BigUInt poly_infty_norm_coeffmod(const BigPoly &poly, const BigUInt &modulus, const MemoryPoolHandle &pool)
{
if (modulus.is_zero())
{
throw invalid_argument("modulus cannot be zero");
}
if (!pool)
{
throw invalid_argument("pool is uninitialized");
}
if (poly.is_zero())
{
return BigUInt();
}
int poly_coeff_count = poly.coeff_count();
int poly_coeff_bit_count = poly.coeff_bit_count();
int poly_coeff_uint64_count = divide_round_up(poly_coeff_bit_count, bits_per_uint64);
Modulus mod(modulus.data(), modulus.uint64_count(), pool);
BigUInt result(modulus.significant_bit_count());
util::poly_infty_norm_coeffmod(poly.data(), poly_coeff_count, poly_coeff_uint64_count, mod, result.data(), pool);
return result;
}
void Evaluator::negate(const BigPoly &encrypted, BigPoly &destination)
{
// Extract encryption parameters.
int coeff_count = poly_modulus_.coeff_count();
int coeff_bit_count = poly_modulus_.coeff_bit_count();
int coeff_uint64_count = divide_round_up(coeff_bit_count, bits_per_uint64);
// Verify parameters.
if (encrypted.coeff_count() != coeff_count || encrypted.coeff_bit_count() != coeff_bit_count)
{
throw invalid_argument("encrypted is not valid for encryption parameters");
}
#ifdef _DEBUG
if (encrypted.significant_coeff_count() == coeff_count || !are_poly_coefficients_less_than(encrypted, coeff_modulus_))
{
throw invalid_argument("encrypted is not valid for encryption parameters");
}
#endif
if (destination.coeff_count() != coeff_count || destination.coeff_bit_count() != coeff_bit_count)
{
destination.resize(coeff_count, coeff_bit_count);
}
// Handle test-mode case.
if (mode_ == TEST_MODE)
{
negate_poly_coeffmod(encrypted.pointer(), coeff_count, plain_modulus_.pointer(), coeff_uint64_count, destination.pointer());
return;
}
// Negate polynomial.
negate_poly_coeffmod(encrypted.pointer(), coeff_count, coeff_modulus_.pointer(), coeff_uint64_count, destination.pointer());
}
BigUInt poly_infty_norm(const BigPoly &poly)
{
if (poly.is_zero())
{
return BigUInt();
}
int coeff_count = poly.coeff_count();
int coeff_bit_count = poly.coeff_bit_count();
int coeff_uint64_count = divide_round_up(coeff_bit_count, bits_per_uint64);
BigUInt result(coeff_bit_count);
util::poly_infty_norm(poly.data(), coeff_count, coeff_uint64_count, result.data());
return result;
}
BigPoly exponentiate_poly_polymod_coeffmod(const BigPoly &operand, const BigUInt &exponent,
const BigPoly &poly_modulus, const BigUInt &coeff_modulus, const MemoryPoolHandle &pool)
{
BigPoly result(poly_modulus.coeff_count(), coeff_modulus.significant_bit_count());
exponentiate_poly_polymod_coeffmod(operand, exponent, poly_modulus, coeff_modulus, result, pool);
return result;
}
void Evaluator::add_many(const std::vector<BigPoly> &encrypteds, BigPoly &destination)
{
if (encrypteds.empty())
{
throw invalid_argument("encrypteds cannot be empty");
}
if (destination.coeff_count() != encrypteds[0].coeff_count() || destination.coeff_bit_count() != encrypteds[0].coeff_bit_count())
{
destination.resize(encrypteds[0].coeff_count(), encrypteds[0].coeff_bit_count());
}
destination = encrypteds[0];
for (vector<BigPoly>::size_type i = 1; i < encrypteds.size(); ++i)
{
add(destination, encrypteds[i], destination);
}
}
void Evaluator::exponentiate_norelin(const BigPoly &encrypted, int exponent, BigPoly &destination)
{
// Extract encryption parameters.
int coeff_count = poly_modulus_.coeff_count();
int coeff_bit_count = poly_modulus_.coeff_bit_count();
int coeff_uint64_count = divide_round_up(coeff_bit_count, bits_per_uint64);
// Verify parameters.
