Now that PrimeField::ReprEndianness exists, users can obtain a
known-endianness representation from the output of PrimeField::char
(which is a PrimeField::Repr, and should return a representation with
the same endianness as PrimeField::into_repr).
This enables generic code to reliably operate on the bits of an encoded
field element, by converting them to and from a known (little)
endianness.
The BitAnd and Shr bounds on PrimeField are now removed, as users can
perform these operations themselves as needed.
The sqrt() function is now part of the Field trait. ff_derive returns an
error on fields for which it does not support generating a square root
function.
Note that Fq6 and Fq12 in pairing::bls12_381 leave the function
unimplemented. They will be dropped once the migration to the bls12_381
crate is complete. The equivalent structs in that crate are not exposed.
Uses the addchain crate to obtain an addition chain for the exponent,
and then generates the corresponding constant-time square-and-multiply
algorithm.
WARNING: THIS IS NOT ACTUALLY CONSTANT TIME YET!
The jubjub and bls12_381 crates will replace our constant-time usages,
but we NEED to fix ff_derive because other users will expect it to
implement the Field trait correctly.
The ff_derive, pairing, zcash_primitives::jubjub, and bellman dummy_engine
changes are minimally implemented on top of the existing *_assign()
functions.
