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OpenMind CKKSencoder CKKS encoder Daniel Huynh
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import numpy as np | |
from numpy.polynomial import Polynomial | |
# Set the parameters | |
M = 8 | |
N = M // 2 | |
scale = 64 | |
xi = np.exp(2 * np.pi * 1j / M) | |
def vandermonde(xi: np.complex128, M: int) -> np.array: | |
N = M // 2 | |
matrix = [] | |
for i in range(N): | |
root = xi ** (2 * i + 1) | |
row = [root ** j for j in range(N)] | |
matrix.append(row) | |
return matrix | |
def sigma_inverse(xi, M, b: np.array) -> Polynomial: | |
A = vandermonde(xi, M) | |
coeffs = np.linalg.solve(A, b) | |
p = Polynomial(coeffs) | |
return p | |
def sigma(xi, M, p: Polynomial) -> np.array: | |
outputs = [] | |
N = M // 2 | |
for i in range(N): | |
root = xi ** (2 * i + 1) | |
output = p(root) | |
outputs.append(output) | |
return np.array(outputs) | |
def create_sigma_R_basis(xi, M): | |
return np.array(vandermonde(xi, M)).T | |
def sigma_R_discretization(xi, M, z): | |
sigma_R_basis = create_sigma_R_basis(xi, M) | |
coordinates = compute_basis_coordinates(sigma_R_basis, z) | |
rounded_coordinates = coordinate_wise_random_rounding(coordinates) | |
y = np.matmul(sigma_R_basis.T, rounded_coordinates) | |
return y | |
def compute_basis_coordinates(sigma_R_basis, z): | |
return np.array([np.real(np.vdot(z, b) / np.vdot(b,b)) for b in sigma_R_basis]) | |
def round_coordinates(coordinates): | |
return coordinates - np.floor(coordinates) | |
def coordinate_wise_random_rounding(coordinates): | |
r = round_coordinates(coordinates) | |
f = np.array([np.random.choice([c, c-1], 1, p=[1-c, c]) for c in r]).reshape(-1) | |
rounded_coordinates = coordinates - f | |
return [int(coeff) for coeff in rounded_coordinates] | |
def pi(M, z: np.array) -> np.array: | |
N = M // 4 | |
return z[:N] | |
def pi_inverse(z: np.array) -> np.array: | |
z_conjugate = [np.conjugate(x) for x in z[::-1]] | |
return np.concatenate([z, z_conjugate]) | |
def encode(xi, M, scale, z: np.array) -> Polynomial: | |
pi_z = pi_inverse(z) | |
scaled_pi_z = scale * pi_z | |
rounded_scale_pi_zi = sigma_R_discretization(xi, M, scaled_pi_z) | |
p = sigma_inverse(xi, M, rounded_scale_pi_zi) | |
coef = np.round(np.real(p.coef)).astype(int) | |
return Polynomial(coef) | |
def decode(xi, M, scale, p: Polynomial) -> np.array: | |
rescaled_p = p / scale | |
z = sigma(xi, M, rescaled_p) | |
return pi(M, z) | |
# Example usage | |
z = np.array([3 + 4j, 2 - 1j]) | |
p = encode(xi, M, scale, z) | |
decoded_z = decode(xi, M, scale, p) |
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