Thomé quasipolynomial algorithm), but they apply to small- and medium-characteristic extension fields, not $$\mathbb{F}_p^\times$$.