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* [[Very smooth hash|VSH - Very Smooth Hash function]] - a provably secure collision-resistant hash function assuming the hardness of finding nontrivial modular square roots modulo composite number (this is assumed to be as hard as integer factorization).
* [[MuHASH]]
* [[Elliptic Curve Only hash function|ECOH - Elliptic Curve Only hash function]] - based on the concept of Elliptic curves, Subset Sum Problem and summation of polynomials. The security proof of the collision resistance was based on weakend assumptions and eventually a second pre-image attack was found.
* [[Fast Syndrome-Based hash function|FSB - Fast Syndrome-Based hash function]] - it can be proven that breaking FSB is at least as difficult as solving a certain NP-complete problem known as Regular Syndrome Decoding.
* [[SWIFFT hash function|SWIFFT]]
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