I have been trying to run a sage code for doing weil-pairing which gives the following error message: ' /usr/lib/sagemath/local/bin/sage-python: line 2: 15172 Segmentation fault (core dumped) sage -python "$@" '
I tried sage versions 7.2, 7.3, and 7.4 but still getting same error. I am using Ubuntu 14.04. But it works in another system running Ubuntu. Someone please help.
# Weil Pairing Example
# Example 5.43 in IMC
# E: y^2 = x^3 + 30x + 34 mod 631
p = 631
a = 30
b = 34
E = EllipticCurve(GF(p), [a, b])
print E
P = E((36, 60))
Q = E((121, 387))
n = 5
S = E((0, 36))
print "P =", P.xy()
print "Q =", Q.xy()
print "#P = #Q =", n
var('x y')
def g(P, Q):
(x_P, y_P) = P.xy()
(x_Q, y_Q) = Q.xy()
if x_P == x_Q and y_P + y_Q == 0:
return x - x_P
if P == Q:
slope = (3 * x_P^2 + a)/(2 * y_P)
else:
slope = (y_P - y_Q)/(x_P - x_Q)
return (y - y_P - slope * (x - x_P))/(x + x_P + x_Q - slope^2)
def miller(m, P):
m = bin(m)[3:]
n = len(m)
T = P
f = 1
for i in range(n):
f = f^2 * g(T, T)
T = T + T
if int(m[i]) == 1:
f = f * g(T, P)
T = T + P
return f
def eval_miller(P, Q):
f = miller(n, P)
(x1, y1) = Q.xy()
return f(x = x1, y = y1)
def weil_pairing(P, Q, S):
num = eval_miller(P, Q+S)/eval_miller(P, S)
den = eval_miller(Q, P-S)/eval_miller(Q, -S)
return (num/den)
e = weil_pairing(P, Q, S)
print "e(P, Q) =", e
# e^n = 1
print "e(P, Q)^n =", e^n
P3 = P * 3
Q4 = Q * 4
e12 = weil_pairing(P3, Q4, S)
print "[3]P =", P3.xy()
print "[4]Q =", Q4.xy()
print "e([3]P, [4]Q) =", e12
print "e(P, Q)^12 =", e^12
