def __init__(self, parent=None):
QtGui.QWidget.__init__(self, parent)
self.setWindowTitle('Encryption')
self.setupUi(self)
self.events(self)
# RSA AUTO SETTINGS
d = -1
while d < 0:
p = func.random_n(10, 100)
q = func.random_n(10, 100)
while len(str(p)) != len(str(q)):
q = func.random_n(10, 100)
while p == q:
q = func.random_n(10, 100)
self.lineEdit.setText(unicode(p))
self.lineEdit_2.setText(unicode(q))
n = p * q
key = (p - 1) * (q - 1)
e = func.random_n(0, 10)
self.lineEdit_3.setText(unicode(e))
while func.gcd(key, e) != 1:
e = func.random_n(0, 10)
tmp = func.egcd(e, key)
d = int(tmp[1])
# EL-GAMAL AUTOSETTINGS
p = func.random_n(30, 100) # value 1
g = random.randint(1, 1000) # value 2
x = random.randint(1, 1000) # value 3
while g > p - 1:
g = random.randint(1, 1000)
while x > p:
x = random.randint(1, 1000)
k = random.randint(1, 1000) # value 4
while func.gcd(k, p - 1) != 1:
k = random.randint(1, 1000)
self.lineEdit_4.setText(unicode(p))
self.lineEdit_5.setText(unicode(g))
self.lineEdit_6.setText(unicode(x))
self.lineEdit_7.setText(unicode(k))
# Rabin AUTO SETTINGS
p, q = func.rand34() # value 1,2
self.lineEdit_8.setText(unicode(p))
self.lineEdit_9.setText(unicode(q))
def f(y, x=1):
keys = set()
found = False
while y > 1:
if (x, y) in memo:
found = True
val = memo[(x, y)]
break
keys.add((x, y))
_gcd = gcd(x, y)
if _gcd != 1:
x //= _gcd
y //= _gcd
else:
x += 1
y -= 1
keys.add((x, y))
for k in keys:
if k not in memo:
if found:
memo[k] = val
else:
memo[k] = x
if found:
return val
return x
def f(y, x=1):
keys = set()
found = False
while y > 1:
if (x, y) in memo:
found = True
val = memo[(x, y)]
break
keys.add((x, y))
_gcd = gcd(x, y)
if _gcd != 1:
x //= _gcd
y //= _gcd
else:
x += 1
y -= 1
keys.add((x, y))
for k in keys:
if k not in memo:
if found:
memo[k] = val
else:
memo[k] = x
if found:
return val
return x
def properFraction(pNume,pDeno): '''pNume: numerator, pDeno: Denominator return [z,x,y] such that pNume/pDeno =z + x/y and gcd(x,y) = 1''' t = gcd(pDeno,pNume) z = pNume / pDeno x,y = (pNume - z*pDeno)/t, pDeno/t return [z,x,y]
def gen_triples(N):
for m in range(1, int(N**.5) + 1):
for n in range(1, m):
if (m - n) % 2 and gcd(m, n) == 1:
c = m**2 + n**2
if c <= N:
a = m**2 - n**2
b = 2 * m * n
yield (a, b, c)
def gen_triples(N):
for m in range(1, int(N**.5) + 1): # 1
for n in range(1, m): # 2
if (m - n) % 2 and gcd(m, n) == 1: # 3
c = m**2 + n**2 # 4
if c <= N: # 5
a = m**2 - n**2 # 6
b = 2 * m * n # 7
yield (a, b, c) # 8
def gen_triples(N):
for m in range(1, int(N**.5) + 1): #1
for n in range(1, m): #2
if (m - n) % 2 and gcd(m, n) == 1: #3
c = m**2 + n**2 #4
if c <= N: #5
a = m**2 - n**2 #6
b = 2 * m * n #7
yield (a, b, c) #8
def main(): s=0 for a in range(2,D/2+1): for b in range(2*a+1,min(3*a,D+1)): if functions.gcd(a,b) == 1: # print 'add:',a,b s+=1 # else: print 'delete',a,b print 'answer:',s
def continued_fraction(x):
"""
Returns the continued fraction of x as a list of tuples (a,b,c),
where:
a + (sqrt(x)+b / c)
represents each step.
