The implementation calls the secp256k1_modinvNN_jacobi_var code, falling back
to computing a square root in the (extremely rare) case it failed converge.
This change eases the use of alternate build systems by moving
the variables in `src/libsecp256k1-config.h` to compiler macros
for each invocation, preventing duplication of these variables
for each build system.
Co-authored-by: Ali Sherief <ali@notatether.com>
Instead of supporting configuration of the field and scalar size independently,
both are now controlled by the availability of a 64x64->128 bit multiplication
(currently only through __int128). This is autodetected from the C code through
__SIZEOF_INT128__, but can be overridden using configure's
--with-test-override-wide-multiply, or by defining
USE_FORCE_WIDEMUL_{INT64,INT128} manually.
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.
