What is Public Key Cryptography?
Public key cryptography (often also termed asymmetric key cryptography) is based on natural asymmetries in the ability to perform certain mathematic computations1. In the 1970s, algorithms were published that leveraged these mathematical principles to provide (among other things) the ability to sign digital data, establishing a mathematically irrefutable endorsement or authorization, as well as a tamper-evident integrity "seal," on the data.
Public key cryptography has been studied rigorously, and implemented widely, with an impeccable track record. It now forms the underpinnings of modern security systems ranging from military applications to the global banking system. Modern asymmetric cryptography signatures are considered computationally unassailable using current technologies.
However, by design, public key cryptography remains vulnerable to inappropriate disclosure of the signing key (more popularly termed the private key to denote the requirement for maintaining its secrecy). Anyone with possession of the private key can forge signatures, authorized or not.