How do you use RSA for both authentication and secrecy?

How do you use RSA for both authentication and secrecy?

RSA is a public key encryption algorithm. The RSA algorithms are based on the mathematical part that it is easy to find and multiply large prime numbers together, but it is extremely difficult to factor their product.

For authentication: One can encrypt the hash (MD4/SHA) of the data with a private key. This is known as digital signature.

For Secrecy: Secrecy/confidentiality is achieved by encrypting the data with public key and decrypting with private key.
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