Cryptography is valuable for protecting sensitive data online, especially in a world in which an increasing number of systems are connected and vulnerable to outside attack. It is also a valuable tool for authentication, allowing a user to verify his identity and statements using a public key encryption system.
Cryptography's chief advantage is as a security tool. Any system connected to the Internet is bound to eventually be attacked by hackers, and it can be extremely difficult to create a system that is impregnable to outsiders. However, the mathematical formulas involved in encryption are complex enough that even if a hacker manages to steal an encrypted file, he may never be able to break through the code and access the contents. Strong encryption can be a last line of defense against outsiders, and can protect data even when it is being transferred through a connection that is not secure.
The public and private keys associated with public key cryptography also offer some unique advantages to their users. If a user encrypts data with his private key, anyone can decrypt it with his public key, verifying that he and only he could have sent the transmission. A public key can also encode data that only that specific user can decode, creating secure one-way communications on the Internet.