Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics Conference Series

Quantum hashing and Fourier transform

Farid Mansurovich Ablayev, Alexander Vasiliev

Published Dec 1, 2020• 4 citations
Publisher

Abstract

In the paper based on the notion of small-biased sets we define the quantum transformation that describes the quantum hash function over the cyclic group. We discuss its similarity to the well-known Quantum Fourier Transform and show possible applications to constructing space-efficient algorithms in various computational scenarios, including two-party quantum communication model, simultaneous message passing model, and the model of quantum online streaming algorithms.

DOI
10.1088/1742-6596/1680/1/012001

Related papers

Quantum hashing for finite abelian groups

Alexander Vasiliev

We propose a generalization of the quantum hashing technique based on the notion of small-bias sets. These sets have proved useful in different areas of computer science, and here their properties give an optimal construction for succinct quantum presentation of elements of any finite abelian group, which can be used in various computational and cryptographic scenarios. We consider two special cases of the proposed quantum hashing which turn out to be the known quantum fingerprinting schemas.

arXiv:1603.02209•Lobachevskii Journal of Mathematics•Nov 1, 2016•33 citations

Analysis of the amplitude form of the quantum hash function

Marat Ablayev, Farid Mansurovich Ablayev, Alexander Vasiliev

In this article, the properties of quantum hash functions are further explored. Previous findings show that so-called small-bias sets (special subsets of the set of elements of a cyclic group) generate a “phase” quantum hash function. Here, it was proved that they also generate an “amplitude” quantum hash function. Namely, it turned out that constructing small-bias sets while generating amplitude quantum functions yields a well-balanced combination of the cryptographic properties of unidirectionality and collision resistance. As a corollary of the obtained theorem, a general statement about the generation of new amplitude quantum hash functions based on universal hash families and small-bias sets was proved.

Učenye zapiski Kazanskogo gosudarstvennogo universiteta. Seriâ Fiziko-matematičeskie nauki/Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki•Nov 13, 2023•2 citations

Constant-Depth Algorithm for Quantum Hashing

Alexander Vasiliev

Abstract Quantum hashing is one of the techniques that allow to construct space-efficient quantum algorithms and protocols. We present a construction that allows to make it extremely time efficient. Our approach is based on the shallow implementation of the quantum fingerprinting technique but uses additional circuit identities specific to the quantum hash function for the cyclic group. The resulting algorithm is equivalent to the one we have implemented earlier using single-photon states with orbital angular momentum encoding.

Russian Microelectronics•Dec 1, 2023•6 citations

Theory and Applications of Quantum Hashing

Farid Mansurovich Ablayev, Kamil Ravilevich Khadiev, Alexander Vasiliev +1 more

We review recent results on quantum one-way functions, including quantum fingerprinting or quantum hashing (we use these two terms as synonyms even though they have very small difference). This includes the analysis of their properties, different modifications, circuit implementation on an IBM Q platform, as well as on an experimental quantum setup. We discuss computational aspects of quantum hashing, its cryptographic properties and possible usage in communication protocols and algorithms.

Quantum Reports•May 15, 2025•8 citations

On the concept of cryptographic quantum hashing

Farid Mansurovich Ablayev, Marat Ablayev

In the letter we define the notion of a quantum resistant ( -resistant) hash function which consists of a combination of pre-image (one-way) resistance ( ε -resistance) and collision resistance ( δ -resistance) properties. We present examples and discussion that supports the idea of quantum hashing. We present an explicit quantum hash function which is ‘balanced’, one-way resistant and collision resistant and demonstrate how to build a large family of quantum hash functions. Balanced quantum hash functions need a high degree of entanglement between the qubits. We use a phase transformation technique to express quantum hashing constructions, which is an effective way of mapping hash states to coherent states in a superposition of time-bin modes. The phase transformation technique is ready to be implemented with current optical technology.

arXiv:1509.01268•Laser Physics Letters•Nov 10, 2015•28 citations

Quantum hashing based on symmetric groups

Mansur Ziatdinov

The notion of quantum hashing formalized by F. Ablayev and A. Vasiliev in 2013. F. Ablayev and M. Ablayev in 2014 introduced the notion of quantum hash generator which is convenient technical tool for constructing quantum hash func- tions. M. Ziatdinov in 2014 presented group approach for constructing quantum hash functions. All these mentioned above results present constructions of quan- tum hash functions based on abelian groups. This paper continue the research on quantum hashing. Our approach allows us to construct quantum hash function working on any (finite) group. Also our approach allows us to construct quantum hash functions based on classical hash function from $NC^1$.

arXiv:1612.07646•Dec 21, 2016•0 citations
In the paper based on the notion of small-biased sets we define the quantum transformation that describes the quantum hash function over the cyclic group. We discuss its similarity to the well-known Quantum Fourier Transform and show possible applications to constructing space-efficient algorithms in various computational scenarios, including two-party quantum communication model, simultaneous message passing model, and the model of quantum online streaming algorithms.
In this article, the properties of quantum hash functions are further explored. Previous findings show that so-called small-bias sets (special subsets of the set of elements of a cyclic group) generate a “phase” quantum hash function. Here, it was proved that they also generate an “amplitude” quantum hash function. Namely, it turned out that constructing small-bias sets while generating amplitude quantum functions yields a well-balanced combination of the cryptographic properties of unidirectionality and collision resistance. As a corollary of the obtained theorem, a general statement about the generation of new amplitude quantum hash functions based on universal hash families and small-bias sets was proved.
Abstract Quantum hashing is one of the techniques that allow to construct space-efficient quantum algorithms and protocols. We present a construction that allows to make it extremely time efficient. Our approach is based on the shallow implementation of the quantum fingerprinting technique but uses additional circuit identities specific to the quantum hash function for the cyclic group. The resulting algorithm is equivalent to the one we have implemented earlier using single-photon states with orbital angular momentum encoding.
In the letter we define the notion of a quantum resistant ( -resistant) hash function which consists of a combination of pre-image (one-way) resistance ( ε -resistance) and collision resistance ( δ -resistance) properties. We present examples and discussion that supports the idea of quantum hashing. We present an explicit quantum hash function which is ‘balanced’, one-way resistant and collision resistant and demonstrate how to build a large family of quantum hash functions. Balanced quantum hash functions need a high degree of entanglement between the qubits. We use a phase transformation technique to express quantum hashing constructions, which is an effective way of mapping hash states to coherent states in a superposition of time-bin modes. The phase transformation technique is ready to be implemented with current optical technology.
The notion of quantum hashing formalized by F. Ablayev and A. Vasiliev in 2013. F. Ablayev and M. Ablayev in 2014 introduced the notion of quantum hash generator which is convenient technical tool for constructing quantum hash func- tions. M. Ziatdinov in 2014 presented group approach for constructing quantum hash functions. All these mentioned above results present constructions of quan- tum hash functions based on abelian groups. This paper continue the research on quantum hashing. Our approach allows us to construct quantum hash function working on any (finite) group. Also our approach allows us to construct quantum hash functions based on classical hash function from NC1NC^1NC1.