Elliptic Curve Keys with OpenSSL

List pre-defined curves in OpenSSL:

$ openssl ecparam -list_curves | grep prime256v1
  prime256v1: X9.62/SECG curve over a 256 bit prime field

Generate private key:

$ openssl ecparam -name prime256v1 -genkey -noout -out prime256v1.key.pem

Generate public key:

$ openssl ec -in prime256v1.key.pem -pubout -out prime256v1.pem

Reference: https://wiki.openssl.org/index.php/Command_Line_Elliptic_Curve_Operations