def decryption():
with open('pubkey.pem') as handle:
r = handle.read()
ne = RSA.import_key(r)
modulus = ne.n
exponent = ne.e
factor_n = primefac.factorint(modulus)
primes = list(factor_n)
primes = [int(i) for i in primes]
p = primes[0]
phi = (p**2) * (p - 1)
d = inverse(exponent, phi)
with open('key') as handle1:
r1 = bytes.fromhex(handle1.read())
aes_key = pow(bytes_to_long(r1), d, modulus)
ltb = long_to_bytes(aes_key)
aes = AES.new(ltb, AES.MODE_ECB)
with open("flag.txt.aes", 'rb') as handle2:
flag = handle2.read().strip()
print("Flag: ", aes.decrypt(flag))
def crack_key(e, n):
write_with_indent('Crack key: -e {} -n {}'.format(e, n))
print()
write_then_dots('Cracking Public_Key')
factors_list = []
for i in primefac.factorint(n):
factors_list.append(i)
p = 0
q = 0
if len(factors_list) == 2:
p = factors_list[0]
q = factors_list[1]
n = p * q
phi = (p - 1) * (q - 1)
d = primefac._primefac.modinv(e, phi)
privatekey = (d, p, q)
write_with_indent()
print()
write_with_indent(
'Private Key found: -d {} -p {} -q {}'.format(*privatekey))
def table_stats(max_val, prime_factors=True):
"""Return some statistics on a pythagoras table of size max_val
Returns a tuple with two dictioaries.
Count the number of occurences of number is a pythagoras table of size max_val.
This is returnes as a dictionary with the number as key and its occurence as value.
Also return a the prime factors of the numbers as a dictionary, whem prime_factors
is True. Otherwise returns an empty dictionary.
"""
count_num = { }
prime_fac = { }
# initialize count of occurrences of a certain number
for i in range(1, max_val*max_val+1):
count_num[i] = 0;
# calculate the pythagorean square and count occurrence of each number
for i in range(1, max_val+1):
for j in range(1, max_val+1):
count_num[i*j] += 1
# make a dictionary of prime factors of all the numbers
if(prime_factors):
for tuple in count_num.items():
prime_fac[tuple[0]] = primefac.factorint(tuple[0])
return (count_num, prime_fac)
def factor_n():
# if n is given but p and q are not, try TO factor n.
if self.p == -1 and self.q == -1 and self.n != -1:
factors = list([int(x) for x in primefac.factorint(self.n)])
if len(factors) == 2:
self.p, self.q = factors
elif len(factors) == 1:
raise NotImplemented("factordb could not factor this!")
else:
# This is the case for Multi-factor RSA!
# raise NotImplemented("We need support for multifactor RSA!")
# Multiply all factors together to get phi
self.phi = reduce(mul, [factor - 1 for factor in factors],
1)
# Calulate the new d private key
self.d = inverse(self.e, self.phi)
# Now calculate the plaintext
self.m = pow(self.c, self.d, self.n)
# Grab the result and give it to Katana
print(self.m)
result = long_to_bytes(self.m).decode()
self.manager.register_data(self, result)
return
def factor_N(N):
f = primefac.factorint(N)
r = []
for p, alpha in f.items():
for i in range(alpha):
r.append(p)
return sorted(r)
def factors(num):
primedict = primefac.factorint(house)
primelist = reduce(lambda x, y: x + [y[0]] * y[1], primedict.iteritems(), [])
combos = reduce(
operator.or_, (set(itertools.combinations(primelist, n)) for n in range(1, len(primelist) + 1)), set()
)
return [reduce(operator.mul, c, 1) for c in combos] + [1]
def hasExDistinctPrimeFactors(number, x):
# pad("Looking for prime factors of "+str(number))
primeFactors = primefac.factorint(number).keys()
if len(primeFactors) >= x:
# pad(str(number)+" has "+str(len(primeFactors))+">="+str(x)+" prime factors")
# pad(str(primeFactors))
return True
