def _lambda(P, other=None):
if other:
Q = other
a = (Q.y - P.y) % P.curve.field
b = Q.x - P.x
aux = abs(a)
d = gcd(aux, b)
a /= d; b /= d
a = (a + P.curve.field) % P.curve.field
if (a % b != 0):
b = invmod(b, P.curve.field)
return a * b % P.curve.field
return a / b
else:
a = (3*P.x*P.x + P.curve.A) % P.curve.field
b = 2*P.y
aux = abs(a)
d = gcd(aux, b)
a /= d; b /= d
a = (a + P.curve.field) % P.curve.field
if (a % b != 0):
b = invmod(b, P.curve.field)
return a * b % P.curve.field
return a / b
def _lambda(P, other=None):
if other:
Q = other
a = (Q.y - P.y) % P.curve.field
b = Q.x - P.x
aux = abs(a)
d = gcd(aux, b)
a /= d
b /= d
a = (a + P.curve.field) % P.curve.field
if (a % b != 0):
b = invmod(b, P.curve.field)
return a * b % P.curve.field
return a / b
else:
a = (3 * P.x * P.x + P.curve.A) % P.curve.field
b = 2 * P.y
aux = abs(a)
d = gcd(aux, b)
a /= d
b /= d
a = (a + P.curve.field) % P.curve.field
if (a % b != 0):
b = invmod(b, P.curve.field)
return a * b % P.curve.field
return a / b
def server_func(n, return_dict):
triples = {}
triple_collided = []
while (True):
arg = server_pipe.recv()
a = arg[0]
b = arg[1]
P = arg[2]
P = str(P)
if (triples.has_key(P)):
triple_collided = arg
break
triples[P] = [a, b]
am = triple_collided[0]
bm = triple_collided[1]
P = str(triple_collided[2])
an = triples.get(P)[0]
bn = triples.get(P)[1]
if (bn == bm):
raise ArithmeticError('Undefined value')
f = an - am
g = invmod(bm - bn, n)
ret = (f * g) % n
x = (ret + n) % n
return_dict[0] = x
def client_func(E, P, Q):
n = E.order
gen = SystemRandom()
an = gen.randrange(n)
bn = gen.randrange(n)
am = an
bm = bn
Xn = P * an + Q * bn
Xm = Xn
while (True):
i = __H(Xn, L)
Xn += R[i]
an += c[i]
bn += d[i]
for j in range(2):
h = __H(Xm, L)
Xm += R[h]
am += c[h]
bm += d[h]
if Xn == Xm:
break
if (bn == bm):
raise ArithmeticError('Undefined value')
f = an - am
g = invmod(bm - bn, n)
ret = (f * g) % n
ret = (ret + n) % n
sendToServer(ret)
def client_func(E, P, Q):
n = E.order
gen = SystemRandom()
an = gen.randrange(n)
bn = gen.randrange(n)
am = an
bm = bn
Xn = P*an + Q*bn
Xm = Xn
while (True):
i = __H(Xn, L)
Xn += R[i]
an += c[i]
bn += d[i]
for j in range(2):
h = __H(Xm, L)
Xm += R[h]
am += c[h]
bm += d[h]
if Xn == Xm:
break
if (bn == bm):
raise ArithmeticError('Undefined value')
f = an-am
g = invmod(bm-bn, n)
ret = (f * g) % n
ret = (ret + n) % n
sendToServer(ret)
def original(E, P, Q):
print 'Algorithm: original'
a = []
b = []
v = []
R = P
n = E.order()
v.append(R)
a.append(1)
b.append(0)
i = 1
while (True):
# print str(i) + ' | a: ' + str(a[-1]) + ' | b: ' + str(b[-1]),
# s = 0
y = v[-1].y
if (y >= 0 and y < 15):
v.append(v[-1] + Q)
a.append(a[-1])
b.append(b[-1] + 1)
# s = 1
elif y >= 15 and y < 30:
v.append(v[-1] * 2)
a.append(2 * a[-1] % n)
b.append(2 * b[-1] % n)
# s = 2
else:
v.append(v[-1] + P)
a.append(a[-1] + 1)
b.append(b[-1])
# s = 3
# print ' | S:' + str(s),
# print '\t| (' + str(v[i].x) + ', ' + str(v[i].y) + ')'
if (v[i].x == v[i / 2].x and v[i].y == v[i / 2].y and i > 2
and i % 2 == 0):
# print 'FOUND!\n' + str(i) + ': (' + str(v[i].x) + ', ' + str(v[i].y) + ')',
# print 'and ' + str(i/2) + ': (' + str(v[i/2].x) + ', ' + str(v[i/2].y) + ')'
am = a[i / 2]
an = a[i]
bm = b[i / 2]
bn = b[i]
break
i += 1
if bm == bn:
raise ArithmeticError('Undefined value')
c = an - am
d = invmod(bm - bn, n)
ret = (c * d) % n
return (ret + n) % n
def original(E, P, Q):
print 'Algorithm: original'
a = []; b = []; v = []
R = P
n = E.order()
v.append(R)
a.append(1)
b.append(0)
i = 1
while (True):
