bulletproofs: add aggregated verification

Ported from sarang's java code
This commit is contained in:
moneromooo-monero 2018-02-03 14:36:29 +00:00
parent e895c3def1
commit bacf0a1e2f
No known key found for this signature in database
GPG Key ID: 686F07454D6CEFC3
11 changed files with 453 additions and 259 deletions

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@ -2988,7 +2988,7 @@ bool Blockchain::check_tx_inputs(transaction& tx, tx_verification_context &tvc,
}
}
if (!rct::verRctSimple(rv, false))
if (!rct::verRctNonSemanticsSimple(rv))
{
MERROR_VER("Failed to check ringct signatures!");
return false;

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@ -896,7 +896,7 @@ namespace cryptonote
return false;
case rct::RCTTypeSimple:
case rct::RCTTypeSimpleBulletproof:
if (!rct::verRctSimple(rv, true))
if (!rct::verRctSemanticsSimple(rv))
{
MERROR_VER("rct signature semantics check failed");
return false;

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@ -889,36 +889,54 @@ Bulletproof bulletproof_PROVE(const std::vector<uint64_t> &v, const rct::keyV &g
}
/* Given a range proof, determine if it is valid */
bool bulletproof_VERIFY(const Bulletproof &proof)
bool bulletproof_VERIFY(const std::vector<const Bulletproof*> &proofs)
{
init_exponents();
PERF_TIMER_START_BP(VERIFY);
// sanity and figure out which proof is longest
size_t max_length = 0;
for (const Bulletproof *p: proofs)
{
const Bulletproof &proof = *p;
CHECK_AND_ASSERT_MES(proof.V.size() >= 1, false, "V does not have at least one element");
CHECK_AND_ASSERT_MES(proof.L.size() == proof.R.size(), false, "Mismatched L and R sizes");
CHECK_AND_ASSERT_MES(proof.L.size() > 0, false, "Empty proof");
max_length = std::max(max_length, proof.L.size());
}
CHECK_AND_ASSERT_MES(max_length < 32, false, "At least one proof is too large");
size_t maxMN = 1u << max_length;
const size_t logN = 6;
const size_t N = 1 << logN;
rct::key tmp, tmp2;
rct::key tmp;
// setup weighted aggregates
rct::key Z0 = rct::identity();
rct::key z1 = rct::zero();
rct::key Z2 = rct::identity();
rct::key z3 = rct::zero();
rct::keyV z4(maxMN, rct::zero()), z5(maxMN, rct::zero());
for (const Bulletproof *p: proofs)
{
const Bulletproof &proof = *p;
size_t M, logM;
for (logM = 0; (M = 1<<logM) <= maxM && M < proof.V.size(); ++logM);
CHECK_AND_ASSERT_MES(proof.L.size() == 6+logM, false, "Proof is not the expected size");
const size_t MN = M*N;
rct::key weight = rct::skGen();
// Reconstruct the challenges
PERF_TIMER_START_BP(VERIFY);
PERF_TIMER_START_BP(VERIFY_start);
rct::key hash_cache = rct::hash_to_scalar(proof.V);
rct::key y = hash_cache_mash(hash_cache, proof.A, proof.S);
rct::key z = hash_cache = rct::hash_to_scalar(y);
rct::key x = hash_cache_mash(hash_cache, z, proof.T1, proof.T2);
PERF_TIMER_STOP(VERIFY_start);
PERF_TIMER_START_BP(VERIFY_line_60);
// Reconstruct the challenges
rct::key x_ip = hash_cache_mash(hash_cache, x, proof.taux, proof.mu, proof.t);
PERF_TIMER_STOP(VERIFY_line_60);
PERF_TIMER_STOP(VERIFY_start);
PERF_TIMER_START_BP(VERIFY_line_61);
// PAPER LINE 61
@ -998,7 +1016,7 @@ bool bulletproof_VERIFY(const Bulletproof &proof)
PERF_TIMER_START_BP(VERIFY_line_62);
// PAPER LINE 62
rct::key P = rct::addKeys(proof.A, rct::scalarmultKey(proof.S, x));
rct::addKeys(Z0, Z0, rct::scalarmultKey(rct::addKeys(proof.A, rct::scalarmultKey(proof.S, x)), weight));
PERF_TIMER_STOP(VERIFY_line_62);
// Compute the number of rounds for the inner product
@ -1028,9 +1046,6 @@ bool bulletproof_VERIFY(const Bulletproof &proof)
