def test(a, p, target):
E.params(a, -a, p)
s = set()
e = E(1, 1) + E(1, 1)
cnt = 1
while e.P != (1, 1):
e = e + E(1, 1)
cnt = cnt + 1
return cnt == target
def test(a, p):
E.params(a, -a, p)
s = set()
e = E(1, 1) + E(1, 1)
cnt = 1
while e.P != (1, 1):
e = e + E(1, 1)
cnt = cnt + 1
print(cnt)
def order(a):
s = set((1, 1))
count = 0
Q = E(1, 1)
while (Q + E(1, 1)).P not in s:
Q = Q + E(1, 1)
s.add(Q.P)
count += 1
print(count)
return count
def doubleAndAdd(P, n):
R = E(0)
Q = P
while n > 0:
if (n % 2) == 1: R = R + Q
n = n // 2
Q = Q + Q
return R
def fastMult(e, poww):
res = E(0)
z = e
while (poww > 0):
res = res + (poww % 2) * z
poww = poww // 2
z = z + z
return res
def check(p):
a = 1
E.params(a, -a, p)
while True:
a += 1
E.params(a, -a, p)
if doubleAndAdd(E(1, 1), 1000000) == E(0):
print(a)
if order(a) == 1000000:
return a
def fastMult(e, poww):
res = E(0)
z = e
while (poww > 0):
res = res + (poww % 2) * z
poww = poww // 2
z = z + z
return res
if __name__ == '__main__':
p = 36028797018964019
q = 36028796930959053
a = 12730951283832694
E.params(a, -a, p)
s = 788139760620004
e = 57233552642126
s1 = fastMult(E(1, 1), e).P[0]
d = 8675309
s2 = ((d + s * s1) * inv(e, q)) % q
print fastMult(E(1, 1), q)
print fastMult(E(1, 1), s)
print s1
print s2
res = res + (poww % 2) * z
poww = poww // 2
z = z + z
return res
def test(a, p, target):
E.params(a, -a, p)
s = set()
e = E(1, 1) + E(1, 1)
cnt = 1
while e.P != (1, 1):
e = e + E(1, 1)
cnt = cnt + 1
return cnt == target
if __name__ == '__main__':
p = 1000003
trials = 100000
target = 1000000
for i in range(trials):
a = random.randrange(1, p)
E.params(a, -a, p)
if E(0) == fastMult(E(1, 1), target): # see if order(E(1, 1)) | target
if test(a, p, target): # see if order(E(1, 1)) == target
print(str(a) + " " + str(p))
a = 12730951283832694
p = 36028797018964019
ph = 36028796930959053
def f(ee, pp, qq, P, Q):
if 0 <= ee.P[0] < p / 3: return (ee + P, (pp + 1) % ph, qq)
elif p / 3 <= ee.P[0] < 2 * p / 3:
return (ee + ee, (pp * 2) % ph, (qq * 2) % ph)
else:
return (ee + Q, pp, (qq + 1) % ph)
if __name__ == '__main__':
E.params(a, -a, p)
P = E(1, 1)
Q = E(32676541629070164, 35161284104701659)
a = f(P, 1, 0, P, Q)
b = f(a[0], a[1], a[2], P, Q)
cnt = 0
while a[0].P != b[0].P:
a = f(a[0], a[1], a[2], P, Q)
b = f(b[0], b[1], b[2], P, Q)
b = f(b[0], b[1], b[2], P, Q)
cnt = cnt + 1
if cnt % 100000 == 0: print(cnt)
from ec import E
p = 977245356317
ph = 977244806323
def fastMult(e, poww):
res = E(0)
z = e
while(poww > 0):
res = res + (poww%2)*z
poww = poww//2
z = z + z
return res
if __name__ == '__main__':
E.params(454619944748, 67189121909, p)
P = E(474177197796,218937542115)
Q = E(287274742986,103070012816)
print(fastMult(P, 777244806324))
E.params(508139, -508139, 900001)
print(fastMult(E(1, 1), 10000))
def fastMult(e, poww):
res = E(0)
z = e
while (poww > 0):
res = res + (poww % 2) * z
poww = poww // 2
z = z + z
return res
if __name__ == '__main__':
p = nextprime((1 << 55) + random.randrange(0, 1 << 8))
a = random.randrange(p / 4, 3 * p / 4)
E.params(a, -a, p)
lb = long(p - 2 * sqrt(p))
ub = long(p + 2 * sqrt(p))
# tries 4*sqrt(p), but rho algorithm takes sqrt(p)... just BRUTE
# let's assume professor's checking code timeouts in a minute. RUN THIS FOR FOUR MINUTES THEN
z = fastMult(E(1, 1), lb)
for q in range(0, long(4 * sqrt(p))):
if q % long(4 * sqrt(p) / 100) == 0:
perc = long(q / (4 * sqrt(p)) * 100 + 0.5)
print(perc)
if z == E(0):
print(a, p, lb + q)