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crypto: Bulletproofs+ with double-blinded commitments extension implemented (nicknamed as bppe), basic tests added

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sowle 2022-04-11 20:43:43 +02:00
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src/crypto/range_proof_bppe.h Normal file
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// Copyright (c) 2022 Zano Project (https://zano.org/)
// Copyright (c) 2022 sowle (val@zano.org, crypto.sowle@gmail.com)
// Distributed under the MIT/X11 software license, see the accompanying
// file COPYING or http://www.opensource.org/licenses/mit-license.php.
#pragma once
//
// This file contains the implementation of range proof protocol.
// Namely, Bulletproofs+ https://eprint.iacr.org/2020/735
// Double-blinded commitments extension implemented as in Appendix D in the Zarcanum whitepaper: https://eprint.iacr.org/2021/1478
namespace crypto
{
struct bppe_signature
{
std::vector<public_key> L; // size = log_2(m * n)
std::vector<public_key> R;
public_key A0;
public_key A;
public_key B;
scalar_t r;
scalar_t s;
scalar_t delta_1;
scalar_t delta_2;
};
#define DBG_VAL_PRINT(x) std::cout << #x ": " << x << ENDL
#define DBG_PRINT(x) std::cout << x << ENDL
template<typename CT>
bool bppe_gen(const scalar_vec_t& values, const scalar_vec_t& masks, const scalar_vec_t& masks2, bppe_signature& sig, std::vector<point_t>& commitments, uint8_t* p_err = nullptr)
{
#define CHECK_AND_FAIL_WITH_ERROR_IF_FALSE(cond, err_code) \
if (!(cond)) { LOG_PRINT_RED("bppe_gen: \"" << #cond << "\" is false at " << LOCATION_SS << ENDL << "error code = " << err_code, LOG_LEVEL_3); \
if (p_err) { *p_err = err_code; } return false; }
CHECK_AND_FAIL_WITH_ERROR_IF_FALSE(values.size() > 0 && values.size() <= CT::c_bpp_values_max && values.size() == masks.size() && masks.size() == masks2.size(), 1);
CHECK_AND_FAIL_WITH_ERROR_IF_FALSE(masks.is_reduced() && masks2.is_reduced(), 3);
const size_t c_bpp_log2_m = constexpr_ceil_log2(values.size());
const size_t c_bpp_m = 1ull << c_bpp_log2_m;
const size_t c_bpp_mn = c_bpp_m * CT::c_bpp_n;
const size_t c_bpp_log2_mn = c_bpp_log2_m + CT::c_bpp_log2_n;
// pre-multiply all output points by c_scalar_1div8
// in order to enforce these points to be in the prime-order subgroup (after mul by 8 in bpp_verify())
// calc commitments vector as commitments[i] = 1/8 * values[i] * G + 1/8 * masks[i] * H + 1/8 * masks2[i] * H2
commitments.resize(values.size());
for (size_t i = 0; i < values.size(); ++i)
CT::calc_pedersen_commitment_2(values[i] * c_scalar_1div8, masks[i] * c_scalar_1div8, masks2[i] * c_scalar_1div8, commitments[i]);
// s.a. BP+ paper, page 15, eq. 11
// decompose v into aL and aR:
// v = aL o (1, 2, 2^2, ..., 2^n-1), o - component-wise product aka Hadamard product
// aR = aL - (1, 1, ... 1)
// aR o aL = 0
// aLs = (aL_0, aL_1, ..., aL_m-1) -- `bit` matrix of c_bpp_m x c_bpp_n, each element is a scalar
scalar_mat_t<CT::c_bpp_n> aLs(c_bpp_mn), aRs(c_bpp_mn);
aLs.zero();
aRs.zero();
// m >= values.size, first set up [0..values.size-1], then -- [values.size..m-1] (padding area)
for (size_t i = 0; i < values.size(); ++i)
{
const scalar_t& v = values[i];
for (size_t j = 0; j < CT::c_bpp_n; ++j)
{
if (v.get_bit(j))
aLs(i, j) = c_scalar_1; // aL = 1, aR = 0
else
aRs(i, j) = c_scalar_Lm1; // aL = 0, aR = -1
}
}
for (size_t i = values.size(); i < c_bpp_m; ++i)
