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Improved batch verification for legacy one-of-many proofs #1038

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merged 4 commits into from
Mar 2, 2022
Merged

Improved batch verification for legacy one-of-many proofs #1038

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e277de3
Sigma verifier batching
AaronFeickert Jun 3, 2021
8a45b42
Namespace fixes
AaronFeickert Jul 8, 2021
38b9601
Simplify types
AaronFeickert Jul 15, 2021
c1e4c8e
Remove unnecessary function declaration
AaronFeickert Sep 20, 2021
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4 changes: 2 additions & 2 deletions src/sigma/sigma_primitives.h
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Original file line number Diff line number Diff line change
Expand Up @@ -35,9 +35,9 @@ class SigmaPrimitives {

static GroupElement commit(const GroupElement& g, const Exponent m, const GroupElement h, const Exponent r);

static void convert_to_sigma(uint64_t num, uint64_t n, uint64_t m, std::vector<Exponent>& out);
static void convert_to_sigma(std::size_t num, std::size_t n, std::size_t m, std::vector<Exponent>& out);

static std::vector<uint64_t> convert_to_nal(uint64_t num, uint64_t n, uint64_t m);
static std::vector<std::size_t> convert_to_nal(std::size_t num, std::size_t n, std::size_t m);

static void generate_challenge(const std::vector<GroupElement>& group_elements,
Exponent& result_out);
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29 changes: 13 additions & 16 deletions src/sigma/sigma_primitives.hpp
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Expand Up @@ -23,18 +23,18 @@ GroupElement SigmaPrimitives<Exponent, GroupElement>::commit(

template<class Exponent, class GroupElement>
void SigmaPrimitives<Exponent, GroupElement>::convert_to_sigma(
uint64_t num,
uint64_t n,
uint64_t m,
std::size_t num,
std::size_t n,
std::size_t m,
std::vector<Exponent>& out) {
uint64_t rem;
uint64_t j = 0;
std::size_t rem;
std::size_t j = 0;

for (j = 0; j < m; ++j)
{
rem = num % n;
num /= n;
for (uint64_t i = 0; i < n; ++i) {
for (std::size_t i = 0; i < n; ++i) {
if(i == rem)
out.push_back(Exponent(uint64_t(1)));
else
Expand All @@ -44,19 +44,16 @@ void SigmaPrimitives<Exponent, GroupElement>::convert_to_sigma(
}

template<class Exponent, class GroupElement>
std::vector<uint64_t> SigmaPrimitives<Exponent, GroupElement>::convert_to_nal(
uint64_t num,
uint64_t n,
uint64_t m) {
std::vector<uint64_t> result;
uint64_t rem;
uint64_t j = 0;
std::vector<std::size_t> SigmaPrimitives<Exponent, GroupElement>::convert_to_nal(
std::size_t num,
std::size_t n,
std::size_t m) {
std::vector<std::size_t> result;
result.reserve(m);
while (num != 0)
{
rem = num % n;
result.emplace_back(num % n);
num /= n;
result.push_back(rem);
j++;
}
result.resize(m);
return result;
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6 changes: 3 additions & 3 deletions src/sigma/sigmaplus_prover.h
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Expand Up @@ -13,7 +13,7 @@ class SigmaPlusProver{

public:
SigmaPlusProver(const GroupElement& g,
const std::vector<GroupElement>& h_gens, int n, int m);
const std::vector<GroupElement>& h_gens, std::size_t n, std::size_t m);
void proof(const std::vector<GroupElement>& commits,
std::size_t l,
const Exponent& r,
Expand All @@ -23,8 +23,8 @@ class SigmaPlusProver{
private:
GroupElement g_;
std::vector<GroupElement> h_;
int n_;
int m_;
std::size_t n_;
std::size_t m_;
};

} // namespace sigma
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30 changes: 15 additions & 15 deletions src/sigma/sigmaplus_prover.hpp
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Expand Up @@ -5,8 +5,8 @@ template<class Exponent, class GroupElement>
SigmaPlusProver<Exponent, GroupElement>::SigmaPlusProver(
const GroupElement& g,
const std::vector<GroupElement>& h_gens,
int n,
int m)
std::size_t n,
std::size_t m)
: g_(g)
, h_(h_gens)
, n_(n)
Expand All @@ -33,7 +33,7 @@ void SigmaPlusProver<Exponent, GroupElement>::proof(
// Values of Ro_k from Figure 5.
std::vector<Exponent> Pk;
Pk.resize(m_);
for (int k = 0; k < m_; ++k) {
for (std::size_t k = 0; k < m_; ++k) {
Pk[k].randomize();
}
R1ProofGenerator<secp_primitives::Scalar, secp_primitives::GroupElement> r1prover(g_, h_, sigma, rB, n_, m_);
Expand All @@ -49,10 +49,10 @@ void SigmaPlusProver<Exponent, GroupElement>::proof(
// last polynomial is special case if fPadding is true
for (std::size_t i = 0; i < (fPadding ? N-1 : N); ++i) {
std::vector<Exponent>& coefficients = P_i_k[i];
std::vector<uint64_t> I = SigmaPrimitives<Exponent, GroupElement>::convert_to_nal(i, n_, m_);
std::vector<std::size_t> I = SigmaPrimitives<Exponent, GroupElement>::convert_to_nal(i, n_, m_);
coefficients.push_back(a[I[0]]);
coefficients.push_back(sigma[I[0]]);
for (int j = 1; j < m_; ++j) {
for (std::size_t j = 1; j < m_; ++j) {
SigmaPrimitives<Exponent, GroupElement>::new_factor(sigma[j * n_ + I[j]], a[j * n_ + I[j]], coefficients);
}
}
Expand All @@ -76,23 +76,23 @@ void SigmaPlusProver<Exponent, GroupElement>::proof(
* \right]
*/

