Collision resistance

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Collision resistance is a property of cryptanalytic hash functions : a hash function is collision insubordinate if it is hard to find two inputs that hash to the like output ; that is, two inputs a and b such that H ( a ) = H ( b ). Every hash officiate with more inputs than outputs will necessarily have collisions. Consider a hash function such as SHA-256 that produces 256 bits of output from an randomly large stimulation. Since it must generate one of 2256 outputs for each member of a much larger fit of inputs, the pigeonhole principle guarantees that some inputs will hash to the lapp output. collision immunity does n’t mean that no collisions exist ; merely that they are difficult to find. The birthday “ paradox ” places an amphetamine boundary on collision immunity : if a hashish function produces N bits of output, an attacker who computes “ only ” 2 N /2 hash operations on random input is likely to find two matching outputs. If there is an easier method than this animal violence attack, it is typically considered a flaw in the hashish officiate.

cryptanalytic hash functions in general habit today are designed to be collision resistant, but alone identical few of them are absolutely so. MD5 and SHA-1 in particular both have published techniques more effective than animal military unit for finding collisions. [ 1 ] [ 2 ] however, some compression functions have a proof that finding collision is at least a unmanageable as some hard mathematical trouble ( such as integer factorization or discrete logarithm ). Those functions are called demonstrably impregnable .

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collision resistance is desirable for several reasons.

  • In some digital signature systems, a party attests to a document by publishing a public key signature on a hash of the document. If it is possible to produce two documents with the same hash, an attacker could get a party to attest to one, and then claim that the party had attested to the other.
  • In some proof-of-work systems, users provide hash collisions as proof that they have performed a certain amount of computation to find them. If there is an easier way to find collisions than brute force, users can cheat the system.
  • In some distributed content systems, parties compare cryptographic hashes of files in order to make sure they have the same version. An attacker who could produce two files with the same hash could trick users into believing they had the same version of a file when they in fact did not.

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