def test_sqrt_composite_all():
print("\nTesting all residues by small composite modules")
ns = [
10,
30,
50,
99,
100,
655,
1025,
1337,
7**3 * 3,
2**6 * 13,
2**4 * 3**3 * 5,
3 * 3 * 5 * 7,
1024,
]
for n in ns:
f = factorize(n)
print(" Testing %s = %s" % (n, f))
for x in range(n):
a = pow(x, 2, n)
is_sqrt = has_sqrtmod(a, f)
if is_sqrt:
check_valid_sqrt_composite(None, a, f)
check_jacobi(a, n, is_sqrt)
assert has_sqrtmod(a, f)
check_valid_sqrt_composite(x, a, f)
def test_sqrt_composite_rand():
print("\nTesting all residues by random composite modules")
for size, ntries in [(2, 2), (3, 3), (5, 10), (7, 20), (10, 20)]:
for i in range(ntries):
n = randint_bits(size)
f = factorize(n)
print(" Testing %s-bit number: %s..." % (size, str(n)[:32]))
for x in range(n):
a = pow(x, 2, n)
is_sqrt = has_sqrtmod(a, f)
if is_sqrt:
check_valid_sqrt_composite(None, a, f)
check_jacobi(a, n, is_sqrt)
assert has_sqrtmod(a, f)
check_valid_sqrt_composite(x, a, f)
def test_sqrt_composite_rand_rand():
print("\nTesting random residues by random composite modules")
for size, ntries in [(10, 20), (20, 20), (24, 20), (30, 20)]:
for i in range(ntries):
n = randint_bits(size)
f = factorize(n)
print(" Testing %s-bit number: %s..." % (size, str(n)[:32]))
for j in range(30):
x = random.randint(0, n - 1)
a = pow(x, 2, n)
is_sqrt = has_sqrtmod(a, f)
if is_sqrt:
check_valid_sqrt_composite(None, a, f)
check_jacobi(a, n, is_sqrt)
assert has_sqrtmod(a, f)
check_valid_sqrt_composite(x, a, f)
def test_sqrt_pp_all():
print("\nTesting all residues by small modules")
pairs = [(2, 11), (3, 7), (5, 5), (7, 4), (11, 3), (13, 3), (97, 2)]
for prime, maxpow in pairs:
for k in range(1, maxpow + 1):
n = prime**k
print(" Testing %s**%s" % (prime, k))
for x in range(n):
a = pow(x, 2, n)
is_sqrt = has_sqrtmod(a, {prime: k})
is_sqrt2 = has_sqrtmod_prime_power(a, prime, k)
assert is_sqrt == is_sqrt2
if is_sqrt:
check_valid_sqrt_pp(None, a, prime, k)
check_jacobi(a, n, is_sqrt)
assert has_sqrtmod_prime_power(a, prime, k)
assert has_sqrtmod(a, {prime: k})
check_valid_sqrt_pp(x, a, prime, k)
def test_has_sqrtmod():
with pytest.raises(TypeError):
has_sqrtmod_prime_power(3, 9, "")
with pytest.raises(TypeError):
has_sqrtmod_prime_power(3, "", 30)
with pytest.raises(TypeError):
has_sqrtmod_prime_power("", 9, 30)
with pytest.raises(ValueError):
has_sqrtmod_prime_power(1, 2, 0) # 1 mod 2**0
with pytest.raises(ValueError):
has_sqrtmod_prime_power(1, 1, 2) # 1 mod 1**2
with pytest.raises(TypeError):
has_sqrtmod(3, {9: ""})
with pytest.raises(TypeError):
has_sqrtmod(3, {"": 2})
with pytest.raises(TypeError):
has_sqrtmod("", {9: 30})
with pytest.raises(TypeError):
has_sqrtmod("", {(9, ): 30})
with pytest.raises(ValueError):
has_sqrtmod(1, {2: 0}) # 1 mod 2**0
with pytest.raises(ValueError):
has_sqrtmod(1, {1: 2}) # 1 mod 1**2
with pytest.raises(ValueError):
has_sqrtmod(3, {})