# print str(i) + ' | a: ' + str(a[-1]) + ' | b: ' + str(b[-1]),
# s = 0
y = v[-1].y
if (y >= 0 and y < 15):
v.append(v[-1] + Q)
a.append(a[-1])
b.append(b[-1] + 1)
# s = 1
elif y >= 15 and y < 30:
v.append(v[-1] * 2)
a.append(2*a[-1] % n)
b.append(2*b[-1] % n)
# s = 2
else:
v.append(v[-1] + P)
a.append(a[-1] + 1)
b.append(b[-1])
# s = 3
# print ' | S:' + str(s),
# print '\t| (' + str(v[i].x) + ', ' + str(v[i].y) + ')'
if (v[i].x == v[i/2].x and
v[i].y == v[i/2].y and
i > 2 and i % 2 == 0):
# print 'FOUND!\n' + str(i) + ': (' + str(v[i].x) + ', ' + str(v[i].y) + ')',
# print 'and ' + str(i/2) + ': (' + str(v[i/2].x) + ', ' + str(v[i/2].y) + ')'
am = a[i/2]
an = a[i]
bm = b[i/2]
bn = b[i]
break
i += 1
if bm == bn:
raise ArithmeticError('Undefined value')
c = an - am
d = invmod(bm - bn, n)
ret = (c * d) % n
return (ret + n) % n
def test_has_invmod():
for modulus in range(2, 1000, 31):
for a in range(2, modulus, 5):
if has_invmod(a, modulus):
x = invmod(a, modulus)
assert (a * x) % modulus == 1
else:
assert gcd(a, modulus) != 1
with pytest.raises(ValueError):
has_invmod(1, 1)
with pytest.raises(ValueError):
has_invmod(1, 0)
with pytest.raises(ValueError):
has_invmod(1, -100)
with pytest.raises(TypeError):
has_invmod("qwe", 10)
with pytest.raises(TypeError):
has_invmod(10, "qwe")
def serial(E, P, Q):
print 'Algorithm: serial'
c = []
d = []
R = []
n = E.order
L = 4
gen = SystemRandom()
for i in range(L):
c.append(gen.randrange(n - 1) + 1)
d.append(gen.randrange(n - 1) + 1)
R.append(P * c[-1] + Q * d[-1])
an = gen.randrange(n)
bn = gen.randrange(n)
am = an
bm = bn
Xn = P * an + Q * bn
Xm = Xn
while (True):
i = __H(Xn, L)
Xn += R[i]
an += c[i]
bn += d[i]
for j in range(2):
h = __H(Xm, L)
Xm += R[h]
am += c[h]
bm += d[h]
if Xn == Xm:
break
if (bn == bm):
raise ArithmeticError("Undefined value")
f = an - am
g = invmod(bm - bn, n)
ret = (f * g) % n
return (ret + n) % n
def serial(E, P, Q):
print 'Algorithm: serial'
c = []; d = []; R = []
n = E.order
L = 4
gen = SystemRandom()
for i in range(L):
c.append(gen.randrange(n-1)+1)
d.append(gen.randrange(n-1)+1)
R.append(P*c[-1] + Q*d[-1])
an = gen.randrange(n)
bn = gen.randrange(n)
am = an
bm = bn
Xn = P*an + Q*bn
Xm = Xn
while (True):
i = __H(Xn, L)
Xn += R[i]
an += c[i]
bn += d[i]
for j in range(2):
h = __H(Xm, L)
Xm += R[h]
am += c[h]
bm += d[h]
if Xn == Xm:
break
if (bn == bm):
raise ArithmeticError("Undefined value")
f = an-am
g = invmod(bm-bn, n)
ret = (f * g) % n
return (ret + n) % n
def test_invmod():
for modulus in range(3, 1001, 37):
for a in range(2, modulus, 5):
if has_invmod(a, modulus):
x = invmod(a, modulus)
assert (a * x) % modulus == 1
else:
with pytest.raises(ValueError):
invmod(a, modulus)
with pytest.raises(ValueError):
invmod(1, 1)
with pytest.raises(ValueError):
invmod(1, 0)
with pytest.raises(ValueError):
invmod(1, -100)
with pytest.raises(TypeError):
invmod("qwe", 10)
with pytest.raises(TypeError):
invmod(10, "qwe")
from fractions import gcd from libnum import modular N1 = 9055404640500300109405801152935663267176218320785348541566663982172162265778445107320065187449062375525002632043722734566593185461999286625234528036605141 N2 = 3367646059138877442579820972831876412006279917097809082279412851693123955964282545145500497393579598954859534731890460229194372339215098506788375050698427369 c = 0xf5ed9da29d8d260f22657e091f34eb930bc42f26f1e023f863ba13bee39071d1ea988ca62b9ad59d4f234fa7d682e22ce3194bbe5b801df3bd976db06b944da e = 65537 q = gcd(N1, N2) d = modular.invmod(e, (q-1)*(N1/q-1)) print hex(pow(c, d, N1))[2:-1]
