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Create a public-private key pair. The pair is stored in the generated mykey.pem file.

$ openssl genrsa -out mykey.pem 1024

Extract the public key and print it out.

$ openssl rsa -in mykey.pem -pubout > mykey.pub

To just output the public part of a private key:

$ openssl rsa -in key.pem -pubout -out pubkey.pem