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Lobachevskii Journal of Mathematics

Collision Resistance of the OAM-based Quantum Hashing

Alexander Vasiliev

Published Feb 1, 2023• 2 citations
Publisher

Abstract

Abstract Recently we have proposed an adapted version of the quantum hash function that minimizes quantum state engineering and experimentally verified the collision resistance of such function. The proposed construction describes a quantum hash as a sequence of single-photon states using orbital angular momentum (OAM) encoding that is a promising platform for optical quantum technologies. In this paper we give an existence proof for parameter sets that will guarantee a very high collision resistance for OAM-based quantum hash function.

DOI
10.1134/s1995080223020361

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Abstract Recently we have proposed an adapted version of the quantum hash function that minimizes quantum state engineering and experimentally verified the collision resistance of such function. The proposed construction describes a quantum hash as a sequence of single-photon states using orbital angular momentum (OAM) encoding that is a promising platform for optical quantum technologies. In this paper we give an existence proof for parameter sets that will guarantee a very high collision resistance for OAM-based quantum hash function.
Quantum hashing is a promising generalization of the cryptographic hashing concept on the quantum domain. In this paper, we construct a quantum hash via a sequence of single-photon states and perform a proof-of-principle experiment using orbital angular momentum (OAM) encoding. We experimentally verify the collision resistance of the quantum hash function depending on the number of qubits in use. Based on these results, we conclude that theoretical estimates are confirmed for different bases of OAM states and the proposed technique can be useful in computational and cryptographic scenarios. The possibility of multiplexing different OAM bases can make this approach even more efficient.
Abstract A new version of quantum hashing technique is developed wherein a quantum hash is constructed as a sequence of single-photon high-dimensional states (qudits). A proof-of-principle implementation of the high-dimensional quantum hashing protocol using orbital-angular momentum encoding of single photons is implemented. It is shown that the number of qudits decreases with increase of their dimension for an optimal ratio between collision probability and decoding probability of the hash. Thus, increasing dimension of information carriers makes quantum hashing with single photons more efficient.
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.
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.