Talk:Universal one-way hash function

Confusing and contradicting
This article needs to be improved. Here are just a few places where the current article is confusing and contradicting: That's already wrong. One of the advantages of UOWHF is that they have weaker assumptions than cryptographic hash functions, hence UOWHF need not necessarily be cryptographic hash functions. Again, wrong. If the hash function is secure then it is only infeasible to find collisions not impossible. Less secure than what? This seems to describe a cryptographic hash function. If I understand it correctly, then UOWHFs require some form of 2nd preimage resistance and not collision resistance. I can't find such a theorem in the papers given as reference. Again, I can't find any reference for using keys in the definition given by Naor and Yung. Taken out of context. Confusing. Why would it be a mistake to design a collision resistant CRHF? This is unclear, because it is taken out of context. Again, unclear because the role of the keys has not been specified. Undefined. What are higher order UOWHFs? Unclear. Does that mean if UOWHFs exist then a secure signature scheme exists or does it mean that some signature schemes in use today are based on UOWHFs?
 * In cryptography a Universal One Way Hash Function (UOWHF), ..., is a cryptographic hash function.
 * Collision Resistant Hash Functions (CRHF) are based on the stronger assumption that finding a collision in hash function is impossible.
 * Any cryptographic system based on CRHF is considered to be less secure.
 * UOWHFs are based on weaker assumption that finding a collision in $$t$$ time units with probability $$\epsilon$$ is impossible, known as $$(t,\epsilon)$$-UOWHF's.
 * And collision resistance is achieved by applying hash functions several time from this family.
 * These functions need keys to operate on them.
 * In CRHF the adversary wins the game once he finds a collision pair.
 * Assuming CRHF and designing hash functions based on that would be a costly mistake.
 * The security bound is $$2^n$$ when the output length is n.
 * In UOWHF the adversary does not win for any collision. He has to specify a state, say S, and then he gets the key K. He now has to find a collision for the specified S and $$h_K$$.
 * To achieve higher order UOWHF at the same time.
 * UOWHF is used for achieving secure signatures.

85.2.41.214 13:06, 9 July 2007 (UTC)

Confusing and contradicting, continued
Used for what?
 * The UOWHF family contains a finite number of hash functions with each having the same probability of being used.

84.226.6.172 (talk) 17:08, 8 September 2013 (UTC)