Universal one-way hash function

Unsolved problem in Cryptography

How to construct UOWHF of higher orders efficiently?

In cryptography a Universal One Way Hash Function (UOWHF) is a cryptographic hash function. UOWHF's are proposed as an alternative to CRHF. Collision Resisant Hash Functions (CRHF) are based on stronger assumption that finding a collision in hash function is impossible. Any cryptographic system based on CRHF is considered to be less secure. To overcome this disadvantage, UOWHFs are proposed. UOWHFs are based on weaker assumption that finding a collision in t - Time units with ɛ - probability is impossible, known as (t, ɛ) UOWHF's.

Universal One Way Hash Function (UOWHF) Family contains finite number of hash functions with each having same probability of being used. And collision resistance is achieved by applying hash functions several time from this family. These functions need keys to operate on them.

Construction of UOWHFs

Informally, UOWHF is like re-hashing. The hash function family H contains finite number of hash functions. Based on the text that has to be hashed and block size, different hash functions will be choosed from H. In many cryptographic applications it is desired to construct a hash function which is UOWHF of a certain degree. The challeges regarding this are

To construct UOWHF without wasting random materials, thus minimizing key length.
To achieve higher order UOWHF at the same time.
To find a efficient way to do all this.

UOWHF is used for achieving securable signatures.

External Links

Moni Naor and Moti Yung, "Universal One-Way Hash Functions and their Cryptographic Applications.", 1986, , from [1]

Reference Book

Oded Goldreich, "Foundations of Cryptography" , Volume 2, Cambrige University Press, 2004, from [2]

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