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Add x() and y() functions for points to bip-schnorr

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This commit is contained in:
Jonas Nick 2019-09-26 21:18:53 +00:00
parent 8d893f9c06
commit 7e273fbda6
1 changed files with 15 additions and 9 deletions
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24
bip-schnorr/reference.py
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@ -11,19 +11,25 @@ def tagged_hash(tag, msg):
tag_hash = hashlib.sha256(tag.encode()).digest()
return hashlib.sha256(tag_hash + tag_hash + msg).digest()
def x(P):
return P[0]
def y(P):
return P[1]
def point_add(P1, P2):
if (P1 is None):
return P2
if (P2 is None):
return P1
if (P1[0] == P2[0] and P1[1] != P2[1]):
if (x(P1) == x(P2) and y(P1) != y(P2)):
return None
if (P1 == P2):
lam = (3 * P1[0] * P1[0] * pow(2 * P1[1], p - 2, p)) % p
lam = (3 * x(P1) * x(P1) * pow(2 * y(P1), p - 2, p)) % p
else:
lam = ((P2[1] - P1[1]) * pow(P2[0] - P1[0], p - 2, p)) % p
x3 = (lam * lam - P1[0] - P2[0]) % p
return (x3, (lam * (P1[0] - x3) - P1[1]) % p)
lam = ((y(P2) - y(P1)) * pow(x(P2) - x(P1), p - 2, p)) % p
x3 = (lam * lam - x(P1) - x(P2)) % p
return (x3, (lam * (x(P1) - x3) - y(P1)) % p)
def point_mul(P, n):
R = None
@ -37,7 +43,7 @@ def bytes_from_int(x):
return x.to_bytes(32, byteorder="big")
def bytes_from_point(P):
return bytes_from_int(P[0])
return bytes_from_int(x(P))
def point_from_bytes(b):
x = int_from_bytes(b)
@ -66,12 +72,12 @@ def schnorr_sign(msg, seckey0):
if not (1 <= seckey0 <= n - 1):
raise ValueError('The secret key must be an integer in the range 1..n-1.')
P = point_mul(G, seckey0)
seckey = seckey0 if (jacobi(P[1]) == 1) else n - seckey0
seckey = seckey0 if (jacobi(y(P)) == 1) else n - seckey0
k0 = int_from_bytes(tagged_hash("BIPSchnorrDerive", bytes_from_int(seckey) + msg)) % n
if k0 == 0:
raise RuntimeError('Failure. This happens only with negligible probability.')
R = point_mul(G, k0)
k = n - k0 if (jacobi(R[1]) != 1) else k0
k = n - k0 if (jacobi(y(R)) != 1) else k0
e = int_from_bytes(tagged_hash("BIPSchnorr", bytes_from_point(R) + bytes_from_point(P) + msg)) % n
return bytes_from_point(R) + bytes_from_int((k + e * seckey) % n)
@ -91,7 +97,7 @@ def schnorr_verify(msg, pubkey, sig):
return False
e = int_from_bytes(tagged_hash("BIPSchnorr", sig[0:32] + pubkey + msg)) % n
R = point_add(point_mul(G, s), point_mul(P, n - e))
if R is None or jacobi(R[1]) != 1 or R[0] != r:
if R is None or jacobi(y(R)) != 1 or x(R) != r:
return False
return True