winv[i] = invert(w[i]);
PERF_TIMER_STOP(VERIFY_line_24_25_invert);
std::vector<MultiexpData> multiexp_data;
multiexp_data.clear();
multiexp_data.reserve(MN*2);
for (size_t i = 0; i < MN; ++i)
{
// Convert the index to binary IN REVERSE and construct the scalar exponent
@ -1062,8 +1077,8 @@ bool bulletproof_VERIFY(const Bulletproof &proof)
sc_muladd(tmp.bytes, z.bytes, ypow.bytes, tmp.bytes);
sc_mulsub(h_scalar.bytes, tmp.bytes, yinvpow.bytes, h_scalar.bytes);
multiexp_data.emplace_back(g_scalar, Gi_p3[i]);
multiexp_data.emplace_back(h_scalar, Hi_p3[i]);
sc_muladd(z4[i].bytes, g_scalar.bytes, weight.bytes, z4[i].bytes);
sc_muladd(z5[i].bytes, h_scalar.bytes, weight.bytes, z5[i].bytes);
if (i != MN-1)
{
@ -1072,36 +1087,50 @@ bool bulletproof_VERIFY(const Bulletproof &proof)
}
}
rct::key inner_prod = multiexp(multiexp_data, true);
PERF_TIMER_STOP(VERIFY_line_24_25);
// PAPER LINE 26
rct::key pprime;
PERF_TIMER_START_BP(VERIFY_line_26_new);
multiexp_data.clear();
multiexp_data.reserve(1+2*rounds);
std::vector<MultiexpData> multiexp_data;
multiexp_data.reserve(2*rounds);
sc_sub(tmp.bytes, rct::zero().bytes, proof.mu.bytes);
rct::addKeys(pprime, P, rct::scalarmultBase(tmp));
sc_muladd(z1.bytes, proof.mu.bytes, weight.bytes, z1.bytes);
for (size_t i = 0; i < rounds; ++i)
{
sc_mul(tmp.bytes, w[i].bytes, w[i].bytes);
sc_mul(tmp2.bytes, winv[i].bytes, winv[i].bytes);
multiexp_data.emplace_back(tmp, proof.L[i]);
multiexp_data.emplace_back(tmp2, proof.R[i]);
sc_mul(tmp.bytes, winv[i].bytes, winv[i].bytes);
multiexp_data.emplace_back(tmp, proof.R[i]);
}
sc_mul(tmp.bytes, proof.t.bytes, x_ip.bytes);
multiexp_data.emplace_back(tmp, rct::H);
addKeys(pprime, pprime, multiexp(multiexp_data, false));
PERF_TIMER_STOP(VERIFY_line_26_new);
PERF_TIMER_START_BP(VERIFY_step2_check);
sc_mul(tmp.bytes, proof.a.bytes, proof.b.bytes);
rct::key acc = multiexp(multiexp_data, false);
rct::addKeys(Z2, Z2, rct::scalarmultKey(acc, weight));
sc_mulsub(tmp.bytes, proof.a.bytes, proof.b.bytes, proof.t.bytes);
sc_mul(tmp.bytes, tmp.bytes, x_ip.bytes);
tmp = rct::scalarmultKey(rct::H, tmp);
rct::addKeys(tmp, tmp, inner_prod);
sc_muladd(z3.bytes, tmp.bytes, weight.bytes, z3.bytes);
PERF_TIMER_STOP(VERIFY_line_26_new);
}
// now check all proofs at once
PERF_TIMER_START_BP(VERIFY_step2_check);
rct::key Y = Z0;
sc_sub(tmp.bytes, rct::zero().bytes, z1.bytes);
rct::addKeys(Y, Y, rct::scalarmultBase(tmp));
rct::addKeys(Y, Y, Z2);
rct::addKeys(Y, Y, rct::scalarmultKey(rct::H, z3));
std::vector<MultiexpData> multiexp_data;
multiexp_data.reserve(2 * maxMN);
for (size_t i = 0; i < maxMN; ++i)
{
sc_sub(tmp.bytes, rct::zero().bytes, z4[i].bytes);
multiexp_data.emplace_back(tmp, Gi_p3[i]);
sc_sub(tmp.bytes, rct::zero().bytes, z5[i].bytes);
multiexp_data.emplace_back(tmp, Hi_p3[i]);
}
rct::addKeys(Y, Y, multiexp(multiexp_data, true));
PERF_TIMER_STOP(VERIFY_step2_check);
if (!(pprime == tmp))
if (!(Y == rct::identity()))
{
MERROR("Verification failure at step 2");
return false;
@ -1111,4 +1140,19 @@ bool bulletproof_VERIFY(const Bulletproof &proof)
return true;
}
bool bulletproof_VERIFY(const std::vector<Bulletproof> &proofs)
{
std::vector<const Bulletproof*> proof_pointers;
for (const Bulletproof &proof: proofs)
proof_pointers.push_back(&proof);
return bulletproof_VERIFY(proof_pointers);
}
bool bulletproof_VERIFY(const Bulletproof &proof)
{
std::vector<const Bulletproof*> proofs;
proofs.push_back(&proof);
return bulletproof_VERIFY(proofs);
}
}

