def compute_wheel(limit):
primes = seive(limit)
circum = reduce(lambda x,y: x*y, primes, 1)
spokes = [i for i in range(1, circum) if gcd(i, circum) == 1]
diffs = [spokes[i+1] - s for i,s in enumerate(spokes[:-1])]
diffs.insert(0, circum - spokes[-1] + 1)
return primes, diffs
def attack2():
prod = reduce(lambda x, y: x*y, keys, 1)
factorise = {}
for key in keys:
div = praxis.gcd(key, (prod % (key*key)) / key)
if div != 1:
factorise[key] = (div, key / div)
return factorise
def attack1():
factorise = {}
for i in range(len(keys)):
for j in range(i):
div = praxis.gcd(keys[i], keys[j])
if div != 1:
factorise[keys[i]] = (div, keys[i] / div)
factorise[keys[j]] = (div, keys[j] / div)
return factorise
def encrypt(message, key_a, key_b):
assert(gcd(key_a, 26) == 1)
cipher = ""
for m in message:
if m.isalpha():
x = ord(m.upper()) - ord("A")
y = (key_a * x + key_b) % 26
cipher += chr(y + ord("A"))
else:
cipher += m
return cipher
def reduce_terms(self):
g = gcd(self.num, self.den)
self.num /= g
self.den /= g