If we are interested on the notation of the form [4;(1,3,1,8)],
we must take the first value from each tuple.
Note: Be careful if the value passed is a perfect square.
"""
res = []
a = floor(x**0.5)
b = -floor(x**0.5)
c = 1
t = (a,b,c)
res.append(t)
while True:
a, b, c = res[-1][0], res[-1][1], res[-1][2]
a1 = floor(c*(x**0.5 - b)/(x - b*b))
b1 = -b * c
c1 = x - b*b
b1 -= a1*c1
_gcd = gcd(b1, c1)
_gcd = gcd(_gcd, c)
b1 //= _gcd
c1 //= _gcd
t = (a1, b1, c1)
if t in res: # All continued fractions are periodic
res.append(t)
break
res.append(t)
return res
def continued_fraction(x):
"""
Returns the continued fraction of x as a list of tuples (a,b,c),
where:
a + (sqrt(x)+b / c)
represents each step.
If we are interested on the notation of the form [4;(1,3,1,8)],
we must take the first value from each tuple.
Note: Be careful if the value passed is a perfect square.
"""
res = []
a = floor(x**0.5)
b = -floor(x**0.5)
c = 1
t = (a, b, c)
res.append(t)
while True:
a, b, c = res[-1][0], res[-1][1], res[-1][2]
a1 = floor(c * (x**0.5 - b) / (x - b * b))
b1 = -b * c
c1 = x - b * b
b1 -= a1 * c1
_gcd = gcd(b1, c1)
_gcd = gcd(_gcd, c)
b1 //= _gcd
c1 //= _gcd
t = (a1, b1, c1)
if t in res: # All continued fractions are periodic
res.append(t)
break
res.append(t)
return res
import math
from sympy import *
from functions import gcd
def multiplyList(myList):
result = 1
for x in myList:
result = result * x
return result
res = []
size = 120000
for c in range(3, size):
for b in range(math.ceil(c / 2), c):
a = c - b
if a < b < c and gcd(b, c) == 1 and gcd(a, c) == 1 and gcd(
a, b) == 1 and multiplyList(factorint(a * b * c)) < c:
print(a, b, c)
res.append((a, b, c))
print(len(res))
print(sum(t[2] for t in res))
# todo overtime
from functions import pythTriplet, gcd
LIMIT = 100000000
solutions = 0
for m in range(2, int(LIMIT**0.5) + 1):
for n in range(1, m):
if (m + n) % 2 == 0:
continue
if gcd(m, n) != 1:
continue
t = pythTriplet(m, n)
# Reorder triplet
if t[0] > t[1]:
t[0], t[1] = t[1], t[0]
if (t[2] % (t[1] - t[0])) == 0:
perimeter = sum(t)
solutions += LIMIT // perimeter
print(solutions)
"""
The triangle 5,5,6 is a triangle in which there is a pythagorean triplet such that 3,4,5 in which there is a number n in [3,4] (not the diagonal) such that 5-2n == 1 or 5-2n == -1
Therefore, we want to generate Pythagorean triplets in which mm + nn - min(mm - nn, 2mn) == 1 or -1
We are only interested in primitive ones because the difference is increased by a factor of d.