std::vector<uint64_t> I = SigmaPrimitives<Exponent, GroupElement>::convert_to_nal(N-1, n_, m_);
std::vector<uint64_t> lj = SigmaPrimitives<Exponent, GroupElement>::convert_to_nal(l, n_, m_);
std::vector<std::size_t> I = SigmaPrimitives<Exponent, GroupElement>::convert_to_nal(N-1, n_, m_);
std::vector<std::size_t> lj = SigmaPrimitives<Exponent, GroupElement>::convert_to_nal(l, n_, m_);

std::vector<Exponent> p_i_sum;
p_i_sum.emplace_back(uint64_t(1));
std::vector<std::vector<Exponent>> partial_p_s;

// Pre-calculate product parts and calculate p_s(x) at the same time, put the latter into p_i_sum
for (int j = m_ - 1; j >= 0; j--) {
for (std::ptrdiff_t j = m_ - 1; j >= 0; j--) {
partial_p_s.push_back(p_i_sum);
SigmaPrimitives<Exponent, GroupElement>::new_factor(sigma[j * n_ + I[j]], a[j * n_ + I[j]], p_i_sum);
SigmaPrimitives<Exponent, GroupElement>::new_factor(sigma[j*n_ + I[j]], a[j*n_ + I[j]], p_i_sum);
}

for (int j = 0; j < m_; j++) {
for (std::size_t j = 0; j < m_; j++) {
// \sum_{i=s_j+1}^{n-1}(\delta_{l_j,i}x+a_{j,i})
Exponent a_sum(uint64_t(0));
for (int i = I[j] + 1; i < n_; i++)
for (std::size_t i = I[j] + 1; i < n_; i++)
a_sum += a[j * n_ + i];
Exponent x_sum(uint64_t(lj[j] >= I[j]+1 ? 1 : 0));

Expand All @@ -101,7 +101,7 @@ void SigmaPlusProver<Exponent, GroupElement>::proof(
SigmaPrimitives<Exponent, GroupElement>::new_factor(x_sum, a_sum, polynomial);

// Multiply by x^j and add to the result
for (int k = 0; k < m_ - j; k++)
for (std::size_t k = 0; k < m_ - j; k++)
p_i_sum[j + k] += polynomial[k];
}

Expand All @@ -111,10 +111,10 @@ void SigmaPlusProver<Exponent, GroupElement>::proof(
//computing G_k`s;
std::vector <GroupElement> Gk;
Gk.reserve(m_);
for (int k = 0; k < m_; ++k) {
for (std::size_t k = 0; k < m_; ++k) {
std::vector <Exponent> P_i;
P_i.reserve(N);
for (size_t i = 0; i < N; ++i) {
for (std::size_t i = 0; i < N; ++i) {
P_i.emplace_back(P_i_k[i][k]);
}
secp_primitives::MultiExponent mult(commits, P_i);
Expand All @@ -138,7 +138,7 @@ void SigmaPlusProver<Exponent, GroupElement>::proof(
z = r * x.exponent(uint64_t(m_));
Exponent sum;
Exponent x_k(uint64_t(1));
for (int k = 0; k < m_; ++k) {
for (std::size_t k = 0; k < m_; ++k) {
sum += (Pk[k] * x_k);
x_k *= x;
}
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12 changes: 8 additions & 4 deletions src/sigma/sigmaplus_verifier.h
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Expand Up @@ -11,12 +11,17 @@ class SigmaPlusVerifier{
public:
SigmaPlusVerifier(const GroupElement& g,
const std::vector<GroupElement>& h_gens,
int n, int m_);
std::size_t n, std::size_t m_);

bool verify(const std::vector<GroupElement>& commits,
const SigmaPlusProof<Exponent, GroupElement>& proof,
bool fPadding) const;

bool verify(const std::vector<GroupElement>& commits,
const SigmaPlusProof<Exponent, GroupElement>& proof,
bool fPadding,
std::size_t setSize) const;

bool batch_verify(const std::vector<GroupElement>& commits,
const std::vector<Exponent>& serials,
const std::vector<bool>& fPadding,
Expand All @@ -25,7 +30,6 @@ class SigmaPlusVerifier{

bool membership_checks(const SigmaPlusProof<Exponent, GroupElement>& proof) const;
bool compute_fs(const SigmaPlusProof<Exponent, GroupElement>& proof, const Exponent& x, std::vector<Exponent>& f_) const;
bool abcd_checks(const SigmaPlusProof<Exponent, GroupElement>& proof, const Exponent& x, const std::vector<Exponent>& f_) const;

void compute_fis(int j, const std::vector<Exponent>& f, std::vector<Exponent>& f_i_) const;
void compute_fis(const Exponent& f_i, int j, const std::vector<Exponent>& f, typename std::vector<Exponent>::iterator& ptr, typename std::vector<Exponent>::iterator end_ptr) const;
Expand All @@ -43,8 +47,8 @@ class SigmaPlusVerifier{
private:
GroupElement g_;
std::vector<GroupElement> h_;
int n;
int m;
std::size_t n;
std::size_t m;
};

} // namespace sigma
Expand Down
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