def generateRPoints(params):
curve = ECCurve(params.a, params.b, params.p, params.n, params.gx,
params.gy)
pointG = ECPoint(params.gx, params.gy)
pointQ = ECPoint(params.qx, params.qy)
rPoints = []
for i in range(NUM_R_POINTS):
a = random.randint(2, curve.n)
b = random.randint(2, curve.n)
aG = curve.multiply(a, pointG)
bQ = curve.multiply(b, pointQ)
r = curve.add(aG, bQ)
e = {}
e['a'] = a
e['b'] = b
e['x'] = r.x
e['y'] = r.y
rPoints.append(e)
return rPoints
def generateRPoints(params):
curve = ECCurve(params.a, params.b, params.p, params.n, params.gx, params.gy)
pointG = ECPoint(params.gx, params.gy)
pointQ = ECPoint(params.qx, params.qy)
rPoints = []
for i in range(NUM_R_POINTS):
a = random.randint(2, curve.n)
b = random.randint(2, curve.n)
aG = curve.multiply(a, pointG)
bQ = curve.multiply(b, pointQ)
r = curve.add(aG, bQ)
e = {}
e['a'] = a
e['b'] = b
e['x'] = r.x
e['y'] = r.y
rPoints.append(e)
return rPoints
class RhoSolver:
point1 = None
p1Len = 0
point2 = None
p2Len = 0
endPoint = None
params = None
curve = None
a1 = None
b1 = None
a2 = None
b2 = None
rPoints = None
solved = False
k = None
'''
Constructs a new RhoSolver object
'''
def __init__(self, params, rPoints, a1, b1, a2, b2, endPoint):
# Get params
self.params = params
self.a1 = a1
self.b1 = b1
self.a2 = a2
self.b2 = b2
self.endPoint = endPoint
self.rPoints = rPoints
# Set up curve
self.curve = ECCurve(params.a, params.b, params.p, params.n, params.gx,
params.gy)
# Compute starting points
g = ECPoint(self.params.gx, self.params.gy)
q = ECPoint(self.params.qx, self.params.qy)
self.point1 = self.curve.add(self.curve.multiply(a1, g),
self.curve.multiply(b1, q))
self.point2 = self.curve.add(self.curve.multiply(a2, g),
self.curve.multiply(b2, q))
# Set up array of random walk points
#self.rPoints = []
#for rPoint in rPoints:
# self.rPoints.append(ECPoint(rPoint['x'], rPoint['y']))
'''
Checks if the end point in the first random walk is the
start point of the second walk
Robin Hood is a reference to character in English
folklore hero who could shoot a second arrow on the
exact trajectory as the first.
'''
def _isRobinHood(self):
currentPoint = self.point1
count = 0
while True:
idx = currentPoint.x & 0x1f
if currentPoint.x == self.point2.x and currentPoint.y == self.point2.y:
return True
if currentPoint.x == self.endPoint.x and currentPoint.y == self.endPoint.y:
return False
# Iterate to next point
currentPoint = self.curve.add(
currentPoint,
ECPoint(self.rPoints[idx]['x'], self.rPoints[idx]['y']))
'''
Gets the total length of the random walk
'''
def _getWalkLength(self, startA, startB, startPoint):
point = startPoint
a = startA
b = startB
i = 0
length = 1
# We want to terminate the walk if it is statistically too long
limit = (2**self.params.dBits) * 4
while True:
idx = point.x & 0x1f
length = length + 1
if point.x == self.endPoint.x and point.y == self.endPoint.y:
print("Found endpoint")
return length
break
# Increment the point and coefficients
r = ECPoint(self.rPoints[idx]['x'], self.rPoints[idx]['y'])
point = self.curve.add(point, r)
a = (a + self.rPoints[idx]['a']) % self.curve.n
b = (b + self.rPoints[idx]['b']) % self.curve.n
if i > limit:
print("Walk is too long. Terminating")
return -1
return length
'''
Gets the next point in the random walk
'''
def _nextPoint(self, a, b, point):
idx = point.x & 0x1f
newPoint = self.curve.add(
point, ECPoint(self.rPoints[idx]['x'], self.rPoints[idx]['y']))
newA = (a + self.rPoints[idx]['a']) % self.curve.n
newB = (b + self.rPoints[idx]['b']) % self.curve.n
return newA, newB, newPoint
def _countWalkLengths(self):
print("Counting walk #1 length")
self.p1Len = self._getWalkLength(self.a1, self.b1, self.point1)
#if self.p1Len < 0:
# return None, None, None, None, None, None
print(str(self.p1Len))
print("Counting walk #2 length")
self.p2Len = self._getWalkLength(self.a2, self.b2, self.point2)
#if p2Len < 0:
# return None, None, None, None, None, None
print(str(self.p2Len))
# For simplicity, we want P1 to always be the longer one
if self.p1Len < self.p2Len:
self.a1, self.a2 = swap(self.a1, self.a2)
self.b1, self.b2 = swap(self.b1, self.b2)
self.point1, self.point2 = swap(self.point1, self.point2)
self.p1Len, self.p2Len = swap(self.p1Len, self.p2Len)
'''
Given two walks with the same ending point, it finds where the walks collide.
