Although Alice may encrypt her message to make it private, there is still a concern that someone might modify her original message message or substitute it with a different one, in order to transfer the money to themselves, for instance. One way of guaranteeing the integrity of Alice's message is to create a concise summary of her message and send this to the bank as well. Upon receipt of the message, the bank creates its own summary and compares it with the one Alice sent. If they agree then the message was received intact.
A summary such as this is called a message digest, one–way function or hash function. Message digests are used to create short, fixed–length representations of longer, variable–length messages. Digest algorithms are designed to produce unique digests for different messages. Message digests are designed to make it too difficult to determine the message from the digest, and also impossible to find two different messages which create the same digest –– thus eliminating the possibility of substituting one message for another while maintaining the same digest.
Another challenge that Alice faces is finding a way to send the digest to the bank securely; when this is achieved, the integrity of the associated message is assured. One way to to this is to include the digest in a digital signature.