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