generate_rsa_keys_from_p_and_q.py

""" pylinted, and code formatted with black """
from math import lcm
from cryptography.hazmat.primitives.asymmetric import rsa
from cryptography.hazmat.backends import default_backend
from cryptography.hazmat.primitives import serialization

# P and Q are prime factors of largest factored sofar RSA-250
#
P = 641352894770715802787901901705773890848250147429434472081168596 * 10**62
P += 32024532344630238623598752668347708737661925585694639798853367

Q = 333720275949781565562260106053551142279407603447675546667845209 * 10**62
Q += 87023841729210037080257448673296881877565718986258036932062711

E = 0x10001

L = lcm(P - 1, Q - 1)


private_key = rsa.RSAPrivateNumbers(
    p=P,
    q=Q,
    d=pow(E, -1, L),
    dmp1=pow(E, -1, P - 1),
    dmq1=pow(E, -1, Q - 1),
    iqmp=pow(Q, -1, P),
    public_numbers=rsa.RSAPublicNumbers(e=E, n=P * Q),
).private_key(default_backend())

pem = private_key.private_bytes(
    encoding=serialization.Encoding.PEM,
    encryption_algorithm=serialization.NoEncryption(),
    format=serialization.PrivateFormat.TraditionalOpenSSL,
)
with open("private_key.pem", "wb") as f:
    f.write(pem)


public_key = private_key.public_key()

pem = public_key.public_bytes(
    encoding=serialization.Encoding.PEM,
    format=serialization.PublicFormat.SubjectPublicKeyInfo,
)
with open("public_key.pem", "wb") as f:
    f.write(pem)

Using openssl with deprecated rsautl can be seen in this gist comment:
https://gist.github.com/Hermann-SW/4aefd5b12ff179700bb6594ba25f9646?permalink_comment_id=5701082#gistcomment-5701082