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

View File

@@ -7,6 +7,8 @@
#ifndef _SECP256K1_ECMULT_IMPL_H_
#define _SECP256K1_ECMULT_IMPL_H_
#include <string.h>
#include "group.h"
#include "scalar.h"
#include "ecmult.h"
@@ -16,6 +18,15 @@
/* optimal for 128-bit and 256-bit exponents. */
#define WINDOW_A 5
#if defined(EXHAUSTIVE_TEST_ORDER)
# if EXHAUSTIVE_TEST_ORDER > 128
# define WINDOW_G 8
# elif EXHAUSTIVE_TEST_ORDER > 8
# define WINDOW_G 4
# else
# define WINDOW_G 2
# endif
#else
/** larger numbers may result in slightly better performance, at the cost of
exponentially larger precomputed tables. */
#ifdef USE_ENDOMORPHISM
@@ -25,6 +36,7 @@
/** One table for window size 16: 1.375 MiB. */
#define WINDOW_G 16
#endif
#endif
/** The number of entries a table with precomputed multiples needs to have. */
#define ECMULT_TABLE_SIZE(w) (1 << ((w)-2))