What is the primary purpose of using digital signatures in cryptography?

The primary purpose of using digital signatures in cryptography is authentication. Digital signatures verify the origin of a message or document and confirm that it has not been altered in transit. This means that the recipient can trust the identity of the sender and the integrity of the message.

When a sender encrypts their message with their private key, any recipient with the sender's public key can decrypt and verify the signature. This process assures the recipient that the document was indeed created by the purported sender, establishing non-repudiation as well; the sender cannot later deny having signed the document.

In contrast, while encryption plays a role in securing the contents of data, obfuscation involves obscuring information without necessarily providing proof of authenticity, and compression refers to reducing the size of data, which does not relate to verifying the source or integrity of information. Thus, authentication stands out as the correct answer when considering the main function served by digital signatures in cryptography.