if (encrypted.coeff_count() != coeff_count || encrypted.coeff_bit_count() != coeff_bit_count)
{
throw invalid_argument("encrypted is not valid for encryption parameters");
}
#ifdef _DEBUG
if (encrypted.significant_coeff_count() == coeff_count || !are_poly_coefficients_less_than(encrypted, coeff_modulus_))
{
throw invalid_argument("encrypted is not valid for encryption parameters");
}
#endif
if (exponent < 0)
{
throw invalid_argument("exponent must be non-negative");
}
if (exponent == 0)
{
if (destination.coeff_count() != coeff_count || destination.coeff_bit_count() != coeff_bit_count)
{
destination.resize(coeff_count, coeff_bit_count);
}
set_uint_uint(coeff_div_plain_modulus_.pointer(), coeff_uint64_count, destination.pointer());
return;
}
if (exponent == 1)
{
encrypted.duplicate_to(destination);
return;
}
vector<BigPoly> exp_vector(exponent, encrypted);
multiply_norelin_many(exp_vector, destination);
// Binary exponentiation
/*
if (exponent % 2 == 0)
{
exponentiate_norelin(multiply_norelin(encrypted, encrypted), exponent >> 1, destination);
return;
}
multiply_norelin(exponentiate_norelin(multiply_norelin(encrypted, encrypted), (exponent - 1) >> 1), encrypted, destination);
*/
}
void Evaluator::relinearize(const BigPoly &encrypted, BigPoly &destination)
{
// Extract encryption parameters.
int coeff_count = poly_modulus_.coeff_count();
int coeff_bit_count = poly_modulus_.coeff_bit_count();
int coeff_uint64_count = divide_round_up(coeff_bit_count, bits_per_uint64);
// Verify parameters.
if (encrypted.coeff_count() != coeff_count || encrypted.coeff_bit_count() != coeff_bit_count)
{
throw invalid_argument("encrypted is not valid for encryption parameters");
}
#ifdef _DEBUG
if (encrypted.significant_coeff_count() == coeff_count || !are_poly_coefficients_less_than(encrypted, coeff_modulus_))
{
throw invalid_argument("encrypted is not valid for encryption parameters");
}
#endif
if (destination.coeff_count() != coeff_count || destination.coeff_bit_count() != coeff_bit_count)
{
destination.resize(coeff_count, coeff_bit_count);
}
// Handle test-mode case.
if (mode_ == TEST_MODE)
{
set_poly_poly(encrypted.pointer(), coeff_count, coeff_uint64_count, destination.pointer());
return;
}
// Get pointer to inputs (duplicated if needed).
ConstPointer encryptedptr = duplicate_poly_if_needed(encrypted, encrypted.pointer() == destination.pointer(), pool_);
// Relinearize polynomial.
relinearize(encryptedptr.get(), destination.pointer());
}
void poly_eval_uint_mod(const BigPoly &poly_to_evaluate, const BigUInt &value, const BigUInt &modulus,
BigUInt &destination, const MemoryPoolHandle &pool)
{
if (poly_to_evaluate.significant_coeff_bit_count() > modulus.significant_bit_count())
{
throw invalid_argument("poly_to_evaluate is not reduced");
}
if (value.significant_bit_count() > modulus.significant_bit_count())
{
throw invalid_argument("value is not reduced");
}
if (!pool)
{
throw invalid_argument("pool is uninitialized");
}
int poly_to_eval_coeff_uint64_count = poly_to_evaluate.coeff_uint64_count();
int modulus_bit_count = modulus.significant_bit_count();
if (poly_to_evaluate.is_zero())
{
destination.set_zero();
}
if (value.is_zero())
{
destination.resize(modulus_bit_count);
modulo_uint(poly_to_evaluate.data(), poly_to_eval_coeff_uint64_count,
Modulus(modulus.data(), modulus.uint64_count(), pool),
destination.data(), pool);
return;
}
ConstPointer value_ptr = duplicate_uint_if_needed(value, modulus.uint64_count(), false, pool);
destination.resize(modulus_bit_count);
util::poly_eval_uint_mod(poly_to_evaluate.data(), poly_to_evaluate.coeff_count(), value_ptr.get(),
Modulus(modulus.data(), modulus.uint64_count(), pool), destination.data(), pool);
}
void KeyGenerator::generate(const BigPoly &secret_key, uint64_t power)
{
// Validate arguments.
