Applied Preimage Attacks
By definition, an ideal hash function is such that the fastest way to compute a first or second preimage is through a brute force attack. For an n-bit hash, this attack has a time complexity, which is considered too high for a typical output size of n=160 bits. If such complexity is the best that can be achieved by an adversary, then the hash function is considered preimage resistant.
Faster preimage attacks can be found by cryptanalysing certain hash functions, and are specific to that function. Some significant preimage attacks have already been discovered, but they are not yet practical. If a practical preimage attack is discovered, it would drastically affect many Internet protocols. In this case, "practical" means that it could be executed by an attacker in a meaningful amount of time for a meaningful amount of money. A preimaging attack that costs trillions of dollars and takes decades to preimage one desired hash value or one message is not practical; one that costs a few thousand dollars and takes a few weeks might be very practical.
All currently known practical or almost-practical attacks on MD5 and SHA-1 are collision attacks. In general, a collision attack is easier to mount than a preimage attack, as its is not restricted by any set value (any two values can be used to collide). The time complexity of the collision attack, in contrast, is
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