for (size_t j = 0; j < CT::c_bpp_n; ++j)
aRs(i, j) = c_scalar_Lm1; // aL = 0, aR = -1
// using e as Fiat-Shamir transcript
scalar_t e = CT::get_initial_transcript();
DBG_PRINT("initial transcript: " << e);
hash_helper_t::hs_t hsc;
CT::update_transcript(hsc, e, commitments);
// Zarcanum paper, page 33, Fig. D.3: The prover chooses alpha_1, alpha_2 and computes A = g^aL h^aR h_1^alpha_1 h_2^alpha_2
// so we calculate A0 = alpha_1 * H + alpha_2 * H_2 + SUM(aL_i * G_i) + SUM(aR_i * H_i)
scalar_t alpha_1 = scalar_t::random(), alpha_2 = scalar_t::random();
point_t A0 = alpha_1 * CT::bpp_H + alpha_2 * CT::bpp_H2;
for (size_t i = 0; i < c_bpp_mn; ++i)
A0 += aLs[i] * CT::get_generator(false, i) + aRs[i] * CT::get_generator(true, i);
// part of 1/8 defense scheme
A0 *= c_scalar_1div8;
A0.to_public_key(sig.A0);
DBG_VAL_PRINT(alpha_1);
DBG_VAL_PRINT(alpha_2);
DBG_VAL_PRINT(A0);
// calculate scalar challenges y and z
hsc.add_scalar(e);
hsc.add_pub_key(sig.A0);
scalar_t y = hsc.calc_hash();
scalar_t z = hash_helper_t::hs(y);
e = z; // transcript for further steps
DBG_VAL_PRINT(y);
DBG_VAL_PRINT(z);
// Computing vector d for aggregated version of the protocol (BP+ paper, page 17)
// (note: elements is stored column-by-column in memory)
// d = | 1 * z^(2*1), 1 * z^(2*2), 1 * z^(2*3), ..., 1 * z^(2*m) |
// | 2 * z^(2*1), 2 * z^(2*2), 2 * z^(2*3), ..., 2 * z^(2*m) |
// | 4 * z^(2*1), 4 * z^(2*2), 4 * z^(2*3), ..., 4 * z^(2*m) |
// | ....................................................................................... |
// | 2^(n-1) * z^(2*1), 2^(n-1) * z^(2*2), 2^(n-1) * z^(2*3), ..., 2^(n-1) * z^(2*m)) |
// Note: sum(d_i) = (2^n - 1) * ((z^2)^1 + (z^2)^2 + ... (z^2)^m)) = (2^n-1) * sum_of_powers(x^2, log(m))
scalar_t z_sq = z * z;
scalar_mat_t<CT::c_bpp_n> d(c_bpp_mn);
d(0, 0) = z_sq;
// first row
for (size_t i = 1; i < c_bpp_m; ++i)
d(i, 0) = d(i - 1, 0) * z_sq;
// all rows
for (size_t j = 1; j < CT::c_bpp_n; ++j)
for (size_t i = 0; i < c_bpp_m; ++i)
d(i, j) = d(i, j - 1) + d(i, j - 1);
DBG_PRINT("Hs(d): " << d.calc_hs());
// calculate extended Vandermonde vector y = (1, y, y^2, ..., y^(mn+1)) (BP+ paper, page 18, Fig. 3)
// (calculate two more elements (1 and y^(mn+1)) for convenience)
scalar_vec_t y_powers(c_bpp_mn + 2);
y_powers[0] = 1;
for (size_t i = 1; i <= c_bpp_mn + 1; ++i)
y_powers[i] = y_powers[i - 1] * y;
const scalar_t& y_mn_p1 = y_powers[c_bpp_mn + 1];
DBG_PRINT("Hs(y_powers): " << y_powers.calc_hs());
// aL_hat = aL - 1*z
scalar_vec_t aLs_hat = aLs - z;
// aL_hat = aR + d o y^leftarr + 1*z where y^leftarr = (y^n, y^(n-1), ..., y) (BP+ paper, page 18, Fig. 3)
scalar_vec_t aRs_hat = aRs + z;
for (size_t i = 0; i < c_bpp_mn; ++i)
aRs_hat[i] += d[i] * y_powers[c_bpp_mn - i];
DBG_PRINT("Hs(aLs_hat): " << aLs_hat.calc_hs());
DBG_PRINT("Hs(aRs_hat): " << aRs_hat.calc_hs());
// calculate alpha_hat
// alpha_hat_1 = alpha_1 + SUM(z^(2j) * gamma_1,j * y^(mn+1)) for j = 1..m
// alpha_hat_2 = alpha_2 + SUM(z^(2j) * gamma_2,j * y^(mn+1)) for j = 1..m
// i.e. \hat{\alpha} = \alpha + y^{m n+1} \sum_{j = 1}^{m} z^{2j} \gamma_j
scalar_t alpha_hat_1 = 0, alpha_hat_2 = 0;
for (size_t i = 0; i < masks.size(); ++i)
{
alpha_hat_1 += d(i, 0) * masks[i];
alpha_hat_2 += d(i, 0) * masks2[i];
}
alpha_hat_1 = alpha_1 + y_mn_p1 * alpha_hat_1;
alpha_hat_2 = alpha_2 + y_mn_p1 * alpha_hat_2;
DBG_VAL_PRINT(alpha_hat_1);
DBG_VAL_PRINT(alpha_hat_2);
// calculate y^-1, y^-2, ...
