# Necessary and sufficient conditions for collision-free hashing

@article{Russell2004NecessaryAS, title={Necessary and sufficient conditions for collision-free hashing}, author={Alexander Russell}, journal={Journal of Cryptology}, year={2004}, volume={8}, pages={87-99} }

This paper determines an exact relationship between collision-free hash functions and other cryptographic primitives. Namely, it introduces a new concept, the pseudopermutation, and shows that the existence of collision-free hash functions is equivalent to the existence of claw-free pairs of pseudopermutations. We also give a simple construction of collision-free hash functions from everywhere-defined claw-free (pseudo-) permutations.

## 5 Citations

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- Mathematics, Computer ScienceTCC
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Several new constructions of collision-resistant hash-functions (CRHFs) from general assumptions are presented, including constructions from two other primitives that are implied by homomorphic-encryption: one-round private information retrieval (PIR) protocols and homomorphic one-way commitments.

On the Complexity of Collision Resistant Hash Functions: New and Old Black-Box Separations

- Computer Science, MathematicsIACR Cryptol. ePrint Arch.
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Black-box separations demonstrate that constructions from one-way functions are unlikely, and theoretical constructions of collision-resistant hash functions are based on rather structured assumptions.

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A continuum of function classes that lie between universal one-way hash functions and collision-resistant functions is introduced, and it is proved that the schedule of the Shoup construction is optimal.

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We prove the existence of an oracle relative to which there exist several well-known cryptographic primitives, including one-way permutations, but excluding (for a suitably strong definition)…

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The relationship between public-coin and secret-coin collision-resistant hash function families (CRHFs) is studied and it is demonstrated that public coins used in parameter generation are collision- resistant.

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- Computer Science, MathematicsIACR Cryptol. ePrint Arch.
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A simple way to sidestep this difficulty that avoids having to key the authors' hash functions is explained, to state theorems in a way that prescribes an explicitly-given reduction, normally a black-box one.

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- Computer Science
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This paper proposes a novel hash table implementa tion called Hashsort function, which reduces the collisions, such that automatically increase the access time in the hash table.

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- Computer Science, MathematicsASIACRYPT
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It is observed that if the variety of possible shapes of hash-chains is polynomial, then the time-stamping scheme becomes provably secure, assuming that the underlying hash function is collision-resistant, and it is shown that conventional black-box techniques are unable to prove that chain-resistance follows from collision-Resistance.

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This work describes a technique that maps unranked trees to their hash codes using a bottom-up deterministic tree automaton (DTA) and provides procedures to build incrementally the pseudo-minimal DTA and the associated hash codes.