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@ -43,6 +43,8 @@ Bulletproof bulletproof_PROVE(uint64_t v, const rct::key &gamma);
Bulletproof bulletproof_PROVE(const rct::keyV &v, const rct::keyV &gamma);
Bulletproof bulletproof_PROVE(const std::vector<uint64_t> &v, const rct::keyV &gamma);
bool bulletproof_VERIFY(const Bulletproof &proof);
bool bulletproof_VERIFY(const std::vector<const Bulletproof*> &proofs);
bool bulletproof_VERIFY(const std::vector<Bulletproof> &proofs);
}

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@ -70,6 +70,13 @@ namespace rct {
catch (...) { return false; }
}
bool verBulletproof(const std::vector<const Bulletproof*> &proofs)
{
try { return bulletproof_VERIFY(proofs); }
// we can get deep throws from ge_frombytes_vartime if input isn't valid
catch (...) { return false; }
}
//Borromean (c.f. gmax/andytoshi's paper)
boroSig genBorromean(const key64 x, const key64 P1, const key64 P2, const bits indices) {
key64 L[2], alpha;
@ -918,15 +925,23 @@ namespace rct {
//ver RingCT simple
//assumes only post-rct style inputs (at least for max anonymity)
bool verRctSimple(const rctSig & rv, bool semantics) {
bool verRctSemanticsSimple(const std::vector<const rctSig*> & rvv) {
try
{
PERF_TIMER(verRctSimple);
PERF_TIMER(verRctSemanticsSimple);
CHECK_AND_ASSERT_MES(rv.type == RCTTypeSimple || rv.type == RCTTypeSimpleBulletproof, false, "verRctSimple called on non simple rctSig");
const bool bulletproof = is_rct_bulletproof(rv.type);
if (semantics)
tools::threadpool& tpool = tools::threadpool::getInstance();
tools::threadpool::waiter waiter;
std::deque<bool> results;
std::vector<const Bulletproof*> proofs;
size_t max_non_bp_proofs = 0, offset = 0;
for (const rctSig *rvp: rvv)
{
CHECK_AND_ASSERT_MES(rvp, false, "rctSig pointer is NULL");
const rctSig &rv = *rvp;
CHECK_AND_ASSERT_MES(rv.type == RCTTypeSimple || rv.type == RCTTypeSimpleBulletproof, false, "verRctSemanticsSimple called on non simple rctSig");
const bool bulletproof = is_rct_bulletproof(rv.type);
if (bulletproof)
{
CHECK_AND_ASSERT_MES(rv.outPk.size() == n_bulletproof_amounts(rv.p.bulletproofs), false, "Mismatched sizes of outPk and bulletproofs");
@ -940,25 +955,19 @@ namespace rct {
CHECK_AND_ASSERT_MES(rv.p.pseudoOuts.empty(), false, "rv.p.pseudoOuts is not empty");
}
CHECK_AND_ASSERT_MES(rv.outPk.size() == rv.ecdhInfo.size(), false, "Mismatched sizes of outPk and rv.ecdhInfo");
if (!bulletproof)
max_non_bp_proofs += rv.p.rangeSigs.size();
}
else
results.resize(max_non_bp_proofs);
for (const rctSig *rvp: rvv)
{
// semantics check is early, and mixRing/MGs aren't resolved yet
if (bulletproof)
CHECK_AND_ASSERT_MES(rv.p.pseudoOuts.size() == rv.mixRing.size(), false, "Mismatched sizes of rv.p.pseudoOuts and mixRing");
else
CHECK_AND_ASSERT_MES(rv.pseudoOuts.size() == rv.mixRing.size(), false, "Mismatched sizes of rv.pseudoOuts and mixRing");
}
const size_t threads = std::max(rv.outPk.size(), rv.mixRing.size());
std::deque<bool> results(threads);
tools::threadpool& tpool = tools::threadpool::getInstance();
tools::threadpool::waiter waiter;
const rctSig &rv = *rvp;
const bool bulletproof = is_rct_bulletproof(rv.type);
const keyV &pseudoOuts = bulletproof ? rv.p.pseudoOuts : rv.pseudoOuts;
if (semantics) {
key sumOutpks = identity();