# pad(str(number)+" does not have "+str(x)+" distinct prime factors")
return False
def factor_N_with_multiplicative_group(N):
f = primefac.factorint(N)
r = []
phi_hint = {}
for p, alpha in f.items():
for i in range(alpha):
r.append(p)
phi_hint[p] = factor_N(p - 1)
return sorted(r), phi_hint
def solve4(n1, n2, n3, n4, n5, n6):
t1 = n2 - n1
t2 = n3 - n2
t3 = n4 - n3
t4 = n5 - n4
t5 = n6 - n5
N = GCD(t3*t1 - t2**2, t5*t2 - t4*t3)
factors = primefac.factorint(N)
while not isPrime(N):
for prime, order in factors.items():
if prime.bit_length() > 128:
continue
N = N / prime**order
return solve3(N, n1, n2, n3)
def find_discrete_log(g, h, p):
"""
Tries to find discrete logarithm for g^x=h mod p
chooses optimal algorithm
"""
d = primefac.factorint(p)
if (len(d.keys()) == 1):
for div in d.keys():
if (d[div] == 1):
return baby_step_giant_step(g, h, p)
else:
return prime_power_groups(g, h, div, d[div])
return -1
else:
return Pohlig_Hellman(d, g, h, p)
def lcm(nums):
factors = Counter()
for n in nums:
factors |= factorint(n)
return reduce(operator.mul, factors.elements(), 1)
def factor(n):
if log2(n) > 128:
return yafu.factor(n, silent=factor_silent)
else:
return primefac.factorint(n)
r.sendline('%d' % point[0])
r.sendline('%d' % point[1])
r.sendline('%d' % point[2])
print "ROUND 3 DONE"
# Part Four
log.info('GOURN 4')
point = handle(lambda x: not isPrime(x))
if not DEBUG:
r.sendline('%d' % point[0])
r.sendline('%d' % point[1])
r.sendline('%d' % point[2])
print "ROUND 4 DONE"
# Part Four
log.info('GOURN 5')
point = handle(lambda x: len(primefac.factorint(x)) == 3)
# point = handle(lambda x: reduce(lambda a,b: a+b, primefac.factorint(x).values()) == 3)
if not DEBUG:
r.sendline('%d' % point[0])
r.sendline('%d' % point[1])
r.sendline('%d' % point[2])
print "ROUND 5 DONE"
r.interactive()
except Exception, e:
print 'F**K!!! {}'.format(e)
r.close()
else:
r.interactive()
def grog(kx,
ky,
k,
N,
M,
Gx,
Gy,
precision=2,
radius=.75,
Dx=None,
Dy=None,
coil_axis=-1,
ret_image=False,
ret_dicts=False,
use_primefac=False,
remove_os=True,
inverse=False):
'''GRAPPA operator gridding.
Parameters
----------
kx, ky : array_like
k-space coordinates (kx, ky) of measured data k. kx, ky
should each be a 1D array. Must both be either float or
double.
k : array_like
Measured k-space data at points (kx, ky).
N, M : int
Desired resolution of Cartesian grid.
Gx, Gy : array_like
Unit GRAPPA operators.
precision : int, optional
Number of decimal places to round fractional matrix powers to.
radius : float, optional
Radius of ball in k-space to from Cartesian targets from
which to select source points.
Dx, Dy : dict, optional
Dictionaries of precomputed fractional matrix powers.
coil_axis : int, optional
Axis holding coil data.
ret_image : bool, optional
Return image space result instead of k-space.
ret_dicts : bool, optional
Return dictionaries of fractional matrix powers.
use_primefac : bool, optional
Use prime factorization to speed-up fractional matrix
power precomputations.
remove_os : bool, optional
Remove oversampling factor.
inverse : bool, optional
Do the inverse gridding operation, i.e., Cartesian points to
(kx, ky).
Returns
-------
res : array_like
Cartesian gridded k-space (or image).
Dx, Dy : dict, optional
Fractional matrix power dictionary for both Gx and Gy.
Raises
------
AssertionError
When (kx, ky) have different types.
AssertionError
When (kx, ky) and k do not have matching types, i.e.,
if (kx, ky) are float32, k must be complex64.