const scalar_t y_inverse = y.reciprocal();
scalar_vec_t y_inverse_powers(c_bpp_mn / 2 + 1); // the greatest power we need is c_bpp_mn/2 (at the first reduction round)
y_inverse_powers[0] = 1;
for (size_t i = 1, size = y_inverse_powers.size(); i < size; ++i)
y_inverse_powers[i] = y_inverse_powers[i - 1] * y_inverse;
// prepare generator's vector
std::vector<point_t> g(c_bpp_mn), h(c_bpp_mn);
for (size_t i = 0; i < c_bpp_mn; ++i)
{
g[i] = CT::get_generator(false, i);
h[i] = CT::get_generator(true, i);
}
// WIP zk-argument called with zk-WIP(g, h, G, H, H2, A_hat, aL_hat, aR_hat, alpha_hat_1, alpha_hat_2)
scalar_vec_t& a = aLs_hat;
scalar_vec_t& b = aRs_hat;
sig.L.resize(c_bpp_log2_mn);
sig.R.resize(c_bpp_log2_mn);
// zk-WIP reduction rounds (s.a. Zarcanum preprint page 24 Fig. D.1)
for (size_t n = c_bpp_mn / 2, ni = 0; n >= 1; n /= 2, ++ni)
{
DBG_PRINT(ENDL << "#" << ni);
// zk-WIP(g, h, G, H, H2, P, a, b, alpha_1, alpha_2)
scalar_t dL = scalar_t::random(), dL2 = scalar_t::random();
DBG_VAL_PRINT(dL); DBG_VAL_PRINT(dL2);
scalar_t dR = scalar_t::random(), dR2 = scalar_t::random();
DBG_VAL_PRINT(dR); DBG_VAL_PRINT(dR2);
// a = (a1, a2), b = (b1, b2) -- vectors of scalars
// cL = <a1, ((y, y^2, ...) o b2)> -- scalar
scalar_t cL = 0;
for (size_t i = 0; i < n; ++i)
cL += a[i] * y_powers[i + 1] * b[n + i];
DBG_VAL_PRINT(cL);
// cR = <a2, ((y, y^2, ...) o b1)> * y^n -- scalar
scalar_t cR = 0;
for (size_t i = 0; i < n; ++i)
cR += a[n + i] * y_powers[i + 1] * b[i];
cR *= y_powers[n];
DBG_VAL_PRINT(cR);
// L = y^-n * a1 * g2 + b2 * h1 + cL * G + dL * H + dL2 * H2 -- point
point_t sum = c_point_0;
for (size_t i = 0; i < n; ++i)
sum += a[i] * g[n + i];
point_t L;
CT::calc_pedersen_commitment_2(cL, dL, dL2, L);
for (size_t i = 0; i < n; ++i)
L += b[n + i] * h[i];
L += y_inverse_powers[n] * sum;
L *= c_scalar_1div8;
DBG_VAL_PRINT(L);
// R = y^n * a2 * g1 + b1 * h2 + cR * G + dR * H + dR2 * H2 -- point
sum.zero();
for (size_t i = 0; i < n; ++i)
sum += a[n + i] * g[i];
point_t R;
CT::calc_pedersen_commitment_2(cR, dR, dR2, R);
for (size_t i = 0; i < n; ++i)
R += b[i] * h[n + i];
R += y_powers[n] * sum;
R *= c_scalar_1div8;
DBG_VAL_PRINT(R);
// put L, R to the sig
L.to_public_key(sig.L[ni]);
R.to_public_key(sig.R[ni]);
// update the transcript
hsc.add_scalar(e);
hsc.add_pub_key(sig.L[ni]);
hsc.add_pub_key(sig.R[ni]);
e = hsc.calc_hash();
DBG_VAL_PRINT(e);
// recalculate arguments for the next round
scalar_t e_squared = e * e;
scalar_t e_inverse = e.reciprocal();
scalar_t e_inverse_squared = e_inverse * e_inverse;
scalar_t e_y_inv_n = e * y_inverse_powers[n];
scalar_t e_inv_y_n = e_inverse * y_powers[n];
// g_hat = e^-1 * g1 + (e * y^-n) * g2 -- vector of points
for (size_t i = 0; i < n; ++i)
g[i] = e_inverse * g[i] + e_y_inv_n * g[n + i];
// h_hat = e * h1 + e^-1 * h2 -- vector of points
for (size_t i = 0; i < n; ++i)
h[i] = e * h[i] + e_inverse * h[n + i];
// P_hat = e^2 * L + P + e^-2 * R -- point
// a_hat = e * a1 + e^-1 * y^n * a2 -- vector of scalars
for (size_t i = 0; i < n; ++i)
a[i] = e * a[i] + e_inv_y_n * a[n + i];
// b_hat = e^-1 * b1 + e * b2 -- vector of scalars
for (size_t i = 0; i < n; ++i)
b[i] = e_inverse * b[i] + e * b[n + i];
// alpha_hat_1 = e^2 * dL + alpha_1 + e^-2 * dR -- scalar
// alpha_hat_2 = e^2 * dL2 + alpha_2 + e^-2 * dR2 -- scalar
alpha_hat_1 += e_squared * dL + e_inverse_squared * dR;
alpha_hat_2 += e_squared * dL2 + e_inverse_squared * dR2;
// run next iteraton zk-WIP(g_hat, h_hat, G, H, H2, P_hat, a_hat, b_hat, alpha_hat_1, alpha_hat_2)
