def generate(bits, randfunc=None, e=65537):
"""allow to generate small keys for test purposes
"""
if e % 2 == 0 or e < 3:
raise ValueError(
"RSA public exponent must be a positive, odd integer larger than 2."
)
if randfunc is None:
randfunc = Random.get_random_bytes
d = n = Integer(1)
e = Integer(e)
while n.size_in_bits() != bits and d < (1 << (bits // 2)):
# Generate the prime factors of n: p and q.
# By construciton, their product is always
# 2^{bits-1} < p*q < 2^bits.
size_q = bits // 2
size_p = bits - size_q
min_p = min_q = (Integer(1) << (2 * size_q - 1)).sqrt()
if size_q != size_p:
min_p = (Integer(1) << (2 * size_p - 1)).sqrt()
def filter_p(candidate):
return candidate > min_p and (candidate - 1).gcd(e) == 1
p = generate_probable_prime(exact_bits=size_p,
randfunc=randfunc,
prime_filter=filter_p)
min_distance = Integer(1) << (max(bits // 2 - 100, 10))
def filter_q(candidate):
return (candidate > min_q and (candidate - 1).gcd(e) == 1
and abs(candidate - p) > min_distance)
q = generate_probable_prime(exact_bits=size_q,
randfunc=randfunc,
prime_filter=filter_q)
n = p * q
lcm = (p - 1).lcm(q - 1)
d = e.inverse(lcm)
if p > q:
p, q = q, p
u = p.inverse(q)
return RSA.RsaKey(n=n, e=e, d=d, p=p, q=q, u=u)
def _generate_key_pair(self) -> Tuple[List[int], List[int]]:
n_bits = self.params.key_bits
pq_bits = (n_bits + 1) // 2
while True:
p = int(generate_probable_prime(exact_bits=pq_bits))
q = int(generate_probable_prime(exact_bits=pq_bits))
n = p * q
if p != q and n.bit_length() == n_bits:
break
n_chunks = self.serialize_pk(n, self.params.key_bytes)
p_chunks = self.serialize_pk(p, self.params.key_bytes)
q_chunks = self.serialize_pk(q, self.params.key_bytes)
return n_chunks, p_chunks + q_chunks
def test_generate_prime_filter(self):
def ending_with_one(number):
return number % 10 == 1
for x in xrange(20):
q = generate_probable_prime(exact_bits=160, prime_filter=ending_with_one)
self.assertEqual(q % 10, 1)
def test_generate_prime_filter(self):
def ending_with_one(number):
return number % 10 == 1
for x in xrange(20):
q = generate_probable_prime(exact_bits=160,
prime_filter=ending_with_one)
self.assertEqual(q % 10, 1)
def _generate_or_load_key_pair(self, address: str) -> KeyPair:
seed = int(address, 16)
rng = Random(seed)
def rand_bytes(n: int) -> bytes:
return bytes([rng.randrange(256) for _ in range(n)])
pk = int(
generate_probable_prime(exact_bits=self.params.key_bits,
randfunc=rand_bytes))
return KeyPair(
PublicKeyValue(self.serialize_pk(pk, self.params.key_bytes),
params=self.params), PrivateKeyValue(pk))
def generate(bits, randfunc=None, e=65537):
"""Create a new RSA key.
The algorithm closely follows NIST `FIPS 186-4`_ in its
sections B.3.1 and B.3.3. The modulus is the product of
two non-strong probable primes.
Each prime passes a suitable number of Miller-Rabin tests
with random bases and a single Lucas test.
:Parameters:
bits : integer
Key length, or size (in bits) of the RSA modulus.
It must be at least 1024.
The FIPS standard only defines 1024, 2048 and 3072.
randfunc : callable
Function that returns random bytes.
The default is `Crypto.Random.get_random_bytes`.
e : integer
Public RSA exponent. It must be an odd positive integer.
It is typically a small number with very few ones in its
binary representation.
The FIPS standard requires the public exponent to be
at least 65537 (the default).
:Return: An RSA key object (`RsaKey`).
