A hash function H is a transformation that takes a variablesize input m and returns a fixedsize 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:

• the input can be of any length,
• the output has a fixed length,
• H(x) is relatively easy to compute for any given x ,
• H(x) is oneway,
• H(x) is collisionfree.

A hash function H is said to be oneway if it is HARD to invert, where "hard to invert" means that given a hash value h, it is computationally infeasible to find some input x such that H(x) = h.

If, given a message x, it is computationally infeasible to find a message y not equal to x such that H(x) = H(y) then H is said to be a weakly collisionfree hash function.

A strongly collisionfree hash function H is one for which it is computationally infeasible to find any two messages x and y such that H(x) = H(y).

A hash function H is a transformation that takes a variablesize input m and returns a fixedsize 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:

A hash function H is said to be oneway if it is hard to invert, where "hard to invert" means that given a hash value h, it is computationally infeasible to find some input x such that H(x) = h.

If, given a message x, it is computationally infeasible to find a message y not equal to x such that H(x) = H(y) then H is said to be a weakly collisionfree hash function.

A strongly collisionfree hash function H is one for which it is computationally infeasible to find any two messages x and y such that H(x) = H(y).