'''
#curve, g, q, a1Start, b1Start, p1Start, a2Start, b2Start, p2Start, endPoint, rPoints, dBits):
def _findCollision(self):
self._countWalkLengths()
print("Checking for Robin Hood")
if self._isRobinHood():
print("It's a Robin Hood :(")
return None, None, None, None, None, None
else:
print("Not a Robin Hood :)")
point1 = self.point1
point2 = self.point2
diff = self.p1Len - self.p2Len
print("Stepping " + str(diff) + " times")
a1 = self.a1
b1 = self.b1
a2 = self.a2
b2 = self.b2
for i in xrange(diff):
a1, b1, point1 = self._nextPoint(a1, b1, point1)
print("Searching for collision")
while True:
if (point1.x == self.endPoint.x and point1.y
== self.endPoint.y) or (point2.x == self.endPoint.x
and point2.y == self.endPoint.y):
print("Reached the end :(")
return None
a1Old = a1
b1Old = b1
point1Old = point1
a2Old = a2
b2Old = b2
point2Old = point2
a1, b1, point1 = self._nextPoint(a1, b1, point1)
a2, b2, point2 = self._nextPoint(a2, b2, point2)
if point1.x == point2.x and point1.y == point2.y:
print("Found collision!")
print(
hex(a1) + " " + hex(b1) + " " + hex(point1.x) + " " +
hex(point1.y))
print(
hex(a2) + " " + hex(b2) + " " + hex(point2.x) + " " +
hex(point2.y))
return a1, b1, point1, a2, b2, point2
def solve(self):
a1, b1, point1, a2, b2, point2 = self._findCollision()
if a1 == None:
self.solved = False
return
k = (((a1 - a2) % self.curve.n) *
invm(b2 - b1, self.curve.n)) % self.curve.n
# Verify
r = self.curve.multiply(k, self.curve.bp)
if r.x != self.params.qx or r.y != self.params.qy:
print("Verification failed")
self.solved = False
else:
print("Verification successful")
self.solved = True
self.k = k
class RhoSolver:
point1 = None
p1Len = 0
point2 = None
p2Len = 0
endPoint = None
params = None
curve = None
a1 = None
b1 = None
a2 = None
b2 = None
rPoints = None
solved = False
k = None
'''
Constructs a new RhoSolver object
'''
def __init__(self, params, rPoints, a1, b1, a2, b2, endPoint):
# Get params
self.params = params
self.a1 = a1
self.b1 = b1
self.a2 = a2
self.b2 = b2
self.endPoint = endPoint
self.rPoints = rPoints
# Set up curve
self.curve = ECCurve(params.a, params.b, params.p, params.n, params.gx, params.gy)
# Compute starting points
g = ECPoint(self.params.gx, self.params.gy)
q = ECPoint(self.params.qx, self.params.qy)
self.point1 = self.curve.add(self.curve.multiply(a1, g), self.curve.multiply(b1, q))
self.point2 = self.curve.add(self.curve.multiply(a2, g), self.curve.multiply(b2, q))
# Set up array of random walk points
#self.rPoints = []
#for rPoint in rPoints:
# self.rPoints.append(ECPoint(rPoint['x'], rPoint['y']))
'''
Checks if the end point in the first random walk is the
start point of the second walk
Robin Hood is a reference to character in English
folklore hero who could shoot a second arrow on the
exact trajectory as the first.
