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poly_test.py
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poly_test.py
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import unittest
import numpy as np
from polynomial import PolynomialRing, Polynomial, get_centered_remainder
class TestPolynomialRing(unittest.TestCase):
def test_init_with_n(self):
n = 4
R = PolynomialRing(n)
quotient = np.array([1, 0, 0, 0, 1])
self.assertTrue(np.array_equal(R.denominator, quotient))
self.assertEqual(R.n, n)
def test_init_with_n_and_q(self):
n = 4
q = 7
Rq = PolynomialRing(n, q)
quotient = np.array([1, 0, 0, 0, 1])
self.assertTrue(np.array_equal(Rq.denominator, quotient))
self.assertEqual(Rq.Q, q)
self.assertEqual(Rq.n, n)
def test_sample_poly_from_r_error(self):
n = 4
R = PolynomialRing(n)
with self.assertRaisesRegex(AssertionError, "The modulus Q must be set to sample a polynomial from R_Q"): R.sample_polynomial()
def test_sample_poly_from_rq(self):
n = 4
q = 8
Rq = PolynomialRing(n, q)
aq1 = Rq.sample_polynomial()
aq2 = Rq.sample_polynomial()
# Ensure that the coefficients of the polynomial are within Z_q = [-q/2, q/2)
for coeff in aq1.coefficients:
self.assertTrue(coeff >= -q // 2 and coeff <= q // 2)
for coeff in aq2.coefficients:
self.assertTrue(coeff >= -q // 2 and coeff <= q // 2)
# Ensure that the degree of the sampled poly is equal or less than d (it might be less if the leading coefficient sampled is 0)
count1 = 0
for coeff in aq1.coefficients:
count1 += 1
count2 = 0
for coeff in aq2.coefficients:
count2 += 1
self.assertTrue(count1 <= Rq.n)
self.assertTrue(count2 <= Rq.n)
class TestPolynomialInRingR(unittest.TestCase):
def test_init_poly_in_ring_R(self):
n = 4
R = PolynomialRing(n)
coefficients = [6, 6, 6, 4, 5]
# a is the polynomial in R reduced by the quotient polynomial
a = Polynomial(coefficients, R)
self.assertTrue(np.array_equal(a.coefficients, [6, 6, 4, -1]))
# The degree of resulting poly should be less than the degree of fx
self.assertTrue(len(a.coefficients) < len(a.ring.denominator))
# After reduction, the polynomial should not be multiple of the quotient
_, remainder = np.polydiv(a.coefficients, a.ring.denominator)
self.assertTrue(np.array_equal(remainder, a.coefficients))
def test_add_poly_in_ring_R(self):
n = 4
R = PolynomialRing(n)
coefficients_1 = [3, 3, 4, 4, 4]
coefficients_2 = [3, 3, 2, 0, 1]
a1 = Polynomial(coefficients_1, R)
a2 = Polynomial(coefficients_2, R)
# a1 + a2
result = np.polyadd(a1.coefficients, a2.coefficients)
# The addition is happening in the ring R.
result = Polynomial(result, R)
# The resulting poly is 6, 6, 6, 4, 5. After reduction, the polynomial is 6, 6, 4, -1.
self.assertTrue(np.array_equal(result.coefficients, [6, 6, 4, -1]))
# After reduction, the polynomial should not be multiple of the quotient
_, remainder = np.polydiv(result.coefficients, result.ring.denominator)
self.assertTrue(np.array_equal(remainder, result.coefficients))
# The degree of the result poly should be the max of the two degrees
self.assertEqual(len(result.coefficients), max(len(a1.coefficients), len(a2.coefficients)))
def test_mul_poly_in_ring_R(self):
n = 4
R = PolynomialRing(n)
coefficients_1 = [3, 0, 4]
coefficients_2 = [2, 0, 1]
a1 = Polynomial(coefficients_1, R)
a2 = Polynomial(coefficients_2, R)
result = np.polymul(a1.coefficients, a2.coefficients)
# The multiplication is happening in the ring R.
result = Polynomial(result, R)
self.assertTrue(np.array_equal(result.coefficients, [11, 0, -2]))
# After reduction, the polynomial should not be multiple of the quotient
_, remainder = np.polydiv(result.coefficients, result.ring.denominator)
self.assertTrue(np.array_equal(remainder, result.coefficients))
# The degree of the result poly should less than the degree of fx
self.assertTrue(len(result.coefficients) < len(result.ring.denominator))
def test_scalar_mul_poly_in_ring_R(self):
n = 4
R = PolynomialRing(n)
coefficients = [4, 3, 0, 4]
a = Polynomial(coefficients, R)
# 2 * a. The resulting poly is 8, 6, 0, 8. Reduction does not change the coefficients.
result = np.polymul(2, a.coefficients)
# The multiplication is happening in the ring R.
result = Polynomial(result, R)
self.assertTrue(np.array_equal(result.coefficients, [8, 6, 0, 8]))
# After reduction, the polynomial should not be multiple of the quotient
_, remainder = np.polydiv(result.coefficients, result.ring.denominator)
self.assertTrue(np.array_equal(remainder, result.coefficients))
class TestPolynomialInRingRq(unittest.TestCase):
def test_init_poly_in_ring_Rq(self):
n = 4
q = 7
Rq = PolynomialRing(n, q)
coefficients = [3, 1, 0]
