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encrypted with Alice's private key. Since Alice would never share
her private key with anyone, we know that this message must
have come from Alice. Since the message Alice sent is not
confidential - anyone with her public key could read the message
- we refer to the operation of encrypting a message with a private
key as 'signing' the message. Note this is not the same as a digital
signature, which we will look at later; a digital signature signs a
hash of the message, not the message itself.

So, rule number three is:
Encrypting a message with a private key provides proof of origin.

The problem with asymmetric algorithms is that they are very
computationally intensive and very slow. Asymmetric algorithms
should not be used to encrypt large messages. That is why
asymmetric cryptography is used to encrypt short messages such
as a symmetric key or to encrypt a hash of a message as a digital
signature.

Message Integrity and Hashing Algorithms
The earliest networks used by computers to communicate were
based on older voice-grade telephone cable and were of poor
quality, analog, and limited bandwidth. This meant that error-
correcting was needed to ensure data integrity. This was
originally done using methods such as parity bits, checksums,
and Cyclic Redundancy Checks (CRC).

These methods were good to detect errors introduced by noise
on the transmission line, but would not be effective to prevent a
malicious individual from intercepting and altering both the
message and the integrity value. In that case, the recipient would
not realize that the message had actually been altered en route.