'''
#def _checkForRobinHood(curve, start, end, start2, rPoints):
def _isRobinHood(self):
currentPoint = self.point1
count = 0
while True:
idx = currentPoint.x & 0x1f
if currentPoint.x == self.point2.x and currentPoint.y == self.point2.y:
return True
if currentPoint.x == self.endPoint.x and currentPoint.y == self.endPoint.y:
return False
# Iterate to next point
currentPoint = self.curve.add(currentPoint, ECPoint(self.rPoints[idx]['x'], self.rPoints[idx]['y']))
'''
Gets the total length of the random walk
'''
#def _getWalkLength(curve, startA, startB, startPoint, endPoint, rPoints, dBits):
def _getWalkLength(self, startA, startB, startPoint):
point = startPoint
a = startA
b = startB
i = 0
length = 1
# We want to terminate the walk if it is statistically too long
limit = (2**self.params.dBits) * 4
while True:
idx = point.x & 0x1f
length = length + 1
if point.x == self.endPoint.x and point.y == self.endPoint.y:
print("Found endpoint")
return length
break
# Increment the point and coefficients
r = ECPoint(self.rPoints[idx]['x'], self.rPoints[idx]['y'])
point = self.curve.add(point, r)
a = (a + self.rPoints[idx]['a']) % self.curve.n
b = (b + self.rPoints[idx]['b']) % self.curve.n
if i > limit:
print("Walk is too long. Terminating")
return -1
return length
'''
Gets the next point in the random walk
'''
def _nextPoint(self, a, b, point):
idx = point.x & 0x1f
newPoint = self.curve.add(point, ECPoint(self.rPoints[idx]['x'], self.rPoints[idx]['y']))
newA = (a + self.rPoints[idx]['a']) % self.curve.n
newB = (b + self.rPoints[idx]['b']) % self.curve.n
return newA, newB, newPoint
def _countWalkLengths(self):
print("Counting walk #1 length")
self.p1Len = self._getWalkLength(self.a1, self.b1, self.point1)
#if self.p1Len < 0:
# return None, None, None, None, None, None
print(str(self.p1Len))
print("Counting walk #2 length")
self.p2Len = self._getWalkLength(self.a2, self.b2, self.point2)
#if p2Len < 0:
# return None, None, None, None, None, None
print(str(self.p2Len))
# For simplicity, we want P1 to always be the longer one
if self.p1Len < self.p2Len:
self.a1, self.a2 = swap(self.a1, self.a2)
self.b1, self.b2 = swap(self.b1, self.b2)
self.point1, self.point2 = swap(self.point1, self.point2)
self.p1Len, self.p2Len = swap(self.p1Len, self.p2Len)
'''
Given two walks with the same ending point, it finds where the walks collide.
'''
#curve, g, q, a1Start, b1Start, p1Start, a2Start, b2Start, p2Start, endPoint, rPoints, dBits):
def _findCollision(self):
self._countWalkLengths()
print("Checking for Robin Hood")
if self._isRobinHood():
print("It's a Robin Hood :(")
return None, None, None, None, None, None
else:
print("Not a Robin Hood :)")
point1 = self.point1
point2 = self.point2
diff = self.p1Len - self.p2Len
print("Stepping " + str(diff) + " times")
a1 = self.a1
b1 = self.b1
a2 = self.a2
b2 = self.b2
for i in xrange(diff):
a1, b1, point1 = self._nextPoint(a1, b1, point1)
print("Searching for collision")
while True:
if (point1.x == self.endPoint.x and point1.y == self.endPoint.y) or (point2.x == self.endPoint.x and point2.y == self.endPoint.y):
print("Reached the end :(")
return None
a1Old = a1
b1Old = b1
point1Old = point1
a2Old = a2
b2Old = b2
point2Old = point2
a1, b1, point1 = self._nextPoint(a1, b1, point1)
a2, b2, point2 = self._nextPoint(a2, b2, point2)
if point1.x == point2.x and point1.y == point2.y:
print("Found collision!")
print(hex(a1) + " " + hex(b1) + " " + hex(point1.x) + " " + hex(point1.y))
print(hex(a2) + " " + hex(b2) + " " + hex(point2.x) + " " + hex(point2.y))
return a1, b1, point1, a2, b2, point2
def solve(self):
a1, b1, point1, a2, b2, point2 = self._findCollision()
if a1 == None:
self.solved = False
return
k = (((a1 - a2)%self.curve.n) * invm(b2 - b1, self.curve.n)) % self.curve.n
# Verify
r = self.curve.multiply(k, self.curve.bp)
if r.x != self.params.qx or r.y != self.params.qy:
print("Verification failed")
self.solved = False
else:
print("Verification successful")
self.solved = True
self.k = k