Function proof_step

tests/crypto/test_crypto.cpp:206–246

}

void proof_step(
    Proof *proof, const P3Vec &g, const P3Vec &h, const EllipticCurvePoint &P, const SVec &a, const SVec &b) {
	if (a.size() == 1 && b.size() == 1) {
		proof->a = a[0];
		proof->b = b[0];
		return;
	}
	const size_t n2 = a.size() / 2;
	const SVec half_zeroes(n2, EllipticCurveScalar{});
	const SVec a1 = first_half(a);
	const SVec a2 = second_half(a);
	const SVec b1 = first_half(b);
	const SVec b2 = second_half(b);

	const auto ip = inner_product(a, b);
	const auto P1 = crypto::to_bytes(big_p(g, h, a1, a2, b1, b2, ip));
	std::cout << "P =" << P << std::endl;
	std::cout << "P1=" << P1 << std::endl;
	const auto L = crypto::to_bytes(big_p(g, h, half_zeroes, a1, b2, half_zeroes, inner_product(a1, b2)));
	const auto R = crypto::to_bytes(big_p(g, h, a2, half_zeroes, half_zeroes, b1, inner_product(a2, b1)));
	proof->L.push_back(L);
	proof->R.push_back(R);
	KeccakStream str;
	str << L << R;
	const auto x = str.hash_to_scalar();
	std::cout << "x=" << x << std::endl;
	const auto invx = crypto::sc_invert(x);
	const auto as   = add(mul(a1, x), mul(a2, invx));
	const auto bs   = add(mul(b1, invx), mul(b2, x));
	const auto PS1  = P3(L) * (x * x) + P3(P) + P3(R) * (invx * invx);
	const auto PS2  = big_p(g, h, mul(as, invx), mul(as, x), mul(bs, x), mul(bs, invx), inner_product(as, bs));
	std::cout << "PS1=" << crypto::to_bytes(PS1) << std::endl;
	std::cout << "PS2=" << crypto::to_bytes(PS2) << std::endl;
	P3Vec gnew(n2);
	P3Vec hnew(n2);
	for (size_t i = 0; i != n2; ++i) {
		gnew[i] = g[i] * invx + g.at(n2 + i) * x;
		hnew[i] = h[i] * x + h.at(n2 + i) * invx;
	}
	proof_step(proof, gnew, hnew, crypto::to_bytes(PS1), as, bs);
}

bool verify_step(const Proof &proof, const P3Vec &g, const P3Vec &h, const EllipticCurvePoint &P, size_t step) {
	std::cout << "verify P=" << P << std::endl;