for (size_t i = 0; i < rv.outPk.size(); i++) {
addKeys(sumOutpks, sumOutpks, rv.outPk[i].mask);
@ -979,24 +988,75 @@ namespace rct {
return false;
}
results.clear();
results.resize(bulletproof ? rv.p.bulletproofs.size() : rv.outPk.size());
if (bulletproof)
{
for (size_t i = 0; i < rv.p.bulletproofs.size(); i++)
tpool.submit(&waiter, [&, i] { results[i] = verBulletproof(rv.p.bulletproofs[i]); });
proofs.push_back(&rv.p.bulletproofs[i]);
}
else
{
for (size_t i = 0; i < rv.p.rangeSigs.size(); i++)
tpool.submit(&waiter, [&, i] { results[i] = verRange(rv.outPk[i].mask, rv.p.rangeSigs[i]); });
waiter.wait(&tpool);
tpool.submit(&waiter, [&, i, offset] { results[i+offset] = verRange(rv.outPk[i].mask, rv.p.rangeSigs[i]); });
offset += rv.p.rangeSigs.size();
}
}
if (!proofs.empty() && !verBulletproof(proofs))
{
LOG_PRINT_L1("Aggregate range proof verified failed");
return false;
}
waiter.wait(&tpool);
for (size_t i = 0; i < results.size(); ++i) {
if (!results[i]) {
LOG_PRINT_L1("Range proof verified failed for proof " << i);
return false;
}
}
return true;
}
else {
// we can get deep throws from ge_frombytes_vartime if input isn't valid
catch (const std::exception &e)
{
LOG_PRINT_L1("Error in verRctSemanticsSimple: " << e.what());
return false;
}
catch (...)
{
LOG_PRINT_L1("Error in verRctSemanticsSimple, but not an actual exception");
return false;
}
}
bool verRctSemanticsSimple(const rctSig & rv)
{
return verRctSemanticsSimple(std::vector<const rctSig*>(1, &rv));
}
//ver RingCT simple
//assumes only post-rct style inputs (at least for max anonymity)
bool verRctNonSemanticsSimple(const rctSig & rv) {
try
{
PERF_TIMER(verRctNonSemanticsSimple);
CHECK_AND_ASSERT_MES(rv.type == RCTTypeSimple || rv.type == RCTTypeSimpleBulletproof, false, "verRctNonSemanticsSimple called on non simple rctSig");
const bool bulletproof = is_rct_bulletproof(rv.type);
// semantics check is early, and mixRing/MGs aren't resolved yet
if (bulletproof)
CHECK_AND_ASSERT_MES(rv.p.pseudoOuts.size() == rv.mixRing.size(), false, "Mismatched sizes of rv.p.pseudoOuts and mixRing");
else
CHECK_AND_ASSERT_MES(rv.pseudoOuts.size() == rv.mixRing.size(), false, "Mismatched sizes of rv.pseudoOuts and mixRing");
const size_t threads = std::max(rv.outPk.size(), rv.mixRing.size());
std::deque<bool> results(threads);
tools::threadpool& tpool = tools::threadpool::getInstance();
tools::threadpool::waiter waiter;
const keyV &pseudoOuts = bulletproof ? rv.p.pseudoOuts : rv.pseudoOuts;
const key message = get_pre_mlsag_hash(rv, hw::get_device("default"));
results.clear();
@ -1004,7 +1064,7 @@ namespace rct {
for (size_t i = 0 ; i < rv.mixRing.size() ; i++) {
tpool.submit(&waiter, [&, i] {
results[i] = verRctMGSimple(message, rv.p.MGs[i], rv.mixRing[i], pseudoOuts[i]);
}, true);
});
}
waiter.wait(&tpool);
@ -1014,19 +1074,18 @@ namespace rct {
return false;
}
}
}
return true;
}
// we can get deep throws from ge_frombytes_vartime if input isn't valid
catch (const std::exception &e)
{
LOG_PRINT_L1("Error in verRct: " << e.what());
LOG_PRINT_L1("Error in verRctNonSemanticsSimple: " << e.what());
return false;
}
catch (...)
{
LOG_PRINT_L1("Error in verRct, but not an actual exception");
LOG_PRINT_L1("Error in verRctNonSemanticsSimple, but not an actual exception");
return false;
}
}

