bool is_one_zero_one_poly(const uint64_t *poly, int coeff_count, int coeff_uint64_count)
{
#ifdef _DEBUG
if (poly == nullptr && coeff_count > 0 && coeff_uint64_count > 0)
{
throw invalid_argument("poly");
}
if (coeff_count < 0)
{
throw invalid_argument("coeff_count");
}
if (coeff_uint64_count < 0)
{
throw invalid_argument("coeff_uint64_count");
}
#endif
if (coeff_count == 0 || coeff_uint64_count == 0)
{
return false;
}
if (!is_equal_uint(get_poly_coeff(poly, 0, coeff_uint64_count), coeff_uint64_count, 1))
{
return false;
}
if (!is_equal_uint(get_poly_coeff(poly, coeff_count - 1, coeff_uint64_count), coeff_uint64_count, 1))
{
return false;
}
if (coeff_count > 2 && !is_zero_poly(poly + coeff_uint64_count, coeff_count - 2, coeff_uint64_count))
{
return false;
}
return true;
}
void Evaluator::relinearize(const uint64_t *encrypted, uint64_t *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);
// Clear destatintion.
set_zero_poly(coeff_count, coeff_uint64_count, destination);
// Create polynomial to store decomposed polynomial (one at a time).
Pointer decomp_poly(allocate_poly(coeff_count, coeff_uint64_count, pool_));
Pointer decomp_eval_poly(allocate_poly(coeff_count, coeff_uint64_count, pool_));
int shift = 0;
for (int decomp_index = 0; decomp_index < evaluation_keys_.count(); ++decomp_index)
{
// Isolate decomposition_bit_count_ bits for each coefficient.
for (int coeff_index = 0; coeff_index < coeff_count; ++coeff_index)
{
const uint64_t *productmoded_coeff = get_poly_coeff(encrypted, coeff_index, coeff_uint64_count);
uint64_t *decomp_coeff = get_poly_coeff(decomp_poly.get(), coeff_index, coeff_uint64_count);
right_shift_uint(productmoded_coeff, shift, coeff_uint64_count, decomp_coeff);
filter_highbits_uint(decomp_coeff, coeff_uint64_count, decomposition_bit_count_);
}
// Multiply decomposed poly by evaluation key and accumulate to result.
const BigPoly &evaluation_key = evaluation_keys_[decomp_index];
multiply_poly_poly_polymod_coeffmod(decomp_poly.get(), evaluation_key.pointer(), polymod_, mod_, decomp_eval_poly.get(), pool_);
add_poly_poly_coeffmod(decomp_eval_poly.get(), destination, coeff_count, coeff_modulus_.pointer(), coeff_uint64_count, destination);
// Increase shift by decomposition_bit_count_ for next iteration.
shift += decomposition_bit_count_;
}
}
void poly_eval_poly(const uint64_t *poly_to_eval,
int poly_to_eval_coeff_count,
int poly_to_eval_coeff_uint64_count,
const uint64_t *value, int value_coeff_count,
int value_coeff_uint64_count, int result_coeff_count,
int result_coeff_uint64_count, uint64_t *result, MemoryPool &pool)
{
#ifdef SEAL_DEBUG
if (poly_to_eval == nullptr)
{
throw invalid_argument("poly_to_eval");
}
if (value == nullptr)
{
throw invalid_argument("value");
}
if (result == nullptr)
{
throw invalid_argument("result");
}
if (poly_to_eval_coeff_count <= 0)
{
throw invalid_argument("poly_to_eval_coeff_count");
}
if (poly_to_eval_coeff_uint64_count <= 0)
{
throw invalid_argument("poly_to_eval_coeff_uint64_count");
}
if (value_coeff_count <= 0)
{
throw invalid_argument("value_coeff_count");
}
if (value_coeff_uint64_count <= 0)
{
throw invalid_argument("value_coeff_uint64_count");
}
if (result_coeff_count <= 0)
{
throw invalid_argument("result_coeff_count");
}
if (result_coeff_uint64_count <= 0)
{
throw invalid_argument("result_coeff_uint64_count");
}
#endif
// Evaluate poly at value using Horner's method
Pointer temp1(allocate_poly(result_coeff_count, result_coeff_uint64_count, pool));
Pointer temp2(allocate_zero_poly(result_coeff_count, result_coeff_uint64_count, pool));
uint64_t *productptr = temp1.get();
uint64_t *intermediateptr = temp2.get();
for (int coeff_index = poly_to_eval_coeff_count - 1; coeff_index >= 0; coeff_index--)
{
multiply_poly_poly(intermediateptr, result_coeff_count, result_coeff_uint64_count, value, value_coeff_count, value_coeff_uint64_count, result_coeff_count, result_coeff_uint64_count, productptr, pool);
const uint64_t *curr_coeff = get_poly_coeff(poly_to_eval, coeff_index, poly_to_eval_coeff_uint64_count);
add_uint_uint(productptr, result_coeff_uint64_count, curr_coeff, poly_to_eval_coeff_uint64_count, false, result_coeff_uint64_count, productptr);
swap(productptr, intermediateptr);
}
set_poly_poly(intermediateptr, result_coeff_count, result_coeff_uint64_count, result);
}
void KeyGenerator::generate()
{
// 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);
// Loop until find a valid secret key.