}
DBG_PRINT("");
// zk-WIP last round
scalar_t r = scalar_t::random();
scalar_t s = scalar_t::random();
scalar_t delta_1 = scalar_t::random(), delta_2 = scalar_t::random();
scalar_t eta_1 = scalar_t::random(), eta_2 = scalar_t::random();
DBG_VAL_PRINT(r);
DBG_VAL_PRINT(s);
DBG_VAL_PRINT(delta_1); DBG_VAL_PRINT(delta_2);
DBG_VAL_PRINT(eta_1); DBG_VAL_PRINT(eta_2);
// A = r * g + s * h + (r y b + s y a) * G + delta_1 * H + delta_2 * H2 -- point
point_t A = c_point_0;
CT::calc_pedersen_commitment_2(y * (r * b[0] + s * a[0]), delta_1, delta_2, A);
A += r * g[0] + s * h[0];
A *= c_scalar_1div8;
A.to_public_key(sig.A);
DBG_VAL_PRINT(A);
// B = (r * y * s) * G + eta_1 * H + eta_2 * H2
point_t B = c_point_0;
CT::calc_pedersen_commitment_2(r * y * s, eta_1, eta_2, B);
B *= c_scalar_1div8;
B.to_public_key(sig.B);
DBG_VAL_PRINT(B);
// update the transcript
hsc.add_scalar(e);
hsc.add_pub_key(sig.A);
hsc.add_pub_key(sig.B);
e = hsc.calc_hash();
DBG_VAL_PRINT(e);
// finalize the signature
sig.r = r + e * a[0];
sig.s = s + e * b[0];
sig.delta_1 = eta_1 + e * delta_1 + e * e * alpha_hat_1;
sig.delta_2 = eta_2 + e * delta_2 + e * e * alpha_hat_2;
DBG_VAL_PRINT(sig.r);
DBG_VAL_PRINT(sig.s);
DBG_VAL_PRINT(sig.delta_1);
DBG_VAL_PRINT(sig.delta_2);
return true;
#undef CHECK_AND_FAIL_WITH_ERROR_IF_FALSE
} // bppe_gen()
struct bppe_sig_commit_ref_t
{
bppe_sig_commit_ref_t(const bppe_signature& sig, const std::vector<point_t>& commitments)
: sig(sig)
, commitments(commitments)
{}
const bppe_signature& sig;
const std::vector<point_t>& commitments;
};
template<typename CT>
bool bppe_verify(const std::vector<bppe_sig_commit_ref_t>& sigs, uint8_t* p_err = nullptr)
{
#define CHECK_AND_FAIL_WITH_ERROR_IF_FALSE(cond, err_code) \
if (!(cond)) { LOG_PRINT_RED("bppe_verify: \"" << #cond << "\" is false at " << LOCATION_SS << ENDL << "error code = " << err_code, LOG_LEVEL_3); \
if (p_err) { *p_err = err_code; } return false; }
DBG_PRINT(ENDL << " . . . . bppe_verify() . . . . ");
const size_t kn = sigs.size();
CHECK_AND_FAIL_WITH_ERROR_IF_FALSE(kn > 0, 1);
struct intermediate_element_t
{
scalar_t y;
scalar_t z;
scalar_t z_sq;
scalar_vec_t e;
scalar_vec_t e_sq;
scalar_t e_final;
scalar_t e_final_sq;
size_t inv_e_offset; // offset in batch_for_inverse
size_t inv_y_offset; // offset in batch_for_inverse
size_t c_bpp_log2_m;
size_t c_bpp_m;
size_t c_bpp_mn;
point_t A;
point_t A0;
point_t B;
std::vector<point_t> L;
std::vector<point_t> R;
};
std::vector<intermediate_element_t> interms(kn);
size_t c_bpp_log2_m_max = 0;
for (size_t k = 0; k < kn; ++k)
{
const bppe_sig_commit_ref_t& bsc = sigs[k];
const bppe_signature& sig = bsc.sig;
CHECK_AND_FAIL_WITH_ERROR_IF_FALSE(bsc.commitments.size() > 0, 2);
CHECK_AND_FAIL_WITH_ERROR_IF_FALSE(sig.L.size() > 0 && sig.L.size() == sig.R.size(), 3);
CHECK_AND_FAIL_WITH_ERROR_IF_FALSE(sig.r.is_reduced() && sig.s.is_reduced() && sig.delta_1.is_reduced() && sig.delta_2.is_reduced(), 4);
intermediate_element_t& interm = interms[k];
interm.c_bpp_log2_m = constexpr_ceil_log2(bsc.commitments.size());
if (c_bpp_log2_m_max < interm.c_bpp_log2_m)
c_bpp_log2_m_max = interm.c_bpp_log2_m;
CHECK_AND_FAIL_WITH_ERROR_IF_FALSE(sig.L.size() == interm.c_bpp_log2_m + CT::c_bpp_log2_n, 5);
interm.c_bpp_m = 1ull << interm.c_bpp_log2_m;
interm.c_bpp_mn = interm.c_bpp_m * CT::c_bpp_n;
CHECK_AND_FAIL_WITH_ERROR_IF_FALSE(interm.A0.from_public_key(sig.A0), 6);
CHECK_AND_FAIL_WITH_ERROR_IF_FALSE(interm.A.from_public_key(sig.A), 7);
