Identifiers starting with an underscore and followed immediately by a capital letter are reserved by the C++ standard.
The only header guards not fixed are those in the headers auto-generated from java.
We observe that when changing the b-value in the elliptic curve formula
`y^2 = x^3 + ax + b`, the group law is unchanged. Therefore our functions
for secp256k1 will be correct if and only if they are correct when applied
to the curve defined by `y^2 = x^3 + 4` defined over the same field. This
curve has a point P of order 199.
This commit adds a test which computes the subgroup generated by P and
exhaustively checks that addition of every pair of points gives the correct
result.
Unfortunately we cannot test const-time scalar multiplication by the same
mechanism. The reason is that these ecmult functions both compute a wNAF
representation of the scalar, and this representation is tied to the order
of the group.
Testing with the incomplete version of gej_add_ge (found in 5de4c5dff^)
shows that this detects the incompleteness when adding P - 106P, which
is exactly what we expected since 106 is a cube root of 1 mod 199.
Use a conditional move of the same kind we use for the affine points
in the storage type instead of multiplying with the infinity flag
and adding. This results in fewer constructions to worry about for
sidechannel behavior.
It also might be faster: It doesn't appear to benchmark as slower for
me at least; but I think the CMOV is faster than the mul_int + add,
but slower than the set+add; making it a wash.
- secp256k1_fe_sqrt now checks that the value it calculated is actually a square root.
- Add return values to secp256k1_fe_sqrt and secp256k1_ge_set_xo.
- Callers of secp256k1_ge_set_xo can use return value instead of explicit validity checks
- Add random value tests for secp256k1_fe_sqrt
