Cryptographic hash function

All the pre-reffered applications presuppose that an authenticating module that includes a certain cryptographic fimction called "hash function" is nested in the implementation of the application. Hash function H(M) is a transformation that takes an input message M and returns a fixed-size string, which is called the hash value h (that is, h = H(M)). Hash functions with just this property have a variety of general computational uses, but when employed in cryptography, the hash functions are usually chosen to have some additional properties. The basic requirements for a cryptographic hash function are as follows. 

Moreover, [DaPP94] contains a construction from an arbitrary so-called collision-intractable family of hash functions, which is fairly efficient at least if one trusts a fast, but not cryptographically strong hash function, and may therefore be a reasonable alternative if number-theoretic assumptions should be disproved. 

NaYu89 Moni Naor, Moti Yung Universal One-way Hash Functions and their Cryptographic Applications 21st Symposium on Theory of Computing (STOC) 1989, ACM, New York 1989, 33-43. 

Since public key operations are expensive, often a hash function—a cryptographic compression function—is applied to a long message or file before it is signed. In this... 

Because hashing is a one-way function and the output of the function has a low probability of collisions, hashing can be used with the cryptographic product or services family for authentication, nonrepudiation, and data integrity. An example of these is the Digital Notary.3 Hashing is also a key element in the DSA. 

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