cryptography Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or ''-logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adver ...

a universal one-way hash function (UOWHF, often pronounced "woof"), is a type of

universal hash function In mathematics and computing, universal hashing (in a randomized algorithm or data structure) refers to selecting a hash function at random from a family of hash functions with a certain mathematical property (see definition below). This guarantees ...

of particular importance to

. UOWHF's are proposed as an alternative to collision-resistant hash functions (CRHFs). CRHFs have a strong collision-resistance property: that it is hard, given randomly chosen hash function parameters, to find any collision of the hash function. In contrast, UOWHFs require that it be hard to find a collision where one

preimage In mathematics, the image of a function is the set of all output values it may produce. More generally, evaluating a given function f at each element of a given subset A of its domain produces a set, called the "image of A under (or through) ...

is chosen independently of the hash function parameters. The primitive was suggested by

Moni Naor Moni Naor ( he, מוני נאור) is an Israeli computer scientist, currently a professor at the Weizmann Institute of Science. Naor received his Ph.D. in 1989 at the University of California, Berkeley. His advisor was Manuel Blum. He works i ...

and

Moti Yung Mordechai M. "Moti" Yung is a cryptographer and computer scientist known for his work on cryptovirology and kleptography. Career Yung earned his PhD from Columbia University in 1988 under the supervision of Zvi Galil. In the past, he worked at the ...

and is also known as "target collision resistant" hash functions; it was employed to construct general digital signature schemes without trapdoor functions, and also within chosen-ciphertext secure public key encryption schemes. The UOWHF family contains a finite number of hash functions with each having the same probability of being used.

Definition

The security property of a UOWHF is as follows. Let

A

be an algorithm that operates in two phases: * Initially,

A

receives no input (or, just a security parameter) and chooses a value

x

. * A hash function

H

is chosen randomly from the family.

A

then receives

H

and must output

y \ne x

such that

H(x) = H(y)

. Then for all polynomial-time

A

the probability that

A

succeeds is negligible.

Applications

UOWHFs are thought to be less computationally expensive than CRHFs, and are most often used for efficiency purposes in schemes where the choice of the hash function happens at some stage of execution, rather than beforehand. For instance, the Cramer–Shoup cryptosystem uses a UOWHF as part of the validity check in its ciphertexts.

External links

and

, ''
Universal One-Way Hash Functions and their Cryptographic Applications
, 1989.'' Cryptographic hash functions

Definition

Applications

See also

Further reading

External links