Add exhaustive test for group functions on a low-order subgroup

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.
This commit is contained in:
Andrew Poelstra
2015-09-17 18:54:52 -05:00
parent 80773a6b74
commit 20b8877be1
7 changed files with 229 additions and 4 deletions

1
.gitignore vendored
View File

@@ -6,6 +6,7 @@ bench_schnorr_verify
bench_recover
bench_internal
tests
exhaustive_tests
gen_context
*.exe
*.so