CHECK_AND_FAIL_WITH_ERROR_IF_FALSE(interm.B.from_public_key(sig.B), 8);
interm.L.resize(sig.L.size());
interm.R.resize(sig.R.size());
for (size_t i = 0; i < interm.L.size(); ++i)
{
CHECK_AND_FAIL_WITH_ERROR_IF_FALSE(interm.L[i].from_public_key(sig.L[i]), 9);
CHECK_AND_FAIL_WITH_ERROR_IF_FALSE(interm.R[i].from_public_key(sig.R[i]), 10);
}
}
const size_t c_bpp_m_max = 1ull << c_bpp_log2_m_max;
const size_t c_bpp_mn_max = c_bpp_m_max * CT::c_bpp_n;
const size_t c_bpp_LR_size_max = c_bpp_log2_m_max + CT::c_bpp_log2_n;
//
// prepare stuff
//
/*
std::vector<point_t> g(c_bpp_mn_max), h(c_bpp_mn_max);
for (size_t i = 0; i < c_bpp_mn_max; ++i)
{
g[i] = CT::get_generator(false, i);
h[i] = CT::get_generator(true, i);
}
*/
scalar_vec_t batch_for_inverse;
batch_for_inverse.reserve(kn + kn * c_bpp_LR_size_max);
for (size_t k = 0; k < kn; ++k)
{
DBG_PRINT(ENDL << "SIG #" << k);
const bppe_sig_commit_ref_t& bsc = sigs[k];
const bppe_signature& sig = bsc.sig;
intermediate_element_t& interm = interms[k];
// restore y and z
// using e as Fiat-Shamir transcript
scalar_t e = CT::get_initial_transcript();
DBG_PRINT("initial transcript: " << e);
hash_helper_t::hs_t hsc;
CT::update_transcript(hsc, e, bsc.commitments);
// calculate scalar challenges y and z
hsc.add_scalar(e);
hsc.add_pub_key(sig.A0);
hsc.assign_calc_hash(interm.y);
interm.z = hash_helper_t::hs(interm.y);
interm.z_sq = interm.z * interm.z;
DBG_VAL_PRINT(interm.y);
DBG_VAL_PRINT(interm.z);
e = interm.z; // transcript for further steps
interm.inv_y_offset = batch_for_inverse.size();
batch_for_inverse.push_back(interm.y);
interm.inv_e_offset = batch_for_inverse.size();
interm.e.resize(sig.L.size());
interm.e_sq.resize(sig.L.size());
for (size_t i = 0; i < sig.L.size(); ++i)
{
hsc.add_scalar(e);
hsc.add_pub_key(sig.L[i]);
hsc.add_pub_key(sig.R[i]);
hsc.assign_calc_hash(e);
interm.e[i] = e;
interm.e_sq[i] = e * e;
DBG_PRINT("e[" << i << "]: " << e);
batch_for_inverse.push_back(e);
}
hsc.add_scalar(e);
hsc.add_pub_key(sig.A);
hsc.add_pub_key(sig.B);
hsc.assign_calc_hash(interm.e_final);
interm.e_final_sq = interm.e_final * interm.e_final;
DBG_VAL_PRINT(interm.e_final);
}
batch_for_inverse.invert();
// Notation:
// 1_vec ^ n = (1, 1, 1, ..., 1)
// 2_vec ^ n = (2^0, 2^1, 2^2, ..., 2^(n-1))
// -1_vec ^ n = ((-1)^0, (-1)^1, (-1)^2, ... (-1)^(n-1)) = (1, -1, 1, -1, ...)
// y<^n = (y^n, y^(n-1), ..., y^1)
// y>^n = (y^1, y^2, ..., y^n)
// from Zarcanum page 24, Fig D.1:
// Verifier outputs Accept IFF the following holds:
// P^e^2 * A^e * B == g ^ (r' e) * h ^ (s' e) * G ^ (r' y s') * H ^ delta'_1 * H2 ^ delta'_2
// (where g and h are calculated in each round)
// The same equation in additive notation:
// e^2 * P + e * A + B == (r' * e) * g + (s' * e) * h + (r' y s') * G + delta'_1 * H + delta'_2 * H2
// <=>
// (r' * e) * g + (s' * e) * h + (r' y s') * G + delta'_1 * H + delta'_2 * H2 - e^2 * P - e * A - B == 0 (*)
// where A, B, r', s', delta'_1, delta'_2 is taken from the signature
// and P_{k+1} = e^2 * L_k + P_k + e^-2 * R_k for all rounds
//
// from Zarcanum preprint page 33, Fig D.3:
// P and V computes:
// A_hat = A0 + (- 1^(mn) * z) * g + (d o y<^(mn) + 1^(mn) * z) * h +
// + y^(mn+1) * (SUM{j=1..m} z^(2j) * V_j) +
// + (z*SUM(y^>mn) - z*y^(mn+1)*SUM(d) - z^2 * SUM(y^>mn)) * G
// (calculated once)
//
// As suggested in BPP preprint Section 6.1 "Practical Optimizations":
// 1) g and h exponentianions can be optimized in order not to be calculated at each round