.. _FIPS 186-4: http://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf
"""
if bits < 1024:
raise ValueError("RSA modulus length must be >= 1024")
if e % 2 == 0 or e < 3:
raise ValueError("RSA public exponent must be a positive, odd integer larger than 2.")
if randfunc is None:
randfunc = Random.get_random_bytes
d = n = Integer(1)
e = Integer(e)
while n.size_in_bits() != bits and d < (1 << (bits // 2)):
# Generate the prime factors of n: p and q.
# By construciton, their product is always
# 2^{bits-1} < p*q < 2^bits.
size_q = bits // 2
size_p = bits - size_q
min_p = min_q = (Integer(1) << (2 * size_q - 1)).sqrt()
if size_q != size_p:
min_p = (Integer(1) << (2 * size_p - 1)).sqrt()
def filter_p(candidate):
return candidate > min_p and (candidate - 1).gcd(e) == 1
p = generate_probable_prime(exact_bits=size_p,
randfunc=randfunc,
prime_filter=filter_p)
min_distance = Integer(1) << (bits // 2 - 100)
def filter_q(candidate):
return candidate > min_q and (candidate - 1).gcd(e) == 1 \
and abs(candidate - p) > min_distance
q = generate_probable_prime(exact_bits=size_q,
randfunc=randfunc,
prime_filter=filter_q)
n = p * q
lcm = (p - 1).lcm(q - 1)
d = e.inverse(lcm)
if p > q:
p, q = q, p
u = p.inverse(q)
key_dict = dict(zip(('n', 'e', 'd', 'p', 'q', 'u'),
(n, e, d, p, q, u)))
return RsaKey(key_dict)
def generate(bits, randfunc=None, e=65537):
"""Create a new RSA key pair.
The algorithm closely follows NIST `FIPS 186-4`_ in its
sections B.3.1 and B.3.3. The modulus is the product of
two non-strong probable primes.
Each prime passes a suitable number of Miller-Rabin tests
with random bases and a single Lucas test.
Args:
bits (integer):
Key length, or size (in bits) of the RSA modulus.
It must be at least 1024, but **2048 is recommended.**
The FIPS standard only defines 1024, 2048 and 3072.
randfunc (callable):
Function that returns random bytes.
The default is :func:`Crypto.Random.get_random_bytes`.
e (integer):
Public RSA exponent. It must be an odd positive integer.
It is typically a small number with very few ones in its
binary representation.
The FIPS standard requires the public exponent to be
at least 65537 (the default).
Returns: an RSA key object (:class:`RsaKey`, with private key).
.. _FIPS 186-4: http://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf
"""
if bits < 1024:
raise ValueError("RSA modulus length must be >= 1024")
if e % 2 == 0 or e < 3:
raise ValueError(
"RSA public exponent must be a positive, odd integer larger than 2."
)
if randfunc is None:
randfunc = Random.get_random_bytes
d = n = Integer(1)
e = Integer(e)
while n.size_in_bits() != bits and d < (1 << (bits // 2)):
# Generate the prime factors of n: p and q.
# By construciton, their product is always
# 2^{bits-1} < p*q < 2^bits.
size_q = bits // 2
size_p = bits - size_q
min_p = min_q = (Integer(1) << (2 * size_q - 1)).sqrt()
if size_q != size_p:
min_p = (Integer(1) << (2 * size_p - 1)).sqrt()
def filter_p(candidate):
return candidate > min_p and (candidate - 1).gcd(e) == 1
p = generate_probable_prime(exact_bits=size_p,
randfunc=randfunc,
prime_filter=filter_p)
min_distance = Integer(1) << (bits // 2 - 100)
def filter_q(candidate):
return (candidate > min_q and (candidate - 1).gcd(e) == 1
and abs(candidate - p) > min_distance)
q = generate_probable_prime(exact_bits=size_q,
randfunc=randfunc,
prime_filter=filter_q)
n = p * q
lcm = (p - 1).lcm(q - 1)
d = e.inverse(lcm)
if p > q:
p, q = q, p
u = p.inverse(q)
return RsaKey(n=n, e=e, d=d, p=p, q=q, u=u)
def test_generate_prime_bit_size(self):
p = generate_probable_prime(exact_bits=512)
self.assertEqual(p.size_in_bits(), 512)
def test_generate_prime_bit_size(self):
p = generate_probable_prime(exact_bits=512)
self.assertEqual(p.size_in_bits(), 512)
