Terms & Definitions

Some of the most important properties of cryptographic / secure hash are:

1. Hash inversion is hard:

   For any x: given only hash(x), it is hard to find x

   This property assumes that the value x is not known. It also assumes that x is not more than the maximum value that can be hashed.

2. Hash forgery is hard:

   Given x, it is hard to find a y != x such that hash(y) = hash(x)

   This property assumes that x and y are not more than the maximum value that can be hashed.

3. Linear hash operations are hard:

   For any x: given only hash(x), and c != 0, it is hard to compute hash(x + c)

   This property assumes that the value x is not known. It also assumes that both x + c and x are not more than the maximum value that can be hashed.