// as the following (page 20, with delta'_2 and H2 added):
//
// (r' * e * s_vec) * g + (s' * e * s'_vec) * h + (r' y s') * G + delta'_1 * H + delta'_2 * H2 -
// - e^2 * A_hat
// - SUM{j=1..log(n)}(e_final^2 * e_j^2 * L_j + e_final^2 * e_j^-2 * R_j)
// - e * A - B = 0 (**)
//
// where:
// g, h - vector of fixed generators
// s_vec_i = y^(1-i) * PROD{j=1..log(n)}(e_j ^ b(i,j))
// s'_vec_i = PROD{j=1..log(n)}(e_j ^ -b(i,j))
// b(i, j) = { 2 * ((1<<(j-1)) & (i-1)) - 1) (counting both from 1) (page 20)
// b(i, j) = { 2 * ((1<<j) & i) - 1) (counting both from 0)
//
// 2) we gonna aggregate all (**) for each round by multiplying them to a random weights and then sum up
// insert A_hat into (**) =>
// (r' * e * s_vec) * g + (s' * e * s'_vec) * h + (r' y s') * G + delta'_1 * H + delta'_2 * H2 -
// - e^2 * (A0 + (- 1^(mn) * z) * g + (d o y<^(mn) + 1^(mn) * z) * h +
// + y^(mn+1) * (SUM{j=1..m} z^(2j) * V_j) +
// + (z*SUM(y^>mn) - z*y^(mn+1)*SUM(d) - z^2 * SUM(y^>mn)) * G
// )
// - SUM{j=1..log(n)}(e_final^2 * e_j^2 * L_j + e_final^2 * e_j^-2 * R_j)
// - e * A - B = 0
// =>
// (for single signature)
//
// (r' * e * s_vec - e^2 * (- 1_vec^(mn) * z)) * g | these are
// + (s' * e * s'_vec - e^2 * (d o y<^(mn) + 1_vec^(mn) * z)) * h | fixed generators
// + (r' y s' - e^2 * ((z - z^2)*SUM(y^>mn) - z*y^(mn+1)*SUM(d)) * G | across all
// + delta'_1 * H | the signatures
// + delta'_2 * H2 | the signatures
//
// - e^2 * A0
// - e^2 * y^(mn+1) * (SUM{j=1..m} z^(2j) * V_j))
// - e^2 * SUM{j=1..log(n)}(e_j^2 * L_j + e_j^-2 * R_j)
// - e * A - B = 0 (***)
//
// All (***) will be muptiplied by random weightning factor and then summed up.
// Calculate cummulative sclalar multiplicand for fixed generators across all the sigs.
scalar_vec_t g_scalars;
g_scalars.resize(c_bpp_mn_max, 0);
scalar_vec_t h_scalars;
h_scalars.resize(c_bpp_mn_max, 0);
scalar_t G_scalar = 0;
scalar_t H_scalar = 0;
scalar_t H2_scalar = 0;
point_t summand = c_point_0;
for (size_t k = 0; k < kn; ++k)
{
DBG_PRINT(ENDL << "SIG #" << k);
const bppe_sig_commit_ref_t& bsc = sigs[k];
const bppe_signature& sig = bsc.sig;
intermediate_element_t& interm = interms[k];
// random weightning factor for speed-optimized batch verification (preprint page 20)
const scalar_t rwf = scalar_t::random();
DBG_PRINT("rwf: " << rwf);
// prepare d vector (see also d structure description in proof function)
scalar_mat_t<CT::c_bpp_n> d(interm.c_bpp_mn);
d(0, 0) = interm.z_sq;
// first row
for (size_t i = 1; i < interm.c_bpp_m; ++i)
d(i, 0) = d(i - 1, 0) * interm.z_sq;
// all rows
for (size_t j = 1; j < CT::c_bpp_n; ++j)
for (size_t i = 0; i < interm.c_bpp_m; ++i)
d(i, j) = d(i, j - 1) + d(i, j - 1);
// sum(d) (see also note in proof function for this)
// TODO: check for not 2^64 version
static const scalar_t c_scalar_2_power_n_minus_1 = { 0xffffffffffffffff, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000 };
const scalar_t sum_d = c_scalar_2_power_n_minus_1 * sum_of_powers(interm.z_sq, interm.c_bpp_log2_m);
DBG_PRINT("Hs(d): " << d.calc_hs());
DBG_PRINT("sum(d): " << sum_d);
const scalar_t& y_inv = batch_for_inverse[interm.inv_y_offset];
auto get_e_inv = [&](size_t i) { return batch_for_inverse[interm.inv_e_offset + i]; }; // i belongs to [0; L.size()-1]
// prepare s_vec (unlike the paper here we moved y-component out of s_vec for convenience, so s_vec'[x] = s_vec[~x & (MN-1)])
// complexity (sc_mul's): MN+2*log2(MN)-2
// the idea is the following:
// s_vec[00000b] = ... * (e_4)^-1 * (e_3)^-1 * (e_2)^-1 * (e_1)^-1 * (e_0)^-1