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@ -125,8 +125,10 @@ namespace rct {
rctSig genRctSimple(const key & message, const ctkeyV & inSk, const keyV & destinations, const std::vector<xmr_amount> & inamounts, const std::vector<xmr_amount> & outamounts, xmr_amount txnFee, const ctkeyM & mixRing, const keyV &amount_keys, const std::vector<multisig_kLRki> *kLRki, multisig_out *msout, const std::vector<unsigned int> & index, ctkeyV &outSk, RangeProofType range_proof_type, hw::device &hwdev);
bool verRct(const rctSig & rv, bool semantics);
static inline bool verRct(const rctSig & rv) { return verRct(rv, true) && verRct(rv, false); }
bool verRctSimple(const rctSig & rv, bool semantics);
static inline bool verRctSimple(const rctSig & rv) { return verRctSimple(rv, true) && verRctSimple(rv, false); }
bool verRctSemanticsSimple(const rctSig & rv);
bool verRctSemanticsSimple(const std::vector<const rctSig*> & rv);
bool verRctNonSemanticsSimple(const rctSig & rv);
static inline bool verRctSimple(const rctSig & rv) { return verRctSemanticsSimple(rv) && verRctNonSemanticsSimple(rv); }
xmr_amount decodeRct(const rctSig & rv, const key & sk, unsigned int i, key & mask, hw::device &hwdev);
xmr_amount decodeRct(const rctSig & rv, const key & sk, unsigned int i, hw::device &hwdev);
xmr_amount decodeRctSimple(const rctSig & rv, const key & sk, unsigned int i, key & mask, hw::device &hwdev);

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@ -60,3 +60,41 @@ public:
private:
rct::Bulletproof proof;
};
template<bool batch, size_t start, size_t repeat, size_t mul, size_t add, size_t N>
class test_aggregated_bulletproof
{
public:
static const size_t loop_count = 500 / (N * repeat);
bool init()
{
size_t o = start;
for (size_t n = 0; n < N; ++n)
{
//printf("adding %zu times %zu\n", repeat, o);
for (size_t i = 0; i < repeat; ++i)
proofs.push_back(rct::bulletproof_PROVE(std::vector<uint64_t>(o, 749327532984), rct::skvGen(o)));
o = o * mul + add;
}
return true;
}
bool test()
{
if (batch)
{
return rct::bulletproof_VERIFY(proofs);
}
else
{
for (const rct::Bulletproof &proof: proofs)
if (!rct::bulletproof_VERIFY(proof))
return false;
return true;
}
}
private:
std::vector<rct::Bulletproof> proofs;
};

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@ -183,6 +183,17 @@ int main(int argc, char** argv)
TEST_PERFORMANCE2(filter, verbose, test_bulletproof, true, 15);
TEST_PERFORMANCE2(filter, verbose, test_bulletproof, false, 15);
TEST_PERFORMANCE6(filter, verbose, test_aggregated_bulletproof, false, 2, 1, 1, 0, 4);
TEST_PERFORMANCE6(filter, verbose, test_aggregated_bulletproof, true, 2, 1, 1, 0, 4);
TEST_PERFORMANCE6(filter, verbose, test_aggregated_bulletproof, false, 8, 1, 1, 0, 4);
TEST_PERFORMANCE6(filter, verbose, test_aggregated_bulletproof, true, 8, 1, 1, 0, 4);
TEST_PERFORMANCE6(filter, verbose, test_aggregated_bulletproof, false, 1, 1, 2, 0, 4);
TEST_PERFORMANCE6(filter, verbose, test_aggregated_bulletproof, true, 1, 1, 2, 0, 4);
TEST_PERFORMANCE6(filter, verbose, test_aggregated_bulletproof, false, 1, 8, 1, 1, 4);
TEST_PERFORMANCE6(filter, verbose, test_aggregated_bulletproof, true, 1, 8, 1, 1, 4);
TEST_PERFORMANCE6(filter, verbose, test_aggregated_bulletproof, false, 2, 1, 1, 0, 64);
TEST_PERFORMANCE6(filter, verbose, test_aggregated_bulletproof, true, 2, 1, 1, 0, 64);
TEST_PERFORMANCE3(filter, verbose, test_ringct_mlsag, 1, 3, false);
TEST_PERFORMANCE3(filter, verbose, test_ringct_mlsag, 1, 5, false);
TEST_PERFORMANCE3(filter, verbose, test_ringct_mlsag, 1, 10, false);

