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About this paper
Alexander Vasiliev
A generalized quantum hashing technique is presented for elements of any finite abelian group, utilizing ε-biased sets to construct quantum hash functions. This method achieves asymptotically optimal succinctness for quantum states while offering strong collision resistance and irreversibility, thereby unifying prior quantum fingerprinting and hashing schemes.
Key insights
- ε-biased sets over finite abelian groups offer a mathematically robust and natural framework for constructing quantum hash functions with essential cryptographic properties.
- The construction yields quantum hashes that are asymptotically optimal in succinctness, requiring O(log log|G| - log ε) qubits for inputs of log|G| bits.
- This generalized approach unifies previously distinct quantum fingerprinting and hashing schemes by demonstrating they are specific instances within this broader framework.
Summary by alphaXiv.
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