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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@@ -104,6 +104,11 @@ AC_ARG_ENABLE(experimental,
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[use_experimental=$enableval],
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[use_experimental=no])
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AC_ARG_ENABLE(exhaustive_tests,
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AS_HELP_STRING([--enable-exhaustive-tests],[compile exhaustive tests (default is yes)]),
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[use_exhaustive_tests=$enableval],
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[use_exhaustive_tests=yes])
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AC_ARG_ENABLE(endomorphism,
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AS_HELP_STRING([--enable-endomorphism],[enable endomorphism (default is no)]),
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[use_endomorphism=$enableval],
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@@ -456,6 +461,7 @@ AC_SUBST(SECP_LIBS)
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AC_SUBST(SECP_TEST_LIBS)
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AC_SUBST(SECP_TEST_INCLUDES)
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AM_CONDITIONAL([USE_TESTS], [test x"$use_tests" != x"no"])
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AM_CONDITIONAL([USE_EXHAUSTIVE_TESTS], [test x"$use_exhaustive_tests" != x"no"])
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AM_CONDITIONAL([USE_BENCHMARK], [test x"$use_benchmark" = x"yes"])
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AM_CONDITIONAL([USE_ECMULT_STATIC_PRECOMPUTATION], [test x"$set_precomp" = x"yes"])
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AM_CONDITIONAL([ENABLE_MODULE_ECDH], [test x"$enable_module_ecdh" = x"yes"])
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