def strong_pseudo(b, n):
for m in range(1, n):
r = int(log2((n - 1)//m))
e = modexp(b, m, n)
for s in range(1, r):
e2 = modexp(b, exp(2, s)*m, n)
if e == 1 or e2 == -1:
print('Strong pseudoprime m={}, r={}, s={}'.format(m, r, s),
end=" ")
if e == 1:
print('(condition 1)')
if e == -1:
print('(condition 2)')
def order(n, m):
e = 1
found = False
while not found:
if modexp(n, e, m) == 1:
found = True
return e
e += 1
def fermat(n):
for x in range(1, n):
a = modexp(x, n - 1, n)
if a != 1:
print('Composite')
return False
else:
print('Pseudoprime, base', x)
return True
def fermat2(n):
pseudos = []
for x in range(1, n):
a = modexp(x, n - 1, n)
if a != 1:
return (False, None)
else:
pseudos.append(x)
return (True, pseudos)
def disc_log(a, b, p):
m = int(p**0.5) + 1 # Ceiling
print('m =', m)
pairs = []
for j in range(m):
g = modexp(a, j, p)
print('giant step a^j: {}^{} = {}'.format(a, j, g))
pairs.append((j, g))
am = modexp(modinv(a, p), m, p) # a^(-m) mod p -> (a^(-1))^m mod p
print('a^{-m} =', am)
ajs = (list(zip(*pairs))[1])
y = b
for i in range(m):
s = (y*am) % p
print('baby step y*am: {}*{} = {}'.format(y, am, s))
if y in ajs:
return i*m + pairs[ajs.index(y)][0] # i*m + j
else:
y = s