Also, the perimeter is 2mm + 2mn
"""
from functions import pythTriplet, gcd
total_perimeter = 0
for m in range(2, 20000):
for n in range(1, m):
if (m + n)%2 == 0:
continue
if gcd(m, n) != 1:
continue
t = pythTriplet(m, n)
if abs(t[2] - 2*t[1]) == 1 or abs(t[2] - 2*t[0]) == 1:
total_perimeter += 2*(t[2] + min(t[0], t[1]))
print(t, 'PER', total_perimeter)
""" ------------------------------------------------------- [program description] ------------------------------------------------------- Author: Max Dann ID: 190274440 Email: [email protected] __updated__ = "2020-02-11" ------------------------------------------------------- """ from functions import gcd print(gcd(9,6))
import functions
for i in range(0, 10000):
functions.fib(20)
for i in range(0, 10000):
functions.gcd(1234, 84, 123)
for i in range(0, 10000):
functions.recursiveAdd(10, 3)
from functions import gcd
N = 50
triples = sorted(
#1
(
(a, b, c) for a, b, c in (
#2
((m**2 - n**2), (2 * m * n), (m**2 + n**2)) #3
for m in range(1,
int(N**.5) + 1) #4
for n in range(1, m) #5
if (m - n) % 2 and gcd(m, n) == 1 #6
) if c <= N),
key=lambda *triple: sum(*triple) #7
)
print(triples)
from functions import gcd
N = 50
triples = sorted( # 1
((a, b, c) for a, b, c in ( # 2
((m**2 - n**2), (2 * m * n), (m**2 + n**2)) # 3
for m in range(1, int(N**.5) + 1) # 4
for n in range(1, m) # 5
if (m - n) % 2 and gcd(m, n) == 1 # 6
) if c <= N), key=lambda *triple: sum(*triple) # 7
)
print(triples)
def dh():
d = -1
print "Do you want manualy enter settings? (y/n)"
manual = str(raw_input("$ "))
if manual == "n":
while d<0:
p = func.random_n(10,100)
q = func.random_n(10,100)
while len(str(p)) != len(str(q)):
q = func.random_n(10,100)
while p == q:
q = func.random_n(10,100)
n = p*q
key = (p-1)*(q-1)
e = func.random_n(0,10)
while func.gcd(key,e) != 1:
print "[ DH ] e generation failure, trying another e..."
e = func.random_n(0,10)
tmp = func.egcd(e,key)
d = int(tmp[1])
print "[ DH ] p =",p,"q =",q
print "[ DH ] n =",n
print "[ DH ] e =",e,"key =",key
print "[ DH ] d =",d
elif manual == "y":
p = int(input("p = "))
q = int(input("q = "))
n = p*q
key = (p-1)*(q-1)
e = int(input("e = "))
tmp = func.egcd(e,key)
d = int(tmp[1])
print "[ DH ] Choose 'encode' or 'decode' for proceed, or exit for quit"
method = str(raw_input("$ "))
while len(method) > 1:
if method == "exit":
os._exit(1)
if method == "encode":
text = str(raw_input("input text [encode] $ "))
start_time = time.time()
size = len(text)
print "[ DH ] text lenght:", size
text_int = []
i = 0
while i < size:
text_int.append(ord(text[i]))
i = i+1
text_crypt = []
i = 0
while i < size:
text_crypt.append(int(text_int[i] ** e % n))
i = i+1
print "[ DH ] Encrypted:",text_crypt
print "[ DH ] Time elapsed:",time.time()-start_time, "ms"
if method == "decode":
text = [eval(i) for i in raw_input('input text [decode] $ ').split()]
print text
start_time = time.time()
size = len(text)
print "[ DH ] text length:",size
text_decrypt = []
i = 0
while i < size:
text_decrypt.append(chr(int(text[i] ** d % n)))
i = i+1
print "[ DH ] Decrypted:",text_decrypt
print "[ DH ] Time elapsed:",time.time()-start_time, "ms"
print "[ DH ] Type encode/decode to continue or 'exit' for exit"
method = str(raw_input("$ "))
""" ------------------------------------------------------------------------ Lab 5, Task 2 - GCD ------------------------------------------------------------------------ Author: Nicolas Mills ID: 180856100 Email: [email protected] __updated__ = 2019-02-11 ------------------------------------------------------------------------ """ from functions import gcd from random import randint m = randint(0, 20000) n = randint(-20000, 20000) ans = gcd(m, n) print("m: {}\tn: {}\tans: {}".format(m, n, ans))
