To generate private key do
openssl ecparam -genkey -name prime256v1 -out ec_private.pem
openssl pkcs8 -topk8 -nocrypt -in ec_private.pem -out ec_private_pkcs8.pemUse key from ec_private_pkcs8.pem as private key
To generate public key do
openssl ec -in ec_private.pem -pubout -out ec_public.pemJava обычно предпочитает ключи в формате PKCS#8.