Reopening `*Residue` naming bikeshed

[tarcieri]

In #70 we discussed FieldElement and Residue as names for these types.

However @fjarri has pointed out, and I agree, that what these types really represent is Montgomery form. It's not just an implementation detail: we have *_montgomery methods which provide conversions and direct access to the Montgomery form.

I think it would probably make sense to rename them to something with *Mont* in the name, although I could go a few different directions on specific names.

cc @haslersn

[fjarri]

Three independent proposals:

1. Drop the Dyn prefix for runtime residues and instead use the Const prefix for constant-time ones. This goes in line with the rest of the naming.
2. Rename "Residue" to "MontgomeryForm" (or "MgForm" for short). Montgomery form is not a mere implementation detail, so it seems logical that it's reflected in the name.
3. Rename "Params" to "Precomputed" or something of the kind.

[dignifiedquire]

In favor for all three suggestions from @fjarri, especially 2 and 3 are more in line with what I have seen in other contexts.

[tarcieri]

MontgomeryForm/MontForm/MontyForm/MgForm or the same thing with Montgomery/Mont/etc/MgRepr (i.e. representative) all seem like reasonable names to me (though elsewhere we and ff/group use Repr for "bytestring representation")

I would probably side on a shorter name, since e.g. ConstMontgomeryForm/BoxedMontgomeryForm are quite verbose.

I like the idea of dropping Dyn and adding Const.

Rename "Params" to "Precomputed" or something of the kind.

I think "params" is fine, and can use whatever "monty" prefix we decide, e.g. MontParams. BoxedMontPrecomputed would get a little verbose.

[dignifiedquire]

• slight favor of MontyForm over the other variants
• openssl uses Ct instead of Const, so could also use that for naming if we want shorter names

[fjarri]

"Ct" is a little confusing because it can also mean "constant time". Also in the other parts of the library we're using "const" prefixes for compile-time stuff, so if we use "ct" here, those should all be changed too.

Edit: I suspect that OpenSSL uses "Ct" in the constant-time sense, since there's no such thing as const context in C, besides macros.

"Precomputed" can be shortened to "Precomp", but I am not sure how it sounds for English speakers :)

[dignifiedquire]

Edit: I suspect that OpenSSL uses "Ct" in the constant-time sense, since there's no such thing as const context in C, besides macros.

ah yes, I actually confused it myself 😅

[tarcieri]

I guess my vote would be:

• BoxedMontForm/BoxedMontParams
• ConstMontForm/ConstMontParams
• MontForm/MontParams

[tarcieri]

The other things we have to name are the trait for abstracting over the various Montgomery form types the way Integer abstracts over the integer types (#448), and a trait for associating a Montgomery form type with a particular integer type. See also #431.

Lacking a better name, I guess Mont/Monty would work for the former. We could probably just add an associated type to Integer for the latter.

[fjarri]

I suppose I'll make a PR then

[tarcieri]

Yeah, as I keep expanding the *Residue tests/benchmarks I keep thinking "more stuff to rename"