# Digital signature forgery

(Redirected from Existential forgery)

In a cryptographic digital signature or MAC system, digital signature forgery is the ability to create a pair consisting of a message $m$ and a signature (or MAC) $\sigma$ that is valid for $m$, where $m$ has not been signed in the past by the legitimate signer. There are three types of forgery: existential, selective, and universal.[1]

## Types[2]:170

### Existential forgery

Existential forgery is the creation (by an adversary) of at least one message/signature pair $(m, \sigma)$, where $\sigma$ was not produced by the legitimate signer. The adversary need not have any control over $m$; $m$ need not have any particular meaning; and indeed it may even be gibberish — as long as the pair $(m, \sigma)$ is valid, the adversary has succeeded in constructing an existential forgery.

Existential forgery is essentially the weakest adversarial goal, therefore the strongest schemes are those that are "existentially unforgeable".

### Selective forgery

Selective forgery is the creation (by an adversary) of a message/signature pair $(m, \sigma)$ where $m$ has been chosen by the adversary prior to the attack. $m$ may be chosen to have interesting mathematical properties with respect to the signature algorithm; however, in selective forgery, $m$ must be fixed before the start of the attack.

The ability to successfully conduct a selective forgery attack implies the ability to successfully conduct an existential forgery attack.

### Universal forgery

Universal forgery is the creation (by an adversary) of a valid signature $\sigma$ for any given message $m$. An adversary capable of universal forgery is able to sign messages he chose himself (as in selective forgery), messages chosen at random, or even specific messages provided by an opponent.

## References

1. ^ Vaudenay, Serge (September 16, 2005). A Classical Introduction to Cryptography: Applications for Communications Security (1st ed.). Springer. p. 254. ISBN 978-0-387-25464-7.
2. ^ Goldwasser, S. and Bellare, M. "Lecture Notes on Cryptography". Summer course on cryptography, MIT, 1996-2001