How to create a PEM file for storing an RSA key?

Question

I have an RSA private key $\{d,n\}$ and a public key $\{e,n\}$, where $n$ is the modulus, and I also have the prime factors $p$ and $q$ of $n$.

I want to create a PEM file containing this information, so that I can decrypt a file encrypted with the public key using OpenSSL. How can I do this?

Answer 1

RFC 2313 specifies the RSAPrivateKey ASN1 structure as a SEQUENCE containing the INTEGERs

• $0$;
• $n$;
• $e$;
• $d$;
• $p$;
• $q$;
• $d\bmod(p-1)$;
• $d\bmod(q-1)$;
• $q^{-1}\bmod p$.

The PEM format consists of such a structure encoded as Base64 and framed by the typical BEGIN/END RSA PRIVATE KEY header and footer lines.

Thus, you can use any ASN1 library you like to encode the private key parameters. For example, with Python's pyasn1 module, a private key file's contents can be obtained as follows:

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

def pempriv(n, e, d, p, q, dP, dQ, qInv):
    template = '-----BEGIN RSA PRIVATE KEY-----\n{}-----END RSA PRIVATE KEY-----\n'
    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'))

The parameters dP, dQ and qInv are most easily (as in: lines of code) computed as follows:

dP = d % (p-1)
dQ = d % (q-1)
qInv = pow(q, p-2, p)