cryptography - Is it possible to encrypt with private key using .net RSACryptoServiceProvider?

Question

I know that RSACryptoServiceProvider can encrypt with the public key, then it can be decrypted with the private key.

Is it possible to encrypt with the private key and decrypt with the public key using the RSACryptoServiceProvider ?

Answer 1

Just to clear things up a bit:

RSA can be used either for encryption (ensuring that Eve cannot read messages that Alice sends to Bob) or for signing (ensuring that if Alice sends a message to Bob, Bob knows that it was actually Alice that sent the message, and not Eve pretending to be Alice)

RSA generates a pair of keys - a public key and a private key. RSA is designed so that if you apply the public key and then apply the private key, or vice versa, you will get the same message back. And the public key can be derived from the private key, but the opposite is impossible.

To use RSA for encryption, Alice encrypts the message using Bob's public key. The only way to read this message is with Bob's private key, which only he has. Thus Eve can't read the message because he does not have this key. On the other hand, this provides no authentication of the source of the message. Eve can also get Bob's public key (since it's public) and send messages to Bob, pretending to be Alice.

To use RSA for signing, Alice takes a hash of the message, encrypts the hash using her own private key, and appends the result (this is the signature) to the message. Eve can of course still decrypt this using Alice's public key. However, Bob can decrypt the signature using Alice's public key and see if it matches. If it does, it must have been encrypted using Alice's private key, which only she has, so it must have come from Alice.

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Now, I'm not familiar with the .NET cryptography API, so I'm not sure if it works exactly as described here. But this explanation might help you understand some of the answers you are getting.