Notes
-----
Implements the GROG algorithm as described in [1]_.
References
----------
.. [1] Seiberlich, Nicole, et al. "Self‐calibrating GRAPPA
operator gridding for radial and spiral trajectories."
Magnetic Resonance in Medicine: An Official Journal of the
International Society for Magnetic Resonance in Medicine
59.4 (2008): 930-935.
'''
# Make sure types are consistent before calling grog funcs
assert kx.dtype == ky.dtype, (
'(kx, ky) must both be either double or float!')
assert (k.dtype == np.complex64 if kx.dtype == np.float32 else k.dtype
== np.complex128), ('(kx, ky) and k must have matching types!')
# Coils to the back
k = np.moveaxis(k, coil_axis, -1)
_ns, nc = k.shape[:]
if not inverse:
# We have samples at (kx, ky). We want new samples on a
# Cartesian grid at, say, (tx, ty). Let's also oversample:
N, M = 2 * N, 2 * M
# Create the target grid (or source grid for inverse gridding)
tx, ty = np.meshgrid(
np.linspace(np.min(kx), np.max(kx), N, dtype=kx.dtype),
np.linspace(np.min(ky), np.max(ky), M, dtype=kx.dtype))
tx, ty = tx.flatten(), ty.flatten()
# We only want to do work inside the region of support:
# estimate as a circle for now, works well with radial
outside = np.argwhere(np.sqrt(tx**2 + ty**2) > np.max(kx)).squeeze()
inside = np.argwhere(np.sqrt(tx**2 + ty**2) <= np.max(kx)).squeeze()
tx = np.delete(tx, outside)
ty = np.delete(ty, outside)
if inverse:
# We want to fill all non-cartesian locations, so the region
# of support is the whole thing (all indices)
k = np.delete(k, outside, axis=0)
inside = np.arange(kx.size, dtype=int)
# Swap coordinates if doing inverse (cartesian to radial)
if inverse:
kx, tx = tx, kx
ky, ty = ty, ky
kxy = np.concatenate((kx[:, None], ky[:, None]), axis=-1)
txy = np.concatenate((tx[:, None], ty[:, None]), axis=-1)
# Find all targets within radius of source points
kdtree = cKDTree(kxy)
idx = kdtree.query_ball_point(txy, r=radius)
# The result will be shaped different if we are doing inverse
# gridding:
if inverse:
res = np.zeros((tx.size, nc), dtype=k.dtype)
else:
res = np.zeros((N * M, nc), dtype=k.dtype)
t0 = time()
# Handle both single and double floating point calculations,
# have to do it in separate functions because Cython...
if tx.dtype == np.float32:
key_x, key_y = grog_powers_float(tx, ty, kx, ky, idx, precision)
else:
key_x, key_y = grog_powers_double(tx, ty, kx, ky, idx, precision)
print('Took %g seconds to find required powers' % (time() - t0))
# If we have provided dictionaries, whitle down the work to only
# those powers not already computed
t0 = time()
if Dx:
key_x = key_x - set(Dx.keys())
else:
Dx = {}
if Dy:
key_y = key_y - set(Dy.keys())
else:
Dy = {}
# Precompute deficient matrix powers
if use_primefac:
