Encryption and decryption address the problem of eavesdropping.
However, tampering and impersonation are still possible.

Public key cryptography addresses the problem of tampering
using a mathematical function called a *one-way hash function* (also
called a message digest function or algorithm). A one-way hash is
a fixed-length number whose value is unique to the data being hashed.
Any change in the data, even deleting or altering a single character,
results in a different value.

For all practical purposes, the content of the hashed data
cannot be deduced from the hash, which is why it is called "one-way."

This principle is the crucial part of digitally signing any
data. Instead of encrypting the data itself, the signing software
creates a one-way hash of the data, then uses your private key to
encrypt the hash. The encrypted hash, along with other information,
such as the hashing algorithm, is known as a *digital signature*.