[openssl] Convert PEM traditional private key to PKCS8 private key

To convert the private key from PKCS#1 to PKCS#8 with openssl:

# openssl pkcs8 -topk8 -inform PEM -outform PEM -nocrypt -in pkcs1.key -out pkcs8.key

That will work as long as you have the PKCS#1 key in PEM (text format) as described in the question.