// s_vec[00101b] = ... * (e_4)^-1 * (e_3)^-1 * (e_2)^+1 * (e_1)^-1 * (e_0)^+1
const size_t log2_mn = sig.L.size(); // at the beginning we made sure that sig.L.size() == c_bpp_log2_m + c_bpp_log2_n
scalar_vec_t s_vec(interm.c_bpp_mn);
s_vec[0] = get_e_inv(0);
for (size_t i = 1; i < log2_mn; ++i)
s_vec[0] *= get_e_inv(i); // s_vec[0] = (e_0)^-1 * (e_1)^-1 * .. (e_{log2_mn-1})^-1
DBG_PRINT("[0] " << s_vec[0]);
for (size_t i = 1; i < interm.c_bpp_mn; ++i)
{
size_t base_el_index = i & (i - 1); // base element index: 0, 0, 2, 0, 4, 4, 6, 0, 8, 8, 10... base element differs in one bit (0) from the current one (1)
size_t bit_index = log2_mn - calc_lsb_32((uint32_t)i) - 1; // the bit index where current element has the difference with the base
s_vec[i] = s_vec[base_el_index] * interm.e_sq[bit_index]; // (e_j)^-1 * (e_j)^2 = (e_j)^+1
DBG_PRINT("[" << i << "] " << " " << base_el_index << ", " << bit_index << " : " << s_vec[i]);
}
// prepare y_inv vector
scalar_vec_t y_inverse_powers(interm.c_bpp_mn);
y_inverse_powers[0] = 1;
for (size_t i = 1; i < interm.c_bpp_mn; ++i)
y_inverse_powers[i] = y_inverse_powers[i - 1] * y_inv;
// y^(mn+1)
scalar_t y_power_mnp1 = interm.y;
for (size_t i = 0; i < log2_mn; ++i)
y_power_mnp1 *= y_power_mnp1;
y_power_mnp1 *= interm.y;
DBG_VAL_PRINT(y_power_mnp1);
// now calculate all multiplicands for common generators
// g vector multiplicands:
// rwf * (r' * e * (1, y^-1, y^-2, ...) o s_vec + e^2 * z) =
// rwf * r' * e * ((1, y^-1, ...) o s_vec) + rwf * e^2 * z * (1, 1, ...)
scalar_t rwf_e_sq_z = rwf * interm.e_final_sq * interm.z;
scalar_t rwf_r_e = rwf * interm.e_final * sig.r;
for (size_t i = 0; i < interm.c_bpp_mn; ++i)
g_scalars[i] += rwf_r_e * y_inverse_powers[i] * s_vec[i] + rwf_e_sq_z;
DBG_PRINT("Hs(g_scalars): " << g_scalars.calc_hs());
// h vector multiplicands:
// rwf * (s' * e * s'_vec - e^2 * (d o y<^(mn) + 1_vec^(mn) * z))
// rwf * s' * e * s'_vec - rwf * e^2 * z * (1, 1...) - rwf * e^2 * (d o y<^(mn))
//scalar_t rwf_e_sq_z = rwf * interm.e_final_sq * interm.z;
scalar_t rwf_s_e = rwf * sig.s * interm.e_final;
scalar_t rwf_e_sq_y = rwf * interm.e_final_sq * interm.y;
for (size_t i = interm.c_bpp_mn - 1; i != SIZE_MAX; --i)
{
h_scalars[i] += rwf_s_e * s_vec[interm.c_bpp_mn - 1 - i] - rwf_e_sq_z - rwf_e_sq_y * d[i];
rwf_e_sq_y *= interm.y;
}
DBG_PRINT("Hs(h_scalars): " << h_scalars.calc_hs());
// G point multiplicands:
// rwf * (r' y s' - e ^ 2 * ((z - z ^ 2)*SUM(y^>mn) - z * y^(mn+1) * SUM(d)) =
// = rwf * r' y s' - rwf * e^2 * (z - z ^ 2)*SUM(y^>mn) + rwf * e^2 * z * y^(mn+1) * SUM(d)
G_scalar += rwf * sig.r * interm.y * sig.s + rwf_e_sq_y * sum_d * interm.z;
G_scalar -= rwf * interm.e_final_sq * (interm.z - interm.z_sq) * sum_of_powers(interm.y, log2_mn);
DBG_PRINT("sum_y: " << sum_of_powers(interm.y, log2_mn));
DBG_PRINT("G_scalar: " << G_scalar);
// H point multiplicands:
// rwf * delta_1
H_scalar += rwf * sig.delta_1;
DBG_PRINT("H_scalar: " << H_scalar);
// H2 point multiplicands:
// rwf * delta_2
H2_scalar += rwf * sig.delta_2;
DBG_PRINT("H2_scalar: " << H2_scalar);
// uncommon generators' multiplicands
point_t summand_8 = c_point_0; // this summand to be multiplied by 8 before adding to the main summand
// - rwf * e^2 * A0
summand_8 -= rwf * interm.e_final_sq * interm.A0;
DBG_PRINT("A0_scalar: " << c_scalar_Lm1 * interm.e_final_sq * rwf);
// - rwf * e^2 * y^(mn+1) * (SUM{j=1..m} (z^2)^j * V_j))
scalar_t e_sq_y_mn1_z_sq_power = rwf * interm.e_final_sq * y_power_mnp1;
