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#!/opt/sage-6.2-x86_64-Linux/sage -python
import sys
sys.path.insert(1, "/usr/lib/python2.7/dist-packages")
import pexpect
from pexpect import fdpexpect
from sage.all import *
DEBUG = False
def get_primes(N):
primes = []
for f,c in factor(N):
primes.extend([f]*c)
return primes
manual_quines = lambda p, e: [i for i in range(p) if pow(i,e,p)==i]
def get_quines_for_prime(p, e):
k = e-1
order = gcd(p-1,k % (p-1))
g = GF(p).multiplicative_generator()
kth_primitive_root= int(pow(g, (p-1)/order, n))
roots = more_roots(kth_primitive_root, p, k)
return roots.union(set([0]))
def more_roots(r, p, k):
roots = set([r])
cur = r
while True:
cur = (cur * r) % p
if cur in roots:
break
roots.add(cur)
return roots
def get_quines(N, e, nq):
"""return a set of nq numbers q with
q**e = q (mod N)."""
print "factoring N (%d bits)" % floor(log(N,2))
p,q = get_primes(N)
print "gen_quines p"
p_quines = get_quines_for_prime(p, e)
print "gen_quines q"
q_quines = get_quines_for_prime(q, e)
print "combine"
quines = set()
for rp in p_quines:
for rq in q_quines:
try:
r = CRT([rp, rq], [p,q])
except Exception, e:
print [rp,rq], [p,q]
raise e
#quines.update(more_roots(r, N, e-1))
quines.add(r)
assert pow(r,e,N) == r
if len(quines) == nq:
break
if len(quines) == nq:
break
print "generated %d quines" % len(quines)
return quines
import socket
#sys.path.append("/usr/local/lib/python2.7/dist-packages")
#import pexpect.fdpexpect
def main():
qs = get_quines(N=50429, e=13567, nq = 10277)
assert len(qs) == 10277
s = socket.socket()
s.connect(("202.112.26.105", 55537))
c = pexpect.fdpexpect.fdspawn(s)
m = c.expect("([0-9]+) Rounds")
rounds = int(c.match.groups()[0])
print "%d rounds" % rounds
for i in xrange(rounds):
print
print "==== Round (%u/%u) ===" % (i+1, rounds)
print
c.expect("N = ([0-9]+)")
N = int(c.match.groups()[0])
c.expect("e = ([0-9]+)")
e = int(c.match.groups()[0])
c.expect("Total ([0-9]+) quine numbers")
nq = int(c.match.groups()[0])
print "N = ", N
print "e = ", e
print "%d quines total" % nq
if nq > 200:
nq = 200
print "%d quines required" % nq
qs = get_quines(N, e, nq)
assert len(qs) >= nq
for i, q in enumerate(list(qs)[:nq]):
s.send("%d\n" % q)
if DEBUG:
res = c.expect(["Good Quine", "Bad Number", "Do not cheat"])
assert res == 0
c.expect("N = ([0-9]+)")
N = int(c.match.groups()[0])
c.expect("e = ([0-9]+)")
e = int(c.match.groups()[0])
c.expect("Flag = ([0-9]+)")
flag = int(c.match.groups()[0])
print "FLAG", N, e, flag
if __name__ == '__main__':
main()
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