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