uint64_t *secret_key = secret_key_.pointer();
set_zero_poly(coeff_count, coeff_uint64_count, secret_key);
Pointer secret_key_inv(allocate_poly(coeff_count, coeff_uint64_count, pool_));
while (true)
{
// Create noise with random [-1, 1] coefficients.
set_poly_coeffs_zero_one_negone(secret_key);
// Calculate secret_key * plaintext_modulus + 1.
multiply_poly_scalar_coeffmod(secret_key, coeff_count, plain_modulus_.pointer(), mod_, secret_key, pool_);
uint64_t *constant_coeff = get_poly_coeff(secret_key, 0, coeff_uint64_count);
increment_uint_mod(constant_coeff, coeff_modulus_.pointer(), coeff_uint64_count, constant_coeff);
// Attempt to invert secret_key.
if (try_invert_poly_coeffmod(secret_key, poly_modulus_.pointer(), coeff_count, mod_, secret_key_inv.get(), pool_))
{
// Secret_key is invertible, so is valid
break;
}
}
// 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, 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 exponentiate_poly(const std::uint64_t *poly,
int poly_coeff_count, int poly_coeff_uint64_count,
const uint64_t *exponent, int exponent_uint64_count,
int result_coeff_count, int result_coeff_uint64_count,
std::uint64_t *result, MemoryPool &pool)
{
#ifdef SEAL_DEBUG
if (poly == nullptr)
{
throw invalid_argument("poly");
}
if (poly_coeff_count <= 0)
{
throw invalid_argument("poly_coeff_count");
}
if (poly_coeff_count <= 0)
{
throw invalid_argument("poly_coeff_uint64_count");
}
if (exponent == nullptr)
{
throw invalid_argument("exponent");
}
if (exponent_uint64_count <= 0)
{
throw invalid_argument("exponent_uint64_count");
}
if (result == nullptr)
{
throw invalid_argument("result");
}
if (result_coeff_count <= 0)
{
throw invalid_argument("result_coeff_count");
}
if (result_coeff_uint64_count <= 0)
{
throw invalid_argument("result_coeff_uint64_count");
}
#endif
// Fast cases
if (is_zero_uint(exponent, exponent_uint64_count))
{
set_zero_poly(result_coeff_count, result_coeff_uint64_count, result);
*result = 1;
return;
}
if (is_equal_uint(exponent, exponent_uint64_count, 1))
{
set_poly_poly(poly, poly_coeff_count, poly_coeff_uint64_count,
result_coeff_count, result_coeff_uint64_count, result);
return;
}
// Need to make a copy of exponent
Pointer exponent_copy(allocate_uint(exponent_uint64_count, pool));
set_uint_uint(exponent, exponent_uint64_count, exponent_copy.get());
// Perform binary exponentiation.
Pointer big_alloc(allocate_uint((static_cast<int64_t>(result_coeff_count) +
result_coeff_count + result_coeff_count) * result_coeff_uint64_count, pool));
uint64_t *powerptr = big_alloc.get();
uint64_t *productptr = get_poly_coeff(powerptr, result_coeff_count, result_coeff_uint64_count);
uint64_t *intermediateptr = get_poly_coeff(productptr, result_coeff_count, result_coeff_uint64_count);
set_poly_poly(poly, poly_coeff_count, poly_coeff_uint64_count, result_coeff_count, result_coeff_uint64_count, powerptr);
set_zero_poly(result_coeff_count, result_coeff_uint64_count, intermediateptr);
*intermediateptr = 1;
// Initially: power = operand and intermediate = 1, product is not initialized.
