OpenSSL3.0 RSA Signature Verification in C

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I have an RSA keypair in the pem format on disk. I am looking for a comprehensive example in C, on how I can load the private keyfile from disk, sign an example message and then verify the signature with the corresponding public key.

There are plenty of examples that utilize deprecated OpenSSL1.X functions (e.g. PEM_read_RSAPrivateKey), but I can't seem to find a comprehensive example that uses OpenSSL3.0. Not even in the official documentation.

Can someone provide a short example, how I would load the keyfile from disk, and utilize it for sigining and verifying? I would show my own progress, but I don't even know where to get started.

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