Digital signature

A digital signature is a mathematical scheme for verifying the authenticity of digital messages or documents. A valid digital signature on a message gives a recipient confidence that the message came from a sender known to the recipient.

Digital signatures are a type of public-key cryptography, and are commonly used for software distribution, financial transactions,^{[citation needed]} contract management software,^{[citation needed]} and in other cases where it is important to detect forgery or tampering.

A digital signature on a message or document is similar to a handwritten signature on paper, but it is not restricted to a physical medium like paper—any bitstring can be digitally signed—and while a handwritten signature on paper could be copied onto other paper in a forgery, a digital signature on a message is mathematically bound to the content of the message so that it is infeasible for anyone to forge a valid digital signature on any other message.

Digital signatures are often used to implement electronic signatures, which include any electronic data that carries the intent of a signature, but not all electronic signatures use digital signatures.

A digital signature scheme consists of three algorithms:

Two main properties are required:

Formally, a digital signature scheme is a triple of probabilistic polynomial-time algorithms, (G, S, V), satisfying:

Here 1ⁿ refers to a unary number in the formalism of computational complexity theory.