Digital signature forgery

In a cryptographic digital signature or MAC system, digital signature forgery is the ability to create a pair consisting of a message, ${\displaystyle m}$, and a signature (or MAC), ${\displaystyle \sigma }$, that is valid for ${\displaystyle m}$, but has not been created in the past by the legitimate signer. There are different types of forgery.

To each of these types, security definitions can be associated. A signature scheme is secure by a specific definition if no forgery of the associated type is possible.