def make_chain(curve, k_vector):
"""
Description:
Finds an elliptic curve chain
Input:
curve - the first curve (q,t,r,k,D) in the chain
k_vector - list of embedding degrees
Output:
curves - elliptic curve chain
"""
curves = [curve]
r = curve[0]
for i in range(0, len(k_vector)):
k = k_vector[i]
r, k, D = cp.gen_params_from_r(r, k)
curve2 = cp.run(r, k, D)
j = 0
while i < len(k_vector) - 1 and (curve2[0] -
1) % k_vector[i + 1] != 0 and j < 100:
curve2 = cp.run(r, k, D)
j += 1
curves.append(curve2)
r = curve2[0]
return curves
def make_chain(curve, k_vector):
"""
Description:
Finds an elliptic curve chain
Input:
curve - the first curve (q,t,r,k,D) in the chain
k_vector - list of embedding degrees
Output:
curves - elliptic curve chain
"""
curves = [curve]
r = curve[0]
for i in range(0, len(k_vector)):
k = k_vector[i]
r,k,D = cp.gen_params_from_r(r,k)
curve2 = cp.run(r,k,D)
j = 0
while i < len(k_vector) - 1 and (curve2[0] - 1) % k_vector[i+1] != 0 and j < 100:
curve2 = cp.run(r,k,D)
j+=1
curves.append(curve2)
r = curve2[0]
return curves
def test_cm(num_tests,num_bits, debug=False):
# runs CM method num_tests times;
# each test uses a random output from the CP method with a num_bits bit prime
print('testing CM...')
fail = 0
for i in range(0, num_tests):
try:
k = randint(5,50)
r,k,D = cp.gen_params_from_bits(num_bits,k)
q,t,r,k,D = cp.run(r,k,D)
E = cm.make_curve(q,t,r,k,D)
assert E
assert cm.test_curve(q,t,r,k,D,E)
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_cm(num_tests, num_bits, debug=False):
# runs CM method num_tests times;
# each test uses a random output from the CP method with a num_bits bit prime
print('testing CM...')
fail = 0
for i in range(0, num_tests):
try:
k = randint(5, 50)
r, k, D = cp.gen_params_from_bits(num_bits, k)
q, t, r, k, D = cp.run(r, k, D)
E = cm.make_curve(q, t, r, k, D)
assert E
assert cm.test_curve(q, t, r, k, D, E)
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_cp2(num_tests,num_bits,k, debug=False):
# runs CP method num_tests times;
# uses the same embedding degree k for every test
print('testing CP...')
fail = 0
k2 = k
for i in range(0, num_tests):
if not k2:
k = randint(5,50)
try:
r,k,D = cp.gen_params_from_bits(num_bits, k)
assert cp.test_promise(r,k,D)
q,t,r,k,D = cp.run(r,k,D)
assert utils.is_suitable_curve(q,t,r,k,D,num_bits)
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 call_cp(n, k):
r, k, D = cp.gen_params_from_bits(n, k)
start = time.time()
cp.run(r, k, D)
return time.time() - start
def call_cp(n,k):
r,k,D = cp.gen_params_from_bits(n,k)
start = time.time();
cp.run(r,k,D)
return time.time()-start
import ecfactory.cocks_pinch as cp from ecfactory.utils import print_curve # Example 1 (using a known value of r) k = 5 # embedding degree r = 1743941 # size of prime order subgroup r, k, D = cp.gen_params_from_r(r, k) # find a valid D q, t, r, k, D = cp.run(r, k, D) # use CP method to solve for q and t print_curve(q, t, r, k, D) # Example 2 (algorithm generates r) k = 7 # embedding degree num_bits = 100 # number of bits in size of prime order subgroup r, k, D = cp.gen_params_from_bits(num_bits, k) q, t, r, k, D = cp.run(r, k, D) # use CP method to solve for q and t print_curve(q, t, r, k, D) # Example 3 (running cocks_pinch_method once with a specified num_times and g) k = 5 r = 1743941 r, k, D = cp.gen_params_from_r(r, k) g = 722825 q, t = cp.method(r, k, D, max_trials=100, g=g) # might not find q and t print_curve(q, t, r, k, D)