Is that this algorithm impressed by a public paper?
Any reference can be useful, as I am unable
to comply with cause concerning the code itself.

I’m not certain about “papers”, however roughly formal articles on modular multiplication in actual fact abound: certainly, the implementation in query “merely” leverages identified properties of modular arithmetic.

As to the specifics, the next is the hyperlink to a put up about an older and considerably less complicated model of secp256k1_fe_mul_inner than the present one, nevertheless it is likely to be sufficient to help additional exploration/reverse-engineering:

That article additionally comprises a hyperlink to the related modular arithmetic, in a pleasant and compact collection of slides, which I’ll repost right here:

(There may very well be some added worth in explaining the current implementation of secp256k1_fe_mul_inner, because it provides few extra optimizations on high of the essential modular arithmetic. However I feel that will require a degree of element and ritual that’s effectively past the scope of the current query.)