while (true)
{
if ((*exponent_copy.get() % 2) == 1)
{
multiply_poly_poly(powerptr, result_coeff_count, result_coeff_uint64_count, intermediateptr, result_coeff_count, result_coeff_uint64_count,
result_coeff_count, result_coeff_uint64_count, productptr, pool);
swap(productptr, intermediateptr);
}
right_shift_uint(exponent_copy.get(), 1, exponent_uint64_count, exponent_copy.get());
if (is_zero_uint(exponent_copy.get(), exponent_uint64_count))
{
break;
}
multiply_poly_poly(powerptr, result_coeff_count, result_coeff_uint64_count, powerptr, result_coeff_count, result_coeff_uint64_count,
result_coeff_count, result_coeff_uint64_count, productptr, pool);
swap(productptr, powerptr);
}
set_poly_poly(intermediateptr, result_coeff_count, result_coeff_uint64_count, result);
}
void multiply_poly_poly(const uint64_t *operand1,
int operand1_coeff_count, int operand1_coeff_uint64_count,
const uint64_t *operand2, int operand2_coeff_count,
int operand2_coeff_uint64_count, int result_coeff_count,
int result_coeff_uint64_count, uint64_t *result, MemoryPool &pool)
{
#ifdef SEAL_DEBUG
if (operand1 == nullptr && operand1_coeff_count > 0 &&
operand1_coeff_uint64_count > 0)
{
throw invalid_argument("operand1");
}
if (operand1_coeff_count < 0)
{
throw invalid_argument("operand1_coeff_count");
}
if (operand1_coeff_uint64_count < 0)
{
throw invalid_argument("operand1_coeff_uint64_count");
}
if (operand2 == nullptr && operand2_coeff_count > 0 &&
operand2_coeff_uint64_count > 0)
{
throw invalid_argument("operand2");
}
if (operand2_coeff_count < 0)
{
throw invalid_argument("operand2_coeff_count");
}
if (operand2_coeff_uint64_count < 0)
{
throw invalid_argument("operand2_coeff_uint64_count");
}
if (result_coeff_count < 0)
{
throw invalid_argument("result_coeff_count");
}
if (result_coeff_uint64_count < 0)
{
throw invalid_argument("result_coeff_uint64_count");
}
if (result == nullptr && result_coeff_count > 0 &&
result_coeff_uint64_count > 0)
{
throw invalid_argument("result");
}
if (result != nullptr &&
(operand1 == result || operand2 == result))
{
throw invalid_argument("result cannot point to the same value as operand1 or operand2");
}
#endif
Pointer intermediate(allocate_uint(result_coeff_uint64_count, pool));
// Clear product.
set_zero_poly(result_coeff_count, result_coeff_uint64_count, result);
operand1_coeff_count = get_significant_coeff_count_poly(
operand1, operand1_coeff_count, operand1_coeff_uint64_count);
operand2_coeff_count = get_significant_coeff_count_poly(
operand2, operand2_coeff_count, operand2_coeff_uint64_count);
for (int operand1_index = 0; operand1_index < operand1_coeff_count; operand1_index++)
{
const uint64_t *operand1_coeff = get_poly_coeff(
operand1, operand1_index, operand1_coeff_uint64_count);
for (int operand2_index = 0; operand2_index < operand2_coeff_count; operand2_index++)
{
int product_coeff_index = operand1_index + operand2_index;
if (product_coeff_index >= result_coeff_count)
{
break;
}
const uint64_t *operand2_coeff = get_poly_coeff(
operand2, operand2_index, operand2_coeff_uint64_count);
multiply_uint_uint(operand1_coeff, operand1_coeff_uint64_count,
operand2_coeff, operand2_coeff_uint64_count, result_coeff_uint64_count, intermediate.get());
uint64_t *result_coeff = get_poly_coeff(
result, product_coeff_index, result_coeff_uint64_count);
add_uint_uint(result_coeff, intermediate.get(), result_coeff_uint64_count, result_coeff);
}
}
}
void Evaluator::multiply(const uint64_t *encrypted1, const uint64_t *encrypted2, uint64_t *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);
// Clear destatintion.
set_zero_poly(coeff_count, coeff_uint64_count, destination);
// Determine if FFT can be used.
bool use_fft = polymod_.coeff_count_power_of_two() >= 0 && polymod_.is_one_zero_one();
if (use_fft)
{
// Use FFT to multiply polynomials.
// Allocate polynomial to store product of two polynomials, with poly but no coeff modulo yet (and signed).
int product_coeff_bit_count = coeff_bit_count + coeff_bit_count + get_significant_bit_count(static_cast<uint64_t>(coeff_count)) + 2;
int product_coeff_uint64_count = divide_round_up(product_coeff_bit_count, bits_per_uint64);
Pointer product(allocate_poly(coeff_count, product_coeff_uint64_count, pool_));
// Use FFT to multiply polynomials.
set_zero_uint(product_coeff_uint64_count, get_poly_coeff(product.get(), coeff_count - 1, product_coeff_uint64_count));
fftmultiply_poly_poly_polymod(encrypted1, encrypted2, polymod_.coeff_count_power_of_two(), coeff_uint64_count, product_coeff_uint64_count, product.get(), pool_);
// For each coefficient in product, multiply by plain_modulus and divide by coeff_modulus and then modulo by coeff_modulus.
