How to create public and private key with OpenSSL?

My questions are:

• How to create
  • a public key
  • and a private key with OpenSSL on Windows?
• How to put the created public key
  • in a .crt file and
  • the private one in a .pkcs8 file?

I want to use these two keys to sign a SAML assertion in Java.

You can generate a public-private keypair with the genrsa context (the last number is the keylength in bits):

openssl genrsa -out keypair.pem 2048

To extract the public part, use the rsa context:

openssl rsa -in keypair.pem -pubout -out publickey.crt

Finally, convert the original keypair to PKCS#8 format with the pkcs8 context:

openssl pkcs8 -topk8 -inform PEM -outform PEM -nocrypt -in keypair.pem -out pkcs8.key