if (secret_key.is_zero())
{
throw invalid_argument("secret_key cannot be zero");
}
if (power == 0)
{
throw invalid_argument("power cannot be zero");
}
// Handle test-mode case.
if (mode_ == TEST_MODE)
{
public_key_.set_zero();
public_key_[0] = 1;
secret_key_.set_zero();
secret_key_[0] = 1;
for (int i = 0; i < evaluation_keys_.count(); ++i)
{
evaluation_keys_[i].set_zero();
evaluation_keys_[i][0] = 1;
}
return;
}
// Extract encryption parameters.
int coeff_count = poly_modulus_.coeff_count();
int coeff_bit_count = poly_modulus_.coeff_bit_count();
int coeff_uint64_count = divide_round_up(coeff_bit_count, bits_per_uint64);
// Verify secret key looks valid.
secret_key_ = secret_key;
if (secret_key_.coeff_count() != coeff_count || secret_key_.coeff_bit_count() != coeff_bit_count)
{
throw invalid_argument("secret_key is not valid for encryption parameters");
}
#ifdef _DEBUG
if (secret_key_.significant_coeff_count() == coeff_count || !are_poly_coefficients_less_than(secret_key_, coeff_modulus_))
{
throw invalid_argument("secret_key is not valid for encryption parameters");
}
#endif
// Raise level of secret key.
if (power > 1)
{
exponentiate_poly_polymod_coeffmod(secret_key_.pointer(), &power, 1, polymod_, mod_, secret_key_.pointer(), pool_);
}
// Attempt to invert secret_key.
Pointer secret_key_inv(allocate_poly(coeff_count, coeff_uint64_count, pool_));
if (!try_invert_poly_coeffmod(secret_key_.pointer(), poly_modulus_.pointer(), coeff_count, mod_, secret_key_inv.get(), pool_))
{
// Secret_key is not invertible, so not valid.
throw invalid_argument("secret_key is not valid for encryption parameters");
}
// Calculate plaintext_modulus * noise * secret_key_inv.
Pointer noise(allocate_poly(coeff_count, coeff_uint64_count, pool_));
set_poly_coeffs_zero_one_negone(noise.get());
uint64_t *public_key = public_key_.pointer();
multiply_poly_poly_polymod_coeffmod(noise.get(), secret_key_inv.get(), polymod_, mod_, noise.get(), pool_);
multiply_poly_scalar_coeffmod(noise.get(), coeff_count, plain_modulus_.pointer(), mod_, public_key, pool_);
// Create evaluation keys.
Pointer evaluation_factor(allocate_uint(coeff_uint64_count, pool_));
set_uint(1, coeff_uint64_count, evaluation_factor.get());
for (int i = 0; i < evaluation_keys_.count(); ++i)
{
// Multiply secret_key by evaluation_factor (mod coeff modulus).
uint64_t *evaluation_key = evaluation_keys_[i].pointer();
multiply_poly_scalar_coeffmod(secret_key_.pointer(), coeff_count, evaluation_factor.get(), mod_, evaluation_key, pool_);
// Multiply public_key*normal noise and add into evaluation_key.
set_poly_coeffs_normal(noise.get());
multiply_poly_poly_polymod_coeffmod(noise.get(), public_key, polymod_, mod_, noise.get(), pool_);
add_poly_poly_coeffmod(noise.get(), evaluation_key, coeff_count, coeff_modulus_.pointer(), coeff_uint64_count, evaluation_key);
// Add-in more normal noise to evaluation_key.
set_poly_coeffs_normal(noise.get());
add_poly_poly_coeffmod(noise.get(), evaluation_key, coeff_count, coeff_modulus_.pointer(), coeff_uint64_count, evaluation_key);
// Left shift evaluation factor.