# Precompute matrix powers using prime factorization
from primefac import factorint # pylint: disable=E0401
scale_fac = 10**precision
# Start a dictionary of fractional matrix powers
frac_mats_x = {}
frac_mats_y = {}
# First thing we need is the scale factor, note that we will
# assume the inverse!
lscale_fac = np.log(scale_fac)
frac_mats_x[lscale_fac] = np.linalg.pinv(fmp(Gx, lscale_fac)).astype(
k.dtype)
frac_mats_y[lscale_fac] = np.linalg.pinv(fmp(Gy, lscale_fac)).astype(
k.dtype)
for keyx0, keyy0 in tqdm(zip(key_x, key_y),
total=len(key_x),
leave=False,
desc='Dxy'):
dx0 = np.exp(np.abs(keyx0)) * scale_fac
dy0 = np.exp(np.abs(keyy0)) * scale_fac
rx = factorint(int(dx0))
ry = factorint(int(dy0))
# Component fractional powers are log of prime factors;
# add in the scale_fac term here so we get it during the
# multi_dot later. We explicitly cast to integer because
# sometimes we run into an MPZ object that doesn't play
# nice with numpy
lpx = np.log(np.array([int(r) for r in rx.keys()] +
[scale_fac])).squeeze()
lpy = np.log(np.array([int(r) for r in ry.keys()] +
[scale_fac])).squeeze()
lpx_unique = np.unique(lpx)
lpy_unique = np.unique(lpy)
# Compute new fractional matrix powers we haven't seen
for lpxu in lpx_unique:
if lpxu not in frac_mats_x:
frac_mats_x[lpxu] = fmp(Gx, lpxu)
for lpyu in lpy_unique:
if lpyu not in frac_mats_y:
frac_mats_y[lpyu] = fmp(Gy, lpyu)
# Now compose all the matrices together for this point
nx = list(rx.values()) + [1] # +1 to account for scale_fac
ny = list(ry.values()) + [1]
Dx[np.abs(keyx0)] = np.linalg.multi_dot([
np.linalg.matrix_power(frac_mats_x[lpx0], n0).astype(k.dtype)
for lpx0, n0 in zip(lpx, nx)
])
Dy[np.abs(keyy0)] = np.linalg.multi_dot([
np.linalg.matrix_power(frac_mats_y[lpy0], n0).astype(k.dtype)
for lpy0, n0 in zip(lpy, ny)
])
if np.sign(keyx0) < 0:
Dx[keyx0] = np.linalg.pinv(Dx[np.abs(keyx0)]).astype(k.dtype)
if np.sign(keyy0) < 0:
Dy[keyy0] = np.linalg.pinv(Dy[np.abs(keyy0)]).astype(k.dtype)
else:
for key0 in tqdm(key_x, leave=False, desc='Dx'):
Dx[np.abs(key0)] = fmp(Gx, np.abs(key0)).astype(k.dtype)
if np.sign(key0) < 0:
Dx[key0] = np.linalg.pinv(Dx[np.abs(key0)]).astype(k.dtype)
for key0 in tqdm(key_y, leave=False, desc='Dy'):
Dy[np.abs(key0)] = fmp(Gy, np.abs(key0)).astype(k.dtype)
if np.sign(key0) < 0:
Dy[key0] = np.linalg.pinv(Dy[np.abs(key0)]).astype(k.dtype)
print('Took %g seconds to precompute fractional matrix powers' %
(time() - t0))
# res is modified inplace
if res.dtype == np.complex64:
grog_gridding_float(tx, ty, kx, ky, k, idx, res, inside, Dx, Dy,
precision)
else:
grog_gridding_double(tx, ty, kx, ky, k, idx, res, inside, Dx, Dy,
precision)
if inverse:
retVal = res
else:
# Remove the oversampling factor and return in kspace or
# imspace
ax = (0, 1)
im = None
if remove_os:
N4, M4 = int(N / 4), int(M / 4)
im = np.fft.fftshift(np.fft.ifft2(np.fft.ifftshift(res.reshape(
(N, M, nc), order='F'),
axes=ax),
axes=ax),
axes=ax)[N4:-N4, M4:-M4, :]
res = np.fft.ifftshift(np.fft.fft2(np.fft.fftshift(im, axes=ax),
axes=ax),
axes=ax)
if ret_image:
if im is None:
retVal = np.fft.fftshift(np.fft.ifft2(np.fft.ifftshift(
res.reshape((N, M, nc), order='F'), axes=ax),
axes=ax),
axes=ax)
else:
retVal = im
else:
retVal = res
# If the user asked for the precomputed dictionaries back, add
# them to the tuple of returned values
if ret_dicts:
retVal = (retVal, Dx, Dy)
return retVal
def totient(n):
totient = n
for factor in factorint(n):
totient -= totient // factor
return totient
import python23_encoding
c = gmpy2.mpz(
