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#include <assert.h>
#include "num.h"
#include "field.h"
#include "group.h"
#include "ecmult.h"
#include "ecdsa.h"
using namespace secp256k1;
void test_run_ecmult_chain() {
Context ctx;
// random starting point A (on the curve)
FieldElem ax; ax.SetHex("8b30bbe9ae2a990696b22f670709dff3727fd8bc04d3362c6c7bf458e2846004");
FieldElem ay; ay.SetHex("a357ae915c4a65281309edf20504740f0eb3343990216b4f81063cb65f2f7e0f");
GroupElemJac a(ax,ay);
// two random initial factors xn and gn
Number xn(ctx); xn.SetHex("84cc5452f7fde1edb4d38a8ce9b1b84ccef31f146e569be9705d357a42985407");
Number gn(ctx); gn.SetHex("a1e58d22553dcd42b23980625d4c57a96e9323d42b3152e5ca2c3990edc7c9de");
// two small multipliers to be applied to xn and gn in every iteration:
Number xf(ctx); xf.SetHex("1337");
Number gf(ctx); gf.SetHex("7113");
// accumulators with the resulting coefficients to A and G
Number ae(ctx); ae.SetHex("01");
Number ge(ctx); ge.SetHex("00");
// the point being computed
GroupElemJac x = a;
const Number &order = GetGroupConst().order;
for (int i=0; i<20000; i++) {
// in each iteration, compute X = xn*X + gn*G;
ECMult(ctx, x, x, xn, gn);
// also compute ae and ge: the actual accumulated factors for A and G
// if X was (ae*A+ge*G), xn*X + gn*G results in (xn*ae*A + (xn*ge+gn)*G)
ae.SetModMul(ctx, ae, xn, order);
ge.SetModMul(ctx, ge, xn, order);
ge.SetAdd(ctx, ge, gn);
ge.SetMod(ctx, ge, order);
// modify xn and gn
xn.SetModMul(ctx, xn, xf, order);
gn.SetModMul(ctx, gn, gf, order);
}
std::string res = x.ToString();
assert(res == "(D6E96687F9B10D092A6F35439D86CEBEA4535D0D409F53586440BD74B933E830,B95CBCA2C77DA786539BE8FD53354D2D3B4F566AE658045407ED6015EE1B2A88)");
// redo the computation, but directly with the resulting ae and ge coefficients:
GroupElemJac x2; ECMult(ctx, x2, a, ae, ge);
std::string res2 = x2.ToString();
assert(res == res2);
}
void test_point_times_order(const GroupElemJac &point) {
// either the point is not on the curve, or multiplying it by the order results in O
if (!point.IsValid())
return;
const GroupConstants &c = GetGroupConst();
Context ctx;
Number zero(ctx); zero.SetInt(0);
GroupElemJac res;
ECMult(ctx, res, point, c.order, zero); // calc res = order * point + 0 * G;
assert(res.IsInfinity());
}
void test_run_point_times_order() {
Context ctx;
FieldElem x; x.SetHex("02");
for (int i=0; i<500; i++) {
GroupElemJac j; j.SetCompressed(x, true);
test_point_times_order(j);
x.SetSquare(x);
}
assert(x.ToString() == "7603CB59B0EF6C63FE6084792A0C378CDB3233A80F8A9A09A877DEAD31B38C45"); // 0x02 ^ (2^500)
}
void test_wnaf(const Number &number, int w) {
Context ctx;
Number x(ctx), two(ctx), t(ctx);
x.SetInt(0);
two.SetInt(2);
WNAF<1023> wnaf(ctx, number, w);
int zeroes = -1;
for (int i=wnaf.GetSize()-1; i>=0; i--) {
x.SetMult(ctx, x, two);
int v = wnaf.Get(i);
if (v) {
assert(zeroes == -1 || zeroes >= w-1); // check that distance between non-zero elements is at least w-1
zeroes=0;
assert((v & 1) == 1); // check non-zero elements are odd
assert(v <= (1 << (w-1)) - 1); // check range below
assert(v >= -(1 << (w-1)) - 1); // check range above
} else {
assert(zeroes != -1); // check that no unnecessary zero padding exists
zeroes++;
}
t.SetInt(v);
x.SetAdd(ctx, x, t);
}
assert(x.Compare(number) == 0); // check that wnaf represents number
}
void test_run_wnaf() {
Context ctx;
Number range(ctx), min(ctx), n(ctx);
range.SetHex("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"); // 2^1024-1
min = range; min.Shift1(); min.Negate();
for (int i=0; i<100; i++) {
n.SetPseudoRand(range); n.SetAdd(ctx,n,min);
test_wnaf(n, 4+(i%10));
}
}
int main(void) {
test_run_wnaf();
test_run_point_times_order();
test_run_ecmult_chain();
return 0;
}