https://www.sciencedirect.com/science/article/pii/0890540187900307

The 1987 paper of Heather Woll, Reductions among number theoretic problems, Information and Computation 72 (1987) 167-179 looks at the reduction between many problems in number theory, including primality, factorization, order-finding, discrete logarithm.

In particular the paper shows that order-finding deterministically reduces to factorization, and that factorization probabilistically reduces to order-finding (see the trick used by Shor’s algorithm).