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* '''Collision resistance''': it should be ''hard'' to find two different messages m1 and m2 such that hash(m1) = hash(m2). Such a pair is called a (cryptographic) hash collision. This property is sometimes referred to as strong collision resistance. It requires a hash value at least twice as long as what is required for pre-image resistance, otherwise collisions may be found by a [[birthday attack]].
The basic question is the meaning of "'''hard'''". There are two approaches to answer this question. First is the intuitive/practical approach: "hard means that it is almost certainly beyond the reach of any adversary who must be prevented from breaking the system for as long as the security of the system is deemed important."
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