left_shift_uint(evaluation_factor.get(), decomposition_bit_count_, coeff_uint64_count, evaluation_factor.get());
}
}
void poly_eval_poly_polymod_coeffmod(const BigPoly &poly_to_evaluate, const BigPoly &poly_to_evaluate_at,
const BigPoly &poly_modulus, const BigUInt &coeff_modulus, BigPoly &destination, const MemoryPoolHandle &pool)
{
if (!pool)
{
throw invalid_argument("pool is uninitialized");
}
if (poly_to_evaluate.significant_coeff_count() > poly_modulus.coeff_count() ||
poly_to_evaluate.significant_coeff_bit_count() > coeff_modulus.significant_bit_count())
{
throw invalid_argument("poly_to_evaluate is not reduced");
}
if (poly_to_evaluate_at.significant_coeff_count() > poly_modulus.coeff_count() ||
poly_to_evaluate_at.significant_coeff_bit_count() > coeff_modulus.significant_bit_count())
{
throw invalid_argument("poly_to_evaluate_at is not reduced");
}
int poly_to_eval_coeff_uint64_count = poly_to_evaluate.coeff_uint64_count();
int coeff_modulus_bit_count = coeff_modulus.significant_bit_count();
if (poly_to_evaluate.is_zero())
{
destination.set_zero();
}
if (poly_to_evaluate_at.is_zero())
{
destination.resize(1, coeff_modulus_bit_count);
modulo_uint(poly_to_evaluate.data(), poly_to_eval_coeff_uint64_count,
Modulus(coeff_modulus.data(), coeff_modulus.uint64_count(), pool),
destination.data(), pool);
return;
}
ConstPointer poly_to_eval_ptr = duplicate_poly_if_needed(poly_to_evaluate, poly_modulus.coeff_count(), coeff_modulus.uint64_count(), false, pool);
ConstPointer poly_to_eval_at_ptr = duplicate_poly_if_needed(poly_to_evaluate_at, poly_modulus.coeff_count(), coeff_modulus.uint64_count(), false, pool);
destination.resize(poly_modulus.coeff_count(), coeff_modulus_bit_count);
util::poly_eval_poly_polymod_coeffmod(poly_to_eval_ptr.get(), poly_to_eval_at_ptr.get(),
PolyModulus(poly_modulus.data(), poly_modulus.coeff_count(), poly_modulus.coeff_uint64_count()),
Modulus(coeff_modulus.data(), coeff_modulus.uint64_count(), pool),
destination.data(), pool);
}
void poly_eval_poly(const BigPoly &poly_to_evaluate, const BigPoly &poly_to_evaluate_at,
BigPoly &destination, const MemoryPoolHandle &pool)
{
if (!pool)
{
throw invalid_argument("pool is uninitialized");
}
int poly_to_eval_coeff_uint64_count = divide_round_up(poly_to_evaluate.coeff_bit_count(), bits_per_uint64);
int value_coeff_uint64_count = divide_round_up(poly_to_evaluate_at.coeff_bit_count(), bits_per_uint64);
if (poly_to_evaluate.is_zero())
{
destination.set_zero();
return;
}
if (poly_to_evaluate_at.is_zero())
{
destination.resize(1, poly_to_evaluate.coeff_bit_count());
set_uint_uint(poly_to_evaluate.data(), poly_to_eval_coeff_uint64_count, destination.data());
return;
}
int result_coeff_count = (poly_to_evaluate.significant_coeff_count() - 1) * (poly_to_evaluate_at.significant_coeff_count() - 1) + 1;
int result_coeff_bit_count = poly_to_evaluate.coeff_bit_count() + (poly_to_evaluate.coeff_count() - 1) * poly_to_evaluate_at.coeff_bit_count();
int result_coeff_uint64_count = divide_round_up(result_coeff_bit_count, bits_per_uint64);
destination.resize(result_coeff_count, result_coeff_bit_count);
util::poly_eval_poly(poly_to_evaluate.data(), poly_to_evaluate.coeff_count(), poly_to_eval_coeff_uint64_count,
poly_to_evaluate_at.data(), poly_to_evaluate_at.coeff_count(), value_coeff_uint64_count,
result_coeff_count, result_coeff_uint64_count, destination.data(), pool);
}
void exponentiate_poly_polymod_coeffmod(const BigPoly &operand, const BigUInt &exponent,
const BigPoly &poly_modulus, const BigUInt &coeff_modulus, BigPoly &destination, const MemoryPoolHandle &pool)
{
if (operand.significant_coeff_count() > poly_modulus.coeff_count() ||
operand.significant_coeff_bit_count() > coeff_modulus.significant_bit_count())
{
throw invalid_argument("operand is not reduced");
}
if (exponent < 0)
{
throw invalid_argument("exponent must be a non-negative integer");
}
if (operand.is_zero() && exponent == 0)
{
throw invalid_argument("undefined operation");
}
if (!pool)
{
throw invalid_argument("pool is uninitialized");
}
if (operand.is_zero())
{
destination.set_zero();
return;
}
if (destination.coeff_bit_count() != coeff_modulus.significant_bit_count() ||
destination.coeff_count() != poly_modulus.coeff_count())
{
destination.resize(poly_modulus.coeff_count(), coeff_modulus.significant_bit_count());
}
ConstPointer operand_ptr = duplicate_poly_if_needed(operand, poly_modulus.coeff_count(), coeff_modulus.uint64_count(), false, pool);
util::exponentiate_poly_polymod_coeffmod(operand_ptr.get(), exponent.data(), exponent.uint64_count(),
PolyModulus(poly_modulus.data(), poly_modulus.coeff_count(), poly_modulus.coeff_uint64_count()),
Modulus(coeff_modulus.data(), coeff_modulus.uint64_count(), pool),
destination.data(), pool);
}
void Evaluator::multiply_plain(const BigPoly &encrypted1, const BigPoly &plain2, BigPoly &destination)
{
// Extract encryption parameters.
