def _assert(d):
alphas = []
while len(set(alphas)) < d and all(a != 0 for a in alphas):
alphas.append(random_prime(100000))
alphas = list(set(alphas))
A = matrix([[alpha ** i for alpha in alphas] for i in range(d)])
v = [random_prime(100000) for _ in range(d)]
x = PolynomialRing(QQ, names="x").gens()[0]
chpy = mul(x - alpha for alpha in alphas)
self.assertEqual(first_elt_of_kern_of_vandermonde(chpy, alphas[0], v),
(A ** (-1) * vector(v))[0])
def gen_random_curve(bits):
"""generates a random curve with prime of given bit length"""
p = random_prime(2**bits, proof=True, lbound=2**(bits - 1))
while True:
a = random.randint(1, p - 1)
b = random.randint(1, p - 1)
if ((4 * (a**3)) + (27 * (b**2))) % p != 0:
F = GF(p)
E = EllipticCurve(F, [a, b])
return (E, F)
def gen_params_from_bits(num_bits,k):
"""
Description:
Generates a prime r with num_bits bits and a fundamental discriminant D to use as input to the Cocks-Pinch method
Input:
num_bits - number of bits in r
k - embedding degree
Output:
r - prime such that r % k == 1 and r is num_bits bits long
k - embedding degree
D - (negative) fundamental discriminant where D is a square mod r
"""
r = random_prime(2**num_bits, lbound=2**(num_bits-1))
while not (r % k == 1 and utils.is_suitable_r(r)):
r = random_prime(2**num_bits, lbound=2**(num_bits-1))
return gen_params_from_r(r,k)
def gen_params_from_bits(num_bits, k):
"""
Description:
Generates a prime r with num_bits bits and a fundamental discriminant D to use as input to the Cocks-Pinch method
Input:
num_bits - number of bits in r
k - embedding degree
Output:
r - prime such that r % k == 1 and r is num_bits bits long
k - embedding degree
D - (negative) fundamental discriminant where D is a square mod r
"""
r = random_prime(2**num_bits, lbound=2**(num_bits - 1))
while not (r % k == 1 and utils.is_suitable_r(r)):
r = random_prime(2**num_bits, lbound=2**(num_bits - 1))
return gen_params_from_r(r, k)
def test_bp(path, cls, testcases, args):
success = True
try:
if args.zimmerman:
c = cls(path, verbose=args.verbose)
else:
prime = random_prime(2**args.secparam - 1)
c = cls(path, verbose=args.verbose, obliviate=args.obliviate)
c.randomize(prime)
except ParseException as e:
print('%s %s' % (utils.clr_warn('Parse Error:'), e))
return False
for k, v in testcases.items():
if c.evaluate(k) != v:
print('%s (%s != %d) ' % (failstr, k, v))
success = False
return success
def test_bp(path, cls, testcases, args):
success = True
try:
if args.zimmerman:
c = cls(path, verbose=args.verbose)
else:
prime = random_prime(2 ** args.secparam - 1)
c = cls(path, verbose=args.verbose, obliviate=args.obliviate)
c.randomize(prime)
except ParseException as e:
print('%s %s' % (utils.clr_warn('Parse Error:'), e))
return False
for k, v in testcases.items():
if c.evaluate(k) != v:
print('%s (%s != %d) ' % (failstr, k, v))
success = False
return success
def test_ec(num_tests, num_bits, debug=False):
print('testing EC chain...')
func_start = time.time()
fail = 0
for i in range(0, num_tests):
try:
k = randint(5, 20)
r = 0
while not (r % k == 1 and is_prime(r)):
r = random_prime(2**(num_bits - 1), 2**num_bits)
k_vector = [k]
k_vector.append(randint(5, 20))
k_vector.append(randint(5, 20))
curves = ec.new_chain(r, k_vector)
assert ec.is_chain(curves)
except AssertionError as e:
fail += 1
if fail == 0:
print('test passed')
return True
else:
print("failed %.2f" % (100 * fail / num_tests) + "% of tests!")
return False
def test_ec(num_tests,num_bits, debug=False):
print('testing EC chain...')
func_start = time.time()
fail = 0
for i in range(0, num_tests):
try:
k = randint(5,20)
r = 0
while not (r % k == 1 and is_prime(r)):
r = random_prime(2**(num_bits-1), 2**num_bits)
k_vector = [k]
k_vector.append(randint(5,20))
k_vector.append(randint(5,20))
curves = ec.new_chain(r, k_vector)
assert ec.is_chain(curves)
except AssertionError as e:
fail += 1
if fail == 0:
print('test passed')
return True
else:
print("failed %.2f" %(100*fail/num_tests) + "% of tests!")
return False
def gen_key(lb1, up1, lb2, up2):
p = random_prime(up1, lbound=lb1, proof=False)
q = random_prime(up2, lbound=lb2, proof=False)
return 65537, p * q
