def test_gao_interpolate_all_zeros():
int_msg = [0, 0, 0, 0, 0, 0, 0, 0]
k = len(int_msg) # length of message
n = 22 # size of encoded message
p = 53 # prime
t = k - 1 # degree of polynomial
x = list(range(n))
encoded = [
sum(int_msg[j] * pow(x[i], j, p) for j in range(k)) % p
for i in range(n)
]
# Check decoding with no errors
decoded, _ = gao_interpolate(x, encoded, k, p)
assert decoded == int_msg
# Corrupt with maximum number of erasures:
cmax = n - 2 * t - 1
corrupted = corrupt(encoded, num_errors=0, num_nones=cmax)
coeffs, _ = gao_interpolate(x, corrupted, k, p)
assert coeffs == int_msg
# Corrupt with maximum number of errors:
emax = (n - 2 * t - 1) // 2
corrupted = corrupt(encoded, num_errors=emax, num_nones=0)
coeffs, _ = gao_interpolate(x, corrupted, k, p)
assert coeffs == int_msg
# Corrupt with a mixture of errors and erasures
e = emax // 2
c = cmax // 4
corrupted = corrupt(encoded, num_errors=e, num_nones=c)
coeffs, _ = gao_interpolate(x, corrupted, k, p)
assert coeffs == int_msg
def robust_decode(self, z, encoded):
x = [self.point(zi).value for zi in z]
args = [x, encoded, self.d + 1, self.modulus]
if self.use_omega_powers:
args += [z, self.point.omega.value, self.point.order]
decoded, error_poly = gao_interpolate(
*args, use_omega_powers=self.use_omega_powers)
if decoded is None:
return None, None
errors = []
if len(error_poly) > 1:
if self.use_omega_powers:
err_eval = fft(error_poly, self.point.omega.value,
self.modulus, self.point.order)[:self.point.n]
else:
x = [self.point(i).value for i in range(self.point.n)]
err_eval = vandermonde_batch_evaluate(x, [error_poly],
self.modulus)[0]
errors = [i for i in range(self.point.n) if err_eval[i] == 0]
return decoded, errors
def test_gao_interpolate_fft(galois_field, galois_field_roots):
int_msg = [2, 3, 2, 8, 7, 5, 9, 5]
k = len(int_msg) # length of message
n = 22 # size of encoded message
p = galois_field.modulus # prime
r = 5 # 2 ** 5 = 32 > 22
omega = galois_field_roots[r]
order = 2**5 # = 32
t = k - 1 # degree of polynomial
z = list(range(n))
x = [pow(omega, zi, p) for zi in z]
encoded = [
sum(int_msg[j] * pow(x[i], j, p) for j in range(k)) % p
for i in range(n)
]
# Check decoding with no errors
decoded, _ = gao_interpolate(x,
encoded,
k,
p,
z=z,
omega=omega,
order=order,
use_omega_powers=True)
# decoded, _ = gao_interpolate(x, encoded, k, p)
assert decoded == int_msg
# Corrupt with maximum number of erasures:
cmax = n - 2 * t - 1
corrupted = corrupt(encoded, num_errors=0, num_nones=cmax)
coeffs, _ = gao_interpolate(x,
corrupted,
k,
p,
z=z,
omega=omega,
order=order,
use_omega_powers=True)
assert coeffs == int_msg
# Corrupt with maximum number of errors:
emax = (n - 2 * t - 1) // 2
corrupted = corrupt(encoded, num_errors=emax, num_nones=0)
coeffs, _ = gao_interpolate(x,
corrupted,
k,
p,
z=z,
omega=omega,
order=order,
use_omega_powers=True)
assert coeffs == int_msg
# Corrupt with a mixture of errors and erasures
e = emax // 2
c = cmax // 4
corrupted = corrupt(encoded, num_errors=e, num_nones=c)
coeffs, _ = gao_interpolate(x,
corrupted,
k,
p,
z=z,
omega=omega,
order=order,
use_omega_powers=True)
assert coeffs == int_msg