Universal one-way hash function
In cryptography a universal one-way hash function (UOWHF, often pronounced "woof"), is a type of universal hash function of particular importance to cryptography. 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 is chosen independently of the hash function parameters. The primitive was suggested by Moni Naor and Moti Yung  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 formula_1 be an algorithm that operates in two phases: Then for all polynomial-time formula_1 the probability that formula_1 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.