This is a "historical question" more than it is a research question, but was the classical reduction to order-finding in Shor's algorithm for factorization initially discovered by Peter Shor, or was it previously known? Is there a paper that describes the reduction that pre-dates Shor, or is it simply a so-called "folk result?" Or was it simply another breakthrough in the same paper?
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I have to admit (surprising as it sounds) that I don't know really the answer. I either discovered or rediscovered this reduction myself.
I discovered the discrete log algorithm first, and the factoring algorithm second, so I knew from discrete log that periodicity was useful. I knew that factoring was equivalent to finding two unequal numbers with equal squares (mod N) — this is the basis for the quadratic sieve algorithm. I had also seen the reduction of factoring to finding the Euler $\phi$ function, which is quite similar.
While I came up with the reduction of this question to order-finding, it's not hard, so I wouldn't be surprised if there was another paper describing this reduction that predates mine. However, I don't think this could be a widely known "folk result". Even if somebody had discovered it, before quantum computing why would anybody care about reducing factoring to the question of order-finding (provably exponential on a classical computer)?
EDIT: Note that order-finding is provably exponential only in an oracle setting; order finding modulo $N$ is equivalent to factoring $N$, and this had been proved earlier by Heather Woll, as the other answer points out.
The random reduction from factorization to order-finding (mod N) was very well known to people working in number theory algorithms in the late 1970's and early 1980's. Indeed, it appears in a paper of Heather Woll, Reductions among number theoretic problems, Information and Computation 72 (1987) 167-179, and Eric Bach and I knew it before then.
I am mystified why Peter Shor says that order-finding is "provably exponential on a classical computer". If one knows the factorization of N and also $\varphi(N)$ (both computable in sub exponential time) and one works modulo each prime power, one can find orders.