int coeff_count = poly_modulus_.coeff_count();
int coeff_bit_count = poly_modulus_.coeff_bit_count();
int coeff_uint64_count = divide_round_up(coeff_bit_count, bits_per_uint64);
// Verify parameters.
if (encrypted1.coeff_count() != coeff_count || encrypted1.coeff_bit_count() != coeff_bit_count)
{
throw invalid_argument("encrypted1 is not valid for encryption parameters");
}
#ifdef _DEBUG
if (encrypted1.significant_coeff_count() == coeff_count || !are_poly_coefficients_less_than(encrypted1, coeff_modulus_))
{
throw invalid_argument("encrypted1 is not valid for encryption parameters");
}
if (plain2.significant_coeff_count() >= coeff_count || !are_poly_coefficients_less_than(plain2, plain_modulus_))
{
throw invalid_argument("plain2 is too large to be represented by encryption parameters");
}
#endif
if (destination.coeff_count() != coeff_count || destination.coeff_bit_count() != coeff_bit_count)
{
destination.resize(coeff_count, coeff_bit_count);
}
// Get pointer to inputs (duplicated if needed).
ConstPointer encrypted1ptr = duplicate_poly_if_needed(encrypted1, encrypted1.pointer() == destination.pointer(), pool_);
// Handle test-mode case.
if (mode_ == TEST_MODE)
{
// Get pointer to inputs (duplicated and resized if needed).
ConstPointer plain2ptr = duplicate_poly_if_needed(plain2, coeff_count, coeff_uint64_count, plain2.pointer() == destination.pointer(), pool_);
// Resize second operand if needed.
multiply_poly_poly_polymod_coeffmod(encrypted1ptr.get(), plain2ptr.get(), polymod_, mod_, destination.pointer(), pool_);
return;
}
// Reposition coefficients.
Pointer moved2ptr(allocate_poly(coeff_count, coeff_uint64_count, pool_));
int plain_coeff_count = min(plain2.significant_coeff_count(), coeff_count);
int plain2_coeff_uint64_count = plain2.coeff_uint64_count();
const uint64_t *plain2_coeff = plain2.pointer();
uint64_t *moved2_coeff = moved2ptr.get();
for (int i = 0; i < plain_coeff_count; ++i)
{
set_uint_uint(plain2_coeff, plain2_coeff_uint64_count, coeff_uint64_count, moved2_coeff);
bool is_upper_half = is_greater_than_or_equal_uint_uint(moved2_coeff, plain_upper_half_threshold_.pointer(), coeff_uint64_count);
if (is_upper_half)
{
add_uint_uint(moved2_coeff, plain_upper_half_increment_.pointer(), coeff_uint64_count, moved2_coeff);
}
moved2_coeff += coeff_uint64_count;
plain2_coeff += plain2_coeff_uint64_count;
}
for (int i = plain_coeff_count; i < coeff_count; ++i)
{
set_zero_uint(coeff_uint64_count, moved2_coeff);
moved2_coeff += coeff_uint64_count;
}
// Use normal polynomial multiplication.
multiply_poly_poly_polymod_coeffmod(encrypted1ptr.get(), moved2ptr.get(), polymod_, mod_, destination.pointer(), pool_);
}
void Evaluator::sub_plain(const BigPoly &encrypted1, const BigPoly &plain2, BigPoly &destination)
{
// Extract encryption parameters.
