frost/secp256k1-zkp
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Add exhaustive test for group functions on a low-order subgroup

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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
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13
Makefile.am
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@@ -87,13 +87,23 @@ bench_internal_LDADD = $(SECP_LIBS) $(COMMON_LIB)
bench_internal_CPPFLAGS = -DSECP256K1_BUILD $(SECP_INCLUDES)
endif
TESTS =
if USE_TESTS
noinst_PROGRAMS += tests
tests_SOURCES = src/tests.c
tests_CPPFLAGS = -DSECP256K1_BUILD -DVERIFY -I$(top_srcdir)/src -I$(top_srcdir)/include $(SECP_INCLUDES) $(SECP_TEST_INCLUDES)
tests_LDADD = $(SECP_LIBS) $(SECP_TEST_LIBS) $(COMMON_LIB)
tests_LDFLAGS = -static
TESTS = tests
TESTS += tests
endif
if USE_EXHAUSTIVE_TESTS
noinst_PROGRAMS += exhaustive_tests
exhaustive_tests_SOURCES = src/tests_exhaustive.c
exhaustive_tests_CPPFLAGS = -DSECP256K1_BUILD -DVERIFY -I$(top_srcdir)/src $(SECP_INCLUDES)
exhaustive_tests_LDADD = $(SECP_LIBS)
exhaustive_tests_LDFLAGS = -static
TESTS += exhaustive_tests
endif
JAVAROOT=src/java
@@ -140,6 +150,7 @@ $(gen_context_BIN): $(gen_context_OBJECTS)
$(libsecp256k1_la_OBJECTS): src/ecmult_static_context.h
$(tests_OBJECTS): src/ecmult_static_context.h
$(exhaustive_tests_OBJECTS): src/ecmult_static_context.h
$(bench_internal_OBJECTS): src/ecmult_static_context.h
src/ecmult_static_context.h: $(gen_context_BIN)