How to use RSA key for generating and verifying JWT Token in assymetric way?

[abhinabanag92]

1. We are planning to Generate a public/private key pair. Expose the public key to business client while storing the private key in an encrypted KVM. Use the private key for generating JWT Token.
2. Another public/private key pair will be generated for another api proxy, while verifying the JWT Token and calling end service of the business client.
3. We will expose only the public keys over network during transaction.

Please suggest how to achieve it using RSA keys.