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#
# Elliptic Curve Equation
#
# y^2 = x^3 + A*x + B (mod P)
#
from .math import Math
from .point import Point
class CurveFp:
def __init__(self, A, B, P, N, Gx, Gy, name, oid, nistName=None):
self.A = A
self.B = B
self.P = P
self.N = N
self.G = Point(Gx, Gy)
self.name = name
self.nistName = nistName
self.oid = oid # ASN.1 Object Identifier
def contains(self, p):
"""
Verify if the point `p` is on the curve
:param p: Point p = Point(x, y)
:return: boolean
"""
if not 0 <= p.x <= self.P - 1:
return False
if not 0 <= p.y <= self.P - 1:
return False
if (p.y**2 - (p.x**3 + self.A * p.x + self.B)) % self.P != 0:
return False
return True
def length(self):
return (1 + len("%x" % self.N)) // 2
def y(self, x, isEven):
ySquared = (pow(x, 3, self.P) + self.A * x + self.B) % self.P
y = Math.modularSquareRoot(ySquared, self.P)
if isEven != (y % 2 == 0):
y = self.P - y
return y
_curvesByOid = {tuple(curve.oid): curve for curve in []}
def add(curve):
_curvesByOid[tuple(curve.oid)] = curve
def getByOid(oid):
if oid not in _curvesByOid:
raise Exception("Unknown curve with oid {oid}; The following are registered: {names}".format(
oid=".".join([str(number) for number in oid]),
names=", ".join([curve.name for curve in _curvesByOid.values()]),
))
return _curvesByOid[oid]
secp256k1 = CurveFp(
name="secp256k1",
A=0x0000000000000000000000000000000000000000000000000000000000000000,
B=0x0000000000000000000000000000000000000000000000000000000000000007,
P=0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f,
N=0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141,
Gx=0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798,
Gy=0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8,
oid=[1, 3, 132, 0, 10]
)
prime256v1 = CurveFp(
name="prime256v1",
nistName="P-256",
A=0xffffffff00000001000000000000000000000000fffffffffffffffffffffffc,
B=0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b,
P=0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff,
N=0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551,
Gx=0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296,
Gy=0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5,
oid=[1, 2, 840, 10045, 3, 1, 7],
)
p256 = prime256v1
add(secp256k1)
add(prime256v1)
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