def ecdsa_sign(curve_obj, hash_int, hash_num_bits, private_key, message, k=None):
"""Sign message using the private key.
Returns the signature (r, s).
@param hash_int: a hash function mapping to an integer, for example
lambda m: util.be2int(hashlib.sha256(m).digest())
@param hash_num_bits: the number of bits in the digest above, for
example 256.
"""
n = curve_obj.order
if k is None:
k = util.randint(1, n - 1)
e = hash_int(message)
L_n = util.count_bits(n)
z = e >> max(hash_num_bits - L_n, 0)
while True:
(x1, y1) = curve.mul(k, curve_obj.base_point, curve_obj.curve)
r = x1 % curve_obj.order
if r == 0:
continue
k_neg = numbertheory.inverse_of(k, n)
s = (k_neg * (z + r * private_key)) % n
if s == 0:
continue
break
return (r, s)
def test_inverse(self):
p = 7873
for n in range(1, 3000):
all_valid = set()
for m in range(p):
if (n * m) % p == 1:
all_valid.add(m)
break
self.assertTrue(inverse_of(n, p) in all_valid)
def ecdsa_verify(curve_obj, hash_int, hash_num_bits, public_key, message,
signature):
"""Verify that signature is over the message using the public key.
Returns True if so, False otherwise.
Otherwise similar to ecdsa_sign() in usage.
"""
n = curve_obj.order
# Verify
if public_key == curve_obj.base_point or \
curve_obj.curve.invert_point(public_key) == curve_obj.base_point: # XXX: Check inverted too?
return False
if not curve_obj.curve.point_on_curve(public_key):
return False
if not curve.mul(curve_obj.order, public_key,
curve_obj.curve) == curve_obj.curve.neutral_point():
return False
(r, s) = signature
if not 1 <= r <= n - 1:
return False
if not 1 <= s <= n - 1:
return False
e = hash_int(message)
L_n = util.count_bits(n)
z = e >> max(hash_num_bits - L_n, 0)
# Verify
w = numbertheory.inverse_of(s, curve_obj.order) % n
u_1 = (z * w) % n
u_2 = (r * w) % n
(x1, y1) = curve_obj.curve.add_points(
curve.mul(u_1, curve_obj.base_point, curve_obj.curve),
curve.mul(u_2, public_key, curve_obj.curve))
return (r % n) == (x1 % n)
def ecdsa_verify(curve_obj, hash_int, hash_num_bits, public_key, message, signature):
"""Verify that signature is over the message using the public key.
Returns True if so, False otherwise.
Otherwise similar to ecdsa_sign() in usage.
"""
n = curve_obj.order
# Verify
if public_key == curve_obj.base_point or \
curve_obj.curve.invert_point(public_key) == curve_obj.base_point: # XXX: Check inverted too?
return False
if not curve_obj.curve.point_on_curve(public_key):
return False
if not curve.mul(curve_obj.order, public_key, curve_obj.curve) == curve_obj.curve.neutral_point():
return False
(r, s) = signature
if not 1 <= r <= n - 1:
return False
if not 1 <= s <= n - 1:
return False
e = hash_int(message)
L_n = util.count_bits(n)
z = e >> max(hash_num_bits - L_n, 0)
# Verify
w = numbertheory.inverse_of(s, curve_obj.order) % n
u_1 = (z * w) % n
u_2 = (r * w) % n
(x1, y1) = curve_obj.curve.add_points(
curve.mul(u_1, curve_obj.base_point, curve_obj.curve),
curve.mul(u_2, public_key, curve_obj.curve)
)
return (r % n) == (x1 % n)
def ecdsa_sign(curve_obj,
hash_int,
hash_num_bits,
private_key,
message,
k=None):
"""Sign message using the private key.
Returns the signature (r, s).
@param hash_int: a hash function mapping to an integer, for example
lambda m: util.be2int(hashlib.sha256(m).digest())
@param hash_num_bits: the number of bits in the digest above, for
example 256.
"""
n = curve_obj.order
if k is None:
k = util.randint(1, n - 1)
e = hash_int(message)
L_n = util.count_bits(n)
z = e >> max(hash_num_bits - L_n, 0)
while True:
(x1, y1) = curve.mul(k, curve_obj.base_point, curve_obj.curve)
r = x1 % curve_obj.order
if r == 0:
continue
k_neg = numbertheory.inverse_of(k, n)
s = (k_neg * (z + r * private_key)) % n
if s == 0:
continue
break
return (r, s)
def mul_inv(self, n):
return numbertheory.inverse_of(n, self.p)
def div(a, b):
return (a * numbertheory.inverse_of(b, curve_obj.order)) % curve_obj.order
def div(a, b):
return (a *
numbertheory.inverse_of(b, curve_obj.order)) % curve_obj.order