int plain_modulus_bit_count = plain_modulus_.significant_bit_count();
int plain_modulus_uint64_count = divide_round_up(plain_modulus_bit_count, bits_per_uint64);
int intermediate_bit_count = product_coeff_bit_count + plain_modulus_bit_count - 1;
int intermediate_uint64_count = divide_round_up(intermediate_bit_count, bits_per_uint64);
Pointer intermediate(allocate_uint(intermediate_uint64_count, pool_));
Pointer quotient(allocate_uint(intermediate_uint64_count, pool_));
for (int coeff_index = 0; coeff_index < coeff_count; ++coeff_index)
{
uint64_t *product_coeff = get_poly_coeff(product.get(), coeff_index, product_coeff_uint64_count);
bool coeff_is_negative = is_high_bit_set_uint(product_coeff, product_coeff_uint64_count);
if (coeff_is_negative)
{
negate_uint(product_coeff, product_coeff_uint64_count, product_coeff);
}
multiply_uint_uint(product_coeff, product_coeff_uint64_count, plain_modulus_.pointer(), plain_modulus_uint64_count, intermediate_uint64_count, intermediate.get());
add_uint_uint(intermediate.get(), wide_coeff_modulus_div_two_.pointer(), intermediate_uint64_count, intermediate.get());
divide_uint_uint_inplace(intermediate.get(), wide_coeff_modulus_.pointer(), intermediate_uint64_count, quotient.get(), pool_);
modulo_uint_inplace(quotient.get(), intermediate_uint64_count, mod_, pool_);
uint64_t *dest_coeff = get_poly_coeff(destination, coeff_index, coeff_uint64_count);
if (coeff_is_negative)
{
negate_uint_mod(quotient.get(), coeff_modulus_.pointer(), coeff_uint64_count, dest_coeff);
}
else
{
set_uint_uint(quotient.get(), coeff_uint64_count, dest_coeff);
}
}
}
else
{
// Use normal multiplication to multiply polynomials.
// Allocate polynomial to store product of two polynomials, with no poly or coeff modulo yet.
int product_coeff_count = coeff_count + coeff_count - 1;
int product_coeff_bit_count = coeff_bit_count + coeff_bit_count + get_significant_bit_count(static_cast<uint64_t>(coeff_count));
int product_coeff_uint64_count = divide_round_up(product_coeff_bit_count, bits_per_uint64);
Pointer product(allocate_poly(product_coeff_count, product_coeff_uint64_count, pool_));
// Multiply polynomials.
multiply_poly_poly(encrypted1, coeff_count, coeff_uint64_count, encrypted2, coeff_count, coeff_uint64_count, product_coeff_count, product_coeff_uint64_count, product.get(), pool_);
// For each coefficient in product, multiply by plain_modulus and divide by coeff_modulus and then modulo by coeff_modulus.
int plain_modulus_bit_count = plain_modulus_.significant_bit_count();
int plain_modulus_uint64_count = divide_round_up(plain_modulus_bit_count, bits_per_uint64);
int intermediate_bit_count = product_coeff_bit_count + plain_modulus_bit_count;
int intermediate_uint64_count = divide_round_up(intermediate_bit_count, bits_per_uint64);
Pointer intermediate(allocate_uint(intermediate_uint64_count, pool_));
Pointer quotient(allocate_uint(intermediate_uint64_count, pool_));
Pointer productmoded(allocate_poly(product_coeff_count, coeff_uint64_count, pool_));
for (int coeff_index = 0; coeff_index < product_coeff_count; ++coeff_index)
{
const uint64_t *product_coeff = get_poly_coeff(product.get(), coeff_index, product_coeff_uint64_count);
multiply_uint_uint(product_coeff, product_coeff_uint64_count, plain_modulus_.pointer(), plain_modulus_uint64_count, intermediate_uint64_count, intermediate.get());
add_uint_uint(intermediate.get(), wide_coeff_modulus_div_two_.pointer(), intermediate_uint64_count, intermediate.get());
divide_uint_uint_inplace(intermediate.get(), wide_coeff_modulus_.pointer(), intermediate_uint64_count, quotient.get(), pool_);
modulo_uint_inplace(quotient.get(), intermediate_uint64_count, mod_, pool_);
uint64_t *productmoded_coeff = get_poly_coeff(productmoded.get(), coeff_index, coeff_uint64_count);
set_uint_uint(quotient.get(), coeff_uint64_count, productmoded_coeff);
}
// Perform polynomial modulo.
modulo_poly_inplace(productmoded.get(), product_coeff_count, polymod_, mod_, pool_);
// Copy to destination.
set_poly_poly(productmoded.get(), coeff_count, coeff_uint64_count, destination);
}
}
