Prints .pem private RSA key given p, q and e

p_q_e_to_pem.py

# This code is compilation of
# 1) code from
# https://0day.work/how-i-recovered-your-private-key-or-why-small-keys-are-bad/
# 2) modified version of code snippet from crypto stackexchange
# https://crypto.stackexchange.com/a/25499

# This code does not perform any checks on p, q and e and can give wrong result
# or throw not informative exception if p, q and/or e are not valid.

import pyasn1.codec.der.encoder
import pyasn1.type.univ
import base64
import sys

def egcd(a, b):
    if a == 0:
        return (b, 0, 1)
    else:
        g, y, x = egcd(b % a, a)
        return (g, x - (b // a) * y, y)

def modinv(a, m):
    gcd, x, y = egcd(a, m)
    if gcd != 1:
        return None  # modular inverse does not exist
    else:
        return x % m

def pempriv(p, q, e):
    d = modinv(e,(p-1)*(q-1))
    n = p*q
    dP = d % p
    dQ = d % q
    qInv = pow(q, p - 2, p)
    
    template = '-----BEGIN RSA PRIVATE KEY-----\n{}-----END RSA PRIVATE KEY-----'
    seq = pyasn1.type.univ.Sequence()
    for i,x in enumerate((0, n, e, d, p, q, dP, dQ, qInv)):
        seq.setComponentByPosition(i, pyasn1.type.univ.Integer(x))
    der = pyasn1.codec.der.encoder.encode(seq)
    return template.format(base64.encodebytes(der).decode('ascii'))

if __name__ == "__main__":
    if (len(sys.argv) != 4):
        print("Wrong number of arguments.")
        print("Usage: \"{}\" prime_p prime_q exponent".format(sys.argv[0]))
    else:
        print(pempriv(int(sys.argv[1]), int(sys.argv[2]), int(sys.argv[3])), end = '')