To create a digital signature for a message, the data to be signed is encrypted by an algorithm that takes as input the private key of the sender. (Alice). Largely due to performance reasons, the entire message data is not typically encrypted, but rather a digital thumbprint of the message (hash / digest) is created and then encrypted.

The hash of the message, which was encrypted with the sender's (Alice) private key, acts as a digital signature for that message. The receiver (Bob) verifies the signature by applying the same hash function as the sender (Alice) to the message that was sent, and decrypting the encrypted message digest using the sender's (Alice) public key. If the two values match, the receiver has successfully authenticated the signature.

The digital signature is created as follows:

1) The sender (Alice) of the message uses a message digest function, such as SHA-1, MD5 to create a message hash / digest of the message contents.

2) The digest is then encrypted using the private key of the sender.

3) This encrypted digest is then attached to the message as the digital signature.

The digital signature is verified as follows:

1) The receiver of the message uses the sender's public key to decrypt the digital signature. If it decrypted successfully, the receiver knows that the message came from the holder of the private key.

If decryption of the digital signature using the sender's public key fails, someone may be attempting to impersonate the sender.

2) The receiver then uses the message digest function to calculate the hash associated with the message contents. If the hash is the same value as the one decrypted from the digital signature, the receiver can be confident that the message was not altered or modified in transit.

If the hash values are different, the message may have been altered after signing, or corrupted in transit. In addition, if the sender and receiver are using different hash functions (MD5 versus SHA-1), the hash comparison will also fail.