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@ -169,3 +169,5 @@ void run_test(const std::string &filter, bool verbose, const char* test_name)
#define TEST_PERFORMANCE2(filter, verbose, test_class, a0, a1) run_test< test_class<a0, a1> >(filter, verbose, QUOTEME(test_class) "<" QUOTEME(a0) ", " QUOTEME(a1) ">")
#define TEST_PERFORMANCE3(filter, verbose, test_class, a0, a1, a2) run_test< test_class<a0, a1, a2> >(filter, verbose, QUOTEME(test_class) "<" QUOTEME(a0) ", " QUOTEME(a1) ", " QUOTEME(a2) ">")
#define TEST_PERFORMANCE4(filter, verbose, test_class, a0, a1, a2, a3) run_test< test_class<a0, a1, a2, a3> >(filter, verbose, QUOTEME(test_class) "<" QUOTEME(a0) ", " QUOTEME(a1) ", " QUOTEME(a2) ", " QUOTEME(a3) ">")
#define TEST_PERFORMANCE5(filter, verbose, test_class, a0, a1, a2, a3, a4) run_test< test_class<a0, a1, a2, a3, a4> >(filter, verbose, QUOTEME(test_class) "<" QUOTEME(a0) ", " QUOTEME(a1) ", " QUOTEME(a2) ", " QUOTEME(a3) ", " QUOTEME(a4) ">")
#define TEST_PERFORMANCE6(filter, verbose, test_class, a0, a1, a2, a3, a4, a5) run_test< test_class<a0, a1, a2, a3, a4, a5> >(filter, verbose, QUOTEME(test_class) "<" QUOTEME(a0) ", " QUOTEME(a1) ", " QUOTEME(a2) ", " QUOTEME(a3) ", " QUOTEME(a4) ", " QUOTEME(a5) ">")

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@ -135,6 +135,25 @@ TEST(bulletproofs, multi_splitting)
}
}
TEST(bulletproofs, valid_aggregated)
{
static const size_t N_PROOFS = 8;
std::vector<rct::Bulletproof> proofs(N_PROOFS);
for (size_t n = 0; n < N_PROOFS; ++n)
{
size_t outputs = 2 + n;
std::vector<uint64_t> amounts;
rct::keyV gamma;
for (size_t i = 0; i < outputs; ++i)
{
amounts.push_back(crypto::rand<uint64_t>());
gamma.push_back(rct::skGen());
}
proofs[n] = bulletproof_PROVE(amounts, gamma);
}
ASSERT_TRUE(rct::bulletproof_VERIFY(proofs));
}
TEST(bulletproofs, invalid_8)
{

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@ -1085,3 +1085,20 @@ TEST(ringct, zeroCommmit)
const rct::key manual = rct::addKeys(a, b);
ASSERT_EQ(z, manual);
}
TEST(ringct, aggregated)
{
static const size_t N_PROOFS = 16;
std::vector<rctSig> s(N_PROOFS);
std::vector<const rctSig*> sp(N_PROOFS);
for (size_t n = 0; n < N_PROOFS; ++n)
{
static const uint64_t inputs[] = {1000, 1000};
static const uint64_t outputs[] = {500, 1500};
s[n] = make_sample_simple_rct_sig(NELTS(inputs), inputs, NELTS(outputs), outputs, 0);
sp[n] = &s[n];
}
ASSERT_TRUE(verRctSemanticsSimple(sp));
}