def interleaving_sliding_window(self, k, l):
"""Algorithm 3.5.1 menezez, 'Interleaving with NAF' """
R = None
naf = [w_NAF(k, self.w1), w_NAF(l, self.w2)]
#print(naf)
_l = max([len(naf[0]), len(naf[1])])
#padding stage
for i in range(_l - len(naf[0])):
naf[0].insert(i, 0)
for i in range(_l - len(naf[1])):
naf[1].insert(i, 0)
for i in range(_l):
if R is None:
R = None
else:
R = R.point_double()
for j in range(2):
if naf[j][i] != 0:
if naf[j][i] > 0:
if j == 0:
R = self._P[naf[j][i]].add(R)
else:
R = self._Q[naf[j][i]].add(R)
else:
if j == 0:
R = self._P[-naf[j][i]].inverse().add(R)
else:
R = self._Q[-naf[j][i]].inverse().add(R)
return R
def sliding_window_left_to_right_scalar_mul(self, d):
d = w_NAF(d, self.w)
Q = None
i = 0
while i < len(d):
if d[i] == 0:
if Q is None:
Q = None
else:
Q = Q.point_double()
i += 1
else:
s = max(len(d) - i - self.w + 1, 0)
s = len(d) - 1 - s
while d[s] == 0:
s -= 1
u = NAF(d[i:s + 1])
for j in range(1, i - s + 2):
if Q is not None:
Q = Q.point_double()
else:
Q = None
if u > 0:
Q = self._P[u].add(Q)
if u < 0:
Q = Q.add(self._P[-u].inverse())
i = 1 + s
return Q
def interleaving_sliding_window(self, k, l):
"""Algorithm 3.5.1 menezez, 'Interleaving with NAF' """
#_P = {}
# _Q = {}
R = None
naf = [w_NAF(k, self.w1), w_NAF(l, self.w2)]
#print(naf)
_l = max([len(naf[0]), len(naf[1])])
#precom stage
# for i in range(1, 2**(w1 - 1), 2):
# _P[i] = self.point1.right_to_left_scalar_mul(i)
# for j in range(1, 2**(w2 - 1), 2):
# _Q[j] = self.point2.right_to_left_scalar_mul(j)
#padding stage
for i in range(_l - len(naf[0])):
naf[0].insert(i, 0)
for i in range(_l - len(naf[1])):
naf[1].insert(i, 0)
for i in range(_l):
if R is None:
R = None
else:
R = R.point_double()
for j in range(2):
if naf[j][i] != 0:
if naf[j][i] > 0:
if j == 0:
R = self._P[naf[j][i]].add(R)
else:
R = self._Q[naf[j][i]].add(R)
else:
if j == 0:
R = self._P[-naf[j][i]].inverse().add(R)
else:
R = self._Q[-naf[j][i]].inverse().add(R)
return R
def window_NAF_multiplication(self, d):
d = w_NAF(d, self.w)
# print(d)
#_P = {}
#for i in range(1, 2**(w-1), 2):
# _P[i] = self.right_to_left_scalar_mul(i)
Q = None
for i in range(0, len(d)):
if Q is None:
Q = None
else:
Q = Q.point_double()
if d[i] != 0:
if d[i] > 0:
Q = self.window_naf_precom[d[i]].add(Q)
else:
Q = self.window_naf_precom[-d[i]].inverse().add(Q)
return Q
def sliding_window_left_to_right_scalar_mul(self, d):
"""
:param P: punct de pe o curba eliptica
:param d: scalarul
:param C: curba eliptica
:return: punctul dP
"""
d = w_NAF(d, self.w)
#print(d)
Q = None
i = 0
#m = 2 * ((2 ** w - (-1)**w) // 3) - 1
#_P = {}
#for _i in range(1, m + 1, 2):
#_P[_i] = self.left_to_right_scalar_mul(_i)
while i < len(d):
# print("Iteratie Noua")
if d[i] == 0:
if Q is None:
Q = None
else:
Q = Q.point_double()
i += 1
else:
s = max(len(d) - i - self.w + 1, 0)
s = len(d) - 1 - s
#print("s is " + str(s))
while d[s] == 0:
s -= 1
u = NAF(d[i:s + 1])
#print("u is " + str(u))
for j in range(1, i - s + 2):
if Q is not None:
Q = Q.point_double()
else:
Q = None
if u > 0:
Q = self._P[u].add(Q)
if u < 0:
Q = Q.add(self._P[-u].inverse())
i = 1 + s
return Q
def left_to_right_scalar_mul(self, d):
""":return dP
:param P : punct de pe o curba eliptica
:param d : scalar
"""
signed_d = w_NAF(d, 2)
result = None
for i in signed_d:
if result is None:
result = None
else:
result = result.point_double()
if i == 1:
result = self.point.add(result)
if i == -1:
result = self.point.inverse().add(result)
return result