# aq is the polynomial in Rq reduced by the quotient polynomial and by the modulus q.
aq = Polynomial(coefficients, Rq)
self.assertTrue(np.array_equal(aq.coefficients, [3, 1, 0]))
# After reduction, the polynomial should not be multiple of the quotient
_, remainder = np.polydiv(aq.coefficients, aq.ring.denominator)
self.assertTrue(np.array_equal(remainder, aq.coefficients))
# All coefficients should be in Z_q - (-q/2, q/2]
Z_q = set()
for i in range(-q//2 + 1, q//2 + 1):
Z_q.add(i)
for coeff in aq.coefficients:
self.assertTrue(coeff in Z_q)
def test_add_poly_in_ring_Rq(self):
n = 4
q = 7
Rq = PolynomialRing(n, q)
coefficients_1 = [3, 3, 4, 4, 4] # r(x)
# 1st reduction
_, remainder = np.polydiv(coefficients_1, Rq.denominator) # r(x)/f(x). where f(x)= x^n + 1
# 2nd reduction
for i in range(len(remainder)):
remainder[i] = get_centered_remainder(remainder[i], Rq.Q)
aq1 = Polynomial(coefficients_1, Rq)
# check that coefficents of aq1 and remainder are the same
self.assertTrue(np.array_equal(aq1.coefficients, remainder))
coefficients_2 = [3, 3, 2, 0, 1]
aq2 = Polynomial(coefficients_2, Rq)
# aq1 + aq2
result = np.polyadd(aq1.coefficients, aq2.coefficients)
# The addition is happening in the ring Rq.
result = Polynomial(result, Rq)
# The resulting poly is 6, 6, 6, 4, 5. After first reduction, the polynomial is 6, 6, 4, -1. After second reduction (modulo q), the polynomial is -1. -1, -3, -1.
self.assertTrue(np.array_equal(result.coefficients, [-1, -1, -3, -1]))
# After reduction, the polynomial should not be multiple of the quotient
_, remainder = np.polydiv(result.coefficients, result.ring.denominator)
self.assertTrue(np.array_equal(remainder, result.coefficients))
# The degree of the result poly should be the max of the two degrees
self.assertEqual(len(result.coefficients), max(len(aq1.coefficients), len(aq2.coefficients)))
def test_mul_poly_in_ring_Rq(self):
n = 4
q = 7
Rq = PolynomialRing(n, q)
coefficients_1 = [3, 0, 4]
coefficients_2 = [2, 0, 1]
aq1 = Polynomial(coefficients_1, Rq)
aq2 = Polynomial(coefficients_2, Rq)
# aq1 * aq2. After reduction, the polynomial is . After second reduction (modulo q), the polynomial is -3, 0, -2.
result = np.polymul(aq1.coefficients, aq2.coefficients)
# The multiplication is happening in the ring Rq.
result = Polynomial(result, Rq)
self.assertTrue(np.array_equal(result.coefficients, [-3, 0, -2]))
# After reduction, the polynomial should not be multiple of the quotient
_, remainder = np.polydiv(result.coefficients, result.ring.denominator)
self.assertTrue(np.array_equal(remainder, result.coefficients))
# The degree of the result poly should less than the degree of fx
self.assertTrue(len(result.coefficients) < len(result.ring.denominator))
def test_scalar_mul_poly_in_ring_Rq(self):
n = 4
q = 7
Rq = PolynomialRing(n, q)
coefficients = [4, 3, 0, 4]
aq = Polynomial(coefficients, Rq)
# The resulting poly is 8, 6, 0, 8. After modulo q reduction, the polynomial is 1, -1, 0, 1.
result = np.polymul(2, aq.coefficients)
# The multiplication is happening in the ring Rq.
result = Polynomial(result, Rq)
self.assertTrue(np.array_equal(result.coefficients, [1, -1, 0, 1]))
# After reduction, the polynomial should not be multiple of the quotient
_, remainder = np.polydiv(result.coefficients, result.ring.denominator)
self.assertTrue(np.array_equal(remainder, result.coefficients))
class TestCustomModulo(unittest.TestCase):
def test_positive_values(self):
self.assertEqual(get_centered_remainder(7, 10), -3) # 7 % 10. Lies in the range (-5, 5]
self.assertEqual(get_centered_remainder(15, 10), 5) # 15 % 10 = 5, which is <= 5
self.assertEqual(get_centered_remainder(17, 10), -3) # 17 % 10 = 7, which is > 5. So, 7 - 10 = -3
def test_negative_values(self):
self.assertEqual(get_centered_remainder(-7, 10), 3) # Lies in the range (-5, 5]
self.assertEqual(get_centered_remainder(-15, 10), 5) # -15 % 10 = 5 (in Python, % returns non-negative), which is <= 5
self.assertEqual(get_centered_remainder(-17, 10), 3) # -17 % 10 = 3, which is <= 5
def test_boundary_values(self):
q = 7
self.assertEqual(get_centered_remainder(-q//2 + 1, q), -q//2 + 1) # The smallest positive number in the range
self.assertEqual(get_centered_remainder(q//2, q), q//2) # The largest number in the range
def test_zero(self):
self.assertEqual(get_centered_remainder(0, 10), 0) # 0 lies in the range (-5, 5]
if __name__ == "__main__":
unittest.main()