# Tag Info

## New answers tagged collision-resistance

0

It is unlikely that a secure X-bit hash function's X/2-bit truncation would not be X/2-bit secure. For example, suppose you have a faster than $2^{128}$ second preimage attack on the 128-bit truncation of a 256-bit hash. Then you can run that attack $2^{128}$ times and expect to find a second preimage for some value of the full 256-bit hash, so that hash ...

1

Recall that randomly chosen functions, used to model good hash functions, are collision resistant if we need on the order of $2^{n/2}$ queries in order to discover a collision with success probability a constant bounded away from zero. Proof by contrapositive: Assume $h$ is NOT collision resistant. Then we can find such collisions much faster than ...

2

A mathematically elegant and rather simple way of hashing are the parity bits of a Hamming code, as small changes in the data will yield different parity bits. You can weakly hash 4-bit strings to 3-bit strings with the standard (7,4) Hamming code, but the general Hamming code construction has high enough rate that you can hash longer strings (say, 26 bits ...

0

You can tune the difficulty of finding collisions very simply by reducing the number of output bits from any hash function. For example, if you take SHA-256 and reduce it to SHA-13 (by only returning the 13 least significant bits of the output), it becomes a far weaker hash function. Now the probability of finding a collision is a mere 1 in 2^13 for each ...

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