Mark, I did just a little browsing on this.  It seems it's well known that egcd beats straightforward exponentiation for this purpose in arbitrary precision contexts, for reasons already sketched (egcd needs narrower arithmetic from the start, benefits from the division narrowing on each iteration, and since the quotient on each iteration usually fits in a single "digit" the multiplication by the quotient goes fast too).

But gonzo implementations switch back to exponentiation, using fancier primitives like Montgomery multiplication.

As usual, I'm not keen on bloating the code for "state of the art" giant int algorithms, but suit yourself!  The focus in this PR is dead simple spelling changes with relatively massive payoffs.