int coeff_count = poly_modulus_.coeff_count();
int coeff_bit_count = poly_modulus_.coeff_bit_count();
int coeff_uint64_count = divide_round_up(coeff_bit_count, bits_per_uint64);
// Verify parameters.
if (encrypted1.coeff_count() != coeff_count || encrypted1.coeff_bit_count() != coeff_bit_count)
{
throw invalid_argument("encrypted1 is not valid for encryption parameters");
}
#ifdef _DEBUG
if (encrypted1.significant_coeff_count() == coeff_count || !are_poly_coefficients_less_than(encrypted1, coeff_modulus_))
{
throw invalid_argument("encrypted1 is not valid for encryption parameters");
}
if (plain2.significant_coeff_count() >= coeff_count || !are_poly_coefficients_less_than(plain2, plain_modulus_))
{
throw invalid_argument("plain2 is too large to be represented by encryption parameters");
}
#endif
if (destination.coeff_count() != coeff_count || destination.coeff_bit_count() != coeff_bit_count)
{
destination.resize(coeff_count, coeff_bit_count);
}
int plain2_coeff_uint64_count = divide_round_up(plain2.coeff_bit_count(), bits_per_uint64);
if (mode_ == TEST_MODE)
{
// Handle test-mode case.
set_poly_poly(plain2.pointer(), plain2.coeff_count(), plain2_coeff_uint64_count, coeff_count, coeff_uint64_count, destination.pointer());
modulo_poly_coeffs(destination.pointer(), coeff_count, mod_, pool_);
sub_poly_poly_coeffmod(encrypted1.pointer(), destination.pointer(), coeff_count, plain_modulus_.pointer(), coeff_uint64_count, destination.pointer());
return;
}
// Multiply plain by scalar coeff_div_plaintext and reposition if in upper-half.
preencrypt(plain2.pointer(), plain2.coeff_count(), plain2_coeff_uint64_count, destination.pointer());
// Subtract encrypted polynomial and encrypted-version of plain2.
sub_poly_poly_coeffmod(encrypted1.pointer(), destination.pointer(), coeff_count, coeff_modulus_.pointer(), coeff_uint64_count, destination.pointer());
}
void Evaluator::multiply_norelin(const BigPoly &encrypted1, const BigPoly &encrypted2, BigPoly &destination)
{
// Extract encryption parameters.
int coeff_count = poly_modulus_.coeff_count();
int coeff_bit_count = poly_modulus_.coeff_bit_count();
// Verify parameters.
if (encrypted1.coeff_count() != coeff_count || encrypted1.coeff_bit_count() != coeff_bit_count)
{
throw invalid_argument("encrypted1 is not valid for encryption parameters");
}
if (encrypted2.coeff_count() != coeff_count || encrypted2.coeff_bit_count() != coeff_bit_count)
{
throw invalid_argument("encrypted2 is not valid for encryption parameters");
}
#ifdef _DEBUG
if (encrypted1.significant_coeff_count() == coeff_count || !are_poly_coefficients_less_than(encrypted1, coeff_modulus_))
{
throw invalid_argument("encrypted1 is not valid for encryption parameters");
}
if (encrypted2.significant_coeff_count() == coeff_count || !are_poly_coefficients_less_than(encrypted2, coeff_modulus_))
{
throw invalid_argument("encrypted2 is not valid for encryption parameters");
}
#endif
if (destination.coeff_count() != coeff_count || destination.coeff_bit_count() != coeff_bit_count)
{
destination.resize(coeff_count, coeff_bit_count);
}
// Get pointer to inputs (duplicated if needed).
ConstPointer encrypted1ptr = duplicate_poly_if_needed(encrypted1, encrypted1.pointer() == destination.pointer(), pool_);
ConstPointer encrypted2ptr = duplicate_poly_if_needed(encrypted2, encrypted2.pointer() == destination.pointer(), pool_);
// Handle test-mode case.
if (mode_ == TEST_MODE)
{
multiply_poly_poly_polymod_coeffmod(encrypted1ptr.get(), encrypted2ptr.get(), polymod_, mod_, destination.pointer(), pool_);
return;
}
// Multiply encrypted polynomials without performing key switching.
multiply(encrypted1ptr.get(), encrypted2ptr.get(), destination.pointer());
}