5499541793182458916572235549176816842668241174266452504513113060755436878677967801073969318886578771261808846567771826513941339489235903308596884669082743082338194484742630141310604711117885643229642732544775605225440292634865971099525895746978617397424574658645139588374017720075991171820873126258830306451326541384750806605195470098194462985494
)
d = gmpy2.mpz(
15664449102383123741256492823637853135125214807384742239549570131336662433268993001893338579081447660916548171028888182200587902832321164315176336792229529488626556438838274357507327295590873540152237706572328731885382033467068457038670389341764040515475556103158917133155868200492242619473451848383350924192696773958592530565397202086200003936447
)
phi = gmpy2.mpz(
25744472610420721576721354142700666534585707423276540379553111662924462766649397845238736588395849560582824664399879219093936415146333463826035714360316647265405615591383999147878527778914526369981160444050742606139799706884875928674153255909145624833489266194817757115584913491575124670523917871310421296173148930930573096639196103714702234087492
)
start_time = time.time()
factors_ = primefac.factorint(phi)
print('[DEBUG] complete integer factorization in %f s' %
(time.time() - start_time))
## parse factors into list
factors = []
for k, v in factors_.items():
for i in range(v):
factors.append(k)
## generate all 2-subsets of factors
indices = range(len(factors))
#!/usr/bin/env python2 import primefac from trmr import * Modulus = 0xD546AA825CF61DE97765F464FBFE4889AD8BF2F25A2175D02C8B6F2AC0C5C27B67035AEC192B3741DD1F4D127531B07AB012EB86241C09C081499E69EF5AEAC78DC6230D475DA7EE17F02F63B6F09A2D381DF9B6928E8D9E0747FEBA248BFFDFF89CDFAF4771658919B6981C9E1428E9A53425CA2A310AA6D760833118EE0D71 p, q = primefac.factorint(Modulus) e = 65537 d = modinv(e, (p - 1) * (q - 1)) print rsapem(d, e, Modulus)
con.sendline(is_feasible)
if is_feasible == "Y":
con.recv()
n = int(p)*int(q)
con.sendline(str(n))
# t.sleep(0.5)
if context.log_level != 50:
print("#### Q2")
output = con.recvuntil("IS THIS POSSIBLE and FEASIBLE? (Y/N):")
p = int(re.findall(r"p : (.*)", output)[0])
n = int(re.findall(r"n : (.*)", output)[0])
# we already have p
newp, q = primefac.factorint(n).keys()
is_feasible = "Y" if newp == p else "N"
con.sendline(is_feasible)
if is_feasible == "Y":
con.recv()
con.sendline(str(q))
# t.sleep(0.5)
if context.log_level != 50:
print("#### Q3")
output = con.recvuntil("IS THIS POSSIBLE and FEASIBLE? (Y/N):")
e = int(re.findall(r"e : (.*)", output)[0])
def smooth(i, b):
f = primefac.factorint(i)
for j in f.keys():
if j > b:
return False
return True
def primefac_library(n):
primes_and_exps = factorint(n)
values = [[(f ** e) for e in range(exp + 1)] for (f, exp) in primes_and_exps.iteritems()]
return set(functools.reduce(operator.mul, v, 1) for v in product(*values))
def get_prime_factors(x):
"""
Factorizes a give number into a list of prime factors
"""
return primefac.factorint(x)
2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357,
2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441,
2447, 2459, 2467, 2473, 2477
]
f = open('output.txt', 'r')
s = []
inp = f.readlines()
N = int(inp[1][3:])
e = 65537
for sig in inp[3:]:
s.append(int(sig[48:]))
p2s = dict(zip(prime_list, s))
forged_sig = 1
challenge = int(input('Enter Challenge Number: '))
for fac, mult in primefac.factorint(challenge).iteritems():
try:
forged_sig *= p2s[fac]**mult
except KeyError:
print 'One or more prime factor signatures not computed.'
print 'Factorization: ' + str(primefac.factorint(challenge))
sys.exit(0)
print 'Final sig: ' + str(forged_sig % N)