for (size_t j = 0; j < bsc.commitments.size(); ++j)
{
e_sq_y_mn1_z_sq_power *= interm.z_sq;
summand_8 -= e_sq_y_mn1_z_sq_power * bsc.commitments[j];
DBG_PRINT("V_scalar[" << j << "]: " << c_scalar_Lm1 * e_sq_y_mn1_z_sq_power);
}
// - rwf * e^2 * SUM{j=1..log(n)}(e_j^2 * L_j + e_j^-2 * R_j)
scalar_t rwf_e_sq = rwf * interm.e_final_sq;
for (size_t j = 0; j < log2_mn; ++j)
{
summand_8 -= rwf_e_sq * (interm.e_sq[j] * interm.L[j] + get_e_inv(j) * get_e_inv(j) * interm.R[j]);
DBG_PRINT("L_scalar[" << j << "]: " << c_scalar_Lm1 * rwf_e_sq * interm.e_sq[j]);
DBG_PRINT("R_scalar[" << j << "]: " << c_scalar_Lm1 * rwf_e_sq * get_e_inv(j) * get_e_inv(j));
}
// - rwf * e * A - rwf * B = 0
summand_8 -= rwf * interm.e_final * interm.A + rwf * interm.B;
DBG_PRINT("A_scalar: " << c_scalar_Lm1 * rwf * interm.e_final);
DBG_PRINT("B_scalar: " << c_scalar_Lm1 * rwf);
summand_8.modify_mul8();
summand += summand_8;
}
point_t GH_exponents = c_point_0;
CT::calc_pedersen_commitment_2(G_scalar, H_scalar, H2_scalar, GH_exponents);
bool result = multiexp_and_check_being_zero<CT>(g_scalars, h_scalars, summand + GH_exponents);
if (result)
DBG_PRINT(ENDL << " . . . . bppe_verify() -- SUCCEEDED!!!" << ENDL);
return result;
#undef CHECK_AND_FAIL_WITH_ERROR_IF_FALSE
}
} // namespace crypto

1
src/crypto/range_proofs.h
View file

@ -148,3 +148,4 @@ namespace crypto
} // namespace crypto
#include "range_proof_bpp.h"
#include "range_proof_bppe.h"

79
tests/functional_tests/crypto_tests_range_proofs.h
View file

@ -180,3 +180,82 @@ TEST(bpp, power_256)
return true;
}
//
// tests for Bulletproofs+ Extended (with double-blinded commitments)
//
TEST(bppe, basics)
{
/*
srand(0);
for (size_t i = 0; i < 10; ++i)
std::cout << scalar_t::random().to_string_as_secret_key() << ENDL;
*/
scalar_vec_t values = { 5 };
scalar_vec_t masks = { 0 };
scalar_vec_t masks_2 = { 0 };
bppe_signature bppe_sig;
std::vector<point_t> commitments;
uint8_t err = 0;
bool r = bppe_gen<bpp_crypto_trait_zano<>>(values, masks, masks_2, bppe_sig, commitments, &err);
ASSERT_TRUE(r);
return true;
}
TEST(bppe, two)
{
std::vector<bppe_signature> signatures_vector;
signatures_vector.reserve(10);
std::vector<std::vector<point_t>> commitments_vector;
commitments_vector.reserve(10);
std::vector<bppe_sig_commit_ref_t> sigs;
uint8_t err = 0;
bool r = false;
{
signatures_vector.resize(signatures_vector.size() + 1);
bppe_signature &bppe_sig = signatures_vector.back();
commitments_vector.resize(commitments_vector.size() + 1);
std::vector<point_t>& commitments = commitments_vector.back();
scalar_vec_t values = { 5 };
scalar_vec_t masks = { scalar_t(77 + 256 * 77) };
scalar_vec_t masks2 = { scalar_t(88 + 256 * 88) };
r = bppe_gen<bpp_crypto_trait_zano<>>(values, masks, masks2, bppe_sig, commitments, &err);
ASSERT_TRUE(r);
sigs.emplace_back(bppe_sig, commitments);
}
{
signatures_vector.resize(signatures_vector.size() + 1);
bppe_signature &bppe_sig = signatures_vector.back();
commitments_vector.resize(commitments_vector.size() + 1);
std::vector<point_t>& commitments = commitments_vector.back();
scalar_vec_t values = { 5, 700, 8 };
scalar_vec_t masks = { scalar_t(77 + 256 * 77), scalar_t(255), scalar_t(17) };
scalar_vec_t masks2 = { scalar_t(88 + 256 * 88), scalar_t(1), scalar_t(19) };
r = bppe_gen<bpp_crypto_trait_zano<>>(values, masks, masks2, bppe_sig, commitments, &err);
ASSERT_TRUE(r);
sigs.emplace_back(bppe_sig, commitments);
}
r = bppe_verify<bpp_crypto_trait_zano<>>(sigs, &err);
ASSERT_TRUE(r);
return true;
}