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 getCurveByName(curveName): curve = None if (curveName == "secp521r1"): curve = secp521r1 if (curveName == "secp256k1"): curve = secp256k1 if (curveName == "ecp131p"): curve = ecp131 if curve == None: return None return ECCurve(curve.a, curve.b, curve.p, curve.n, curve.x, curve.y)
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))
def createContext(params, name, email): ctx = ECDLPContext(name) ctx.params = params ctx.rPoints = generateRPoints(ctx.params) Database.createContext(ctx.name, ctx.email, ctx.params, ctx.rPoints) ctx.curve = ECCurve(ctx.params.a, ctx.params.b, ctx.params.p, ctx.params.n, ctx.params.gx, ctx.params.gy) ctx.pointG = ECPoint(ctx.params.gx, ctx.params.gy) ctx.pointQ = ECPoint(ctx.params.qx, ctx.params.qy) ctx.database = Database.getConnection(ctx.name) return ctx
def loadContext(name): ctx = ECDLPContext(name) ctx.database = Database.getConnection(ctx.name) ctx.database.open() ctx.rPoints = ctx.database.getRPoints() ctx.params = ctx.database.getParams() ctx.status = ctx.database.getStatus() ctx.solution = ctx.database.getSolution() ctx.collisions = ctx.database.getNumCollisions() ctx.database.close() ctx.curve = ECCurve(ctx.params.a, ctx.params.b, ctx.params.p, ctx.params.n, ctx.params.gx, ctx.params.gy) ctx.pointG = ECPoint(ctx.params.gx, ctx.params.gy) ctx.pointQ = ECPoint(ctx.params.qx, ctx.params.qy) return ctx
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