What dimensions do digital signatures and hash digests add to public key encryption and how do they work?

Although encryption methods still posses limitations and potential flaws, they have dramatically increased the security of data transfer on the Internet. The use of hash functions and digital signatures has been a driving force in addressing the limitations of encryption. In basic format, encryption still faces issues with authentication, repudiation and integrity. With the use of hash functions and digital signatures, the scope of these limitations are substantially decreased.

This article addresses: What dimensions do digital signatures and hash digests add to public key encryption and how do they work?