def factorize(n,e,d):
s=0
s2=2
u=e*d-1
while u%2 == 0:
s=s+1
s2*=2
u/=2
g=1
u=int(u)
if pow(2,s)*u == e*d-1 and u%2 == 1:
print("Decomposition ok")
print("s is {}".format(s))
print("u is {}".format(u))
print("e*d-1 is {}".format(e*d-1))
while g ==1 or g==n:
a=random.randrange(1,n)
print("New Value for a generated : {}".format(a))
ggT=euclid.gcd(a,n)
print("gcd(a,n)={}".format(ggT))
if ggT != 1:
return [a, n/a ]
au=sam2.multiply(a,u,n)
print("a^u is : {}".format(au))
for j in range(0,s):
g=euclid.gcd(sam2.multiply(au,pow(2,j),n)-1,n)
print("Iteration {}: {}".format(j,g))
if g != 1 and g != n:
return [g, n/g]
def check_identity(N):
for i in range(N):
for j in range(N):
for m in range(1, N):
if (i * j) % m == 1:
assert gcd(i, m) == 1
assert gcd(j, m) == 1
if gcd(i, m) == 1 and gcd(j, m) == 1:
assert (i * j) % m == 1
def __init__(self, x, y):
divisor = euclid.gcd(x, y)
self._x = x / divisor
if y != 0:
self._y = y / divisor
else:
print('被除数不能为0')
def rprime(x,y): """True if x is relatively prime to y >>> rprime(25,36) True >>> rprime(25,30) False """ return gcd(x,y) == 1
def factorRho(n,x_1):
""" Factor using pollard's rho method """
x = x_1;
xp = f(x) % n
p = gcd(x - xp,n)
#print ("x_i's: {")
while p == 1:
#print(x),
# in the ith iteration x = x_i and x' = x_2i
x = f(x) % n
xp = f(xp) % n
xp = f(xp) % n
p = gcd(x-xp,n)
#print ("}")
if p == n: return -1
else: return p
def factor(n,b):
""" Factor using Pollard's p-1 method """
a = 2;
for j in range(2,b):
a = a**j % n
d = gcd(a-1,n);
print ("d:",d,"a-1:",a-1)
if 1 < d < n: return d;
else: return -1;
def factor(n,b): """ Factor using Pollard's p-1 method """ a = 2; for j in range(2,b): a = a**j % n d = gcd(a-1,n); print "d:",d,"a-1:",a-1 if 1 < d < n: return d; else: return -1;
def factorRho(n,x_1):
""" Factor using pollard's rho method """
x = x_1;
xp = f(x) % n
p = gcd(x - xp,n)
print "x_i's: {"
while p == 1:
print x,
# in the ith iteration x = x_i and x' = x_2i
x = f(x) % n
xp = f(xp) % n
xp = f(xp) % n
p = gcd(x-xp,n)
print "}"
if p == n: return -1
else: return p
def factorRho(n, x_1):
""" Factor using pollard's rho method """
x = x_1
xp = f(x) % n
p = gcd(x - xp, n)
print "x_i's: {"
while p == 1:
print x,
# in the ith iteration x = x_i and x' = x_2i
x = f(x) % n
xp = f(xp) % n
xp = f(xp) % n
p = gcd(x - xp, n)
print "}"
if p == n: return -1
else: return p
def compute_params(phi_n):
'''Function to compute e and d'''
d = 0
e = 0
found_e = False
while found_e == False:
e = random.randint(1, phi_n - 1)
if gcd(e, phi_n) == 1:
found_e = True
_, d, _ = extgcd(e, phi_n)
if (d < 0):
d += phi_n
return d, e
def find_keylength(crypt, n=3):
"""
Returns a dictionary of potential keylengths for provided crypt text
The lhs of an entry tells us the potential keylength while the rhs
tells us how likely it is to be correct.
The n variable determins the length of segments to check on the crypt
text. The greater the segment the fewer
and more likely keylenghts gets returned,
but the longer it takes to compute
"""
gcd_dict = {}
for segment in set(
window(crypt, n)
): # Notice that set is used. We don't iterate over duplicated strings
# If segment matches something, save where the match started to a list
# Matches is a list of positions where common segments occur
matches = [match.start() for match in re.finditer(segment, crypt)]
# Calcylate the offsets between each matching segment
offsets = [
matches[i + 1] - matches[i] for i in range(len(matches) - 1)
]
# Calcylate the gcd between each offset.
gcds = [
gcd(offsets[i], offsets[i + 1]) for i in range(len(offsets) - 1)
]
# Count all gcds
for g in gcds:
gcd_dict[g] = gcd_dict.get(g, 0) + 1
if n < 1 and len(gcd_dict) == 0:
gcd_dict = find_keylength(crypt, n - 1)
return gcd_dict
def pythmx(s):
count = 0
s2 = s // 2
mmx = math.ceil(math.sqrt(s2))
tem = []
for m in range(2, mmx):
if s2 % m == 0:
sm = s2 // m
while sm % 2 == 0:
sm //= 2
k = m + 1 + m % 2
while k < 2 * m and k <= sm:
if sm % k == 0 and euclid.gcd(k, m) == 1:
d = s2 // (k * m)
n = k - m
a = d * (m * m - n * n)
b = 2 * d * m * n
c = d * (m * m + n * n)
tem.append((a, b, c))
k += 2
return tem
def factor(n): base = [2,3,5,7,11,13,17,19,23]; start = int(sqrt(n)) pairs = []; factors = []; for i in range(start,n): for j in range(len(base)): lhs = i**2 % n rhs = base[j]**2 % n if lhs == rhs: print "%i^2 = %i = %i^2 = %i mod %i" % (i,lhs,base[j],rhs,n) pairs.append([i,base[j]]); print "pairs:",pairs for i in range(len(pairs)): factor = gcd(pairs[i][0]-pairs[i][1],n) if(factor != 1): print "factor:",factor
def factor(n):
base = [2, 3, 5, 7, 11, 13, 17, 19, 23]
start = int(sqrt(n))
pairs = []
factors = []
for i in range(start, n):
for j in range(len(base)):
lhs = i**2 % n
rhs = base[j]**2 % n
if lhs == rhs:
print "%i^2 = %i = %i^2 = %i mod %i" % (i, lhs, base[j], rhs,
n)
pairs.append([i, base[j]])
print "pairs:", pairs
for i in range(len(pairs)):
factor = gcd(pairs[i][0] - pairs[i][1], n)
if (factor != 1): print "factor:", factor
