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Baltic Journal of Modern Computing

Quantum Fingerprinting and Quantum Hashing. Computational and Cryptographical Aspects

Farid Mansurovich Ablayev, Marat Ablayev, Alexander Vasiliev, Mansur Ziatdinov

Published Dec 19, 2016• 24 citations
Publisher

Abstract

Rusins Freivalds was one of the first researchers who introduced methods (later called fingerprinting) for constructing efficient classical randomized and quantum algorithms.Fingerprinting and cryptographic hashing have quite different usages in computer science, but have similar properties.Interpretation of their properties is determined by the area of their usage: fingerprinting methods are methods for constructing efficient randomized and quantum algorithms for computational problems, while hashing methods are one of the central cryptographical primitives.Fingerprinting and hashing methods are being developed from the mid of the previous century, while quantum fingerprinting and quantum hashing have a short history.In the paper we present computational aspects of quantum fingerprinting, discuss cryptographical properties of quantum hashing, and present the possible use of quantum hashing for quantum hash-based message authentication codes.

DOI
10.22364/bjmc.2016.4.4.17

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Rusins Freivalds was one of the first researchers who introduced methods (later called fingerprinting) for constructing efficient classical randomized and quantum algorithms.Fingerprinting and cryptographic hashing have quite different usages in computer science, but have similar properties.Interpretation of their properties is determined by the area of their usage: fingerprinting methods are methods for constructing efficient randomized and quantum algorithms for computational problems, while hashing methods are one of the central cryptographical primitives.Fingerprinting and hashing methods are being developed from the mid of the previous century, while quantum fingerprinting and quantum hashing have a short history.In the paper we present computational aspects of quantum fingerprinting, discuss cryptographical properties of quantum hashing, and present the possible use of quantum hashing for quantum hash-based message authentication codes.
Fingerprinting and cryptographic hashing have quite different usages in computer science, but have similar properties. Interpretation of their properties is determined by the area of their usage: fingerprinting methods are methods for constructing efficient randomized and quantum algorithms for computational problems, whereas hashing methods are one of the central cryptographical primitives. Fingerprinting and hashing methods are being developed from the mid of the previous century, whereas quantum fingerprinting and quantum hashing have a short history. In this chapter, we investigate quantum fingerprinting and quantum hashing. We present computational aspects of quantum fingerprinting and quantum hashing and discuss cryptographical properties of quantum hashing.
Quantum cryptographic primitives beyond key distribution remain a less well understood area of research. In classical cryptography, one-way functions underpin nearly all standard cryptographic protocols, motivating the search for meaningful quantum analogues and for a clear understanding of the physical and computational mechanisms that could enforce one-wayness. In this article, we review quantum one-way functions and a range of closely related quantum-state primitives, including one-way state generators, pseudorandom quantum states, and efficiently indistinguishable pairs of states. We discuss both computational and information-theoretic notions of quantum one-wayness, emphasizing the different adversarial models and security assumptions that underlie these constructions. We compare and contrast the various proposed primitives, and clarify their conceptual relationships. Particular emphasis is placed on questions of physical realizability, experimental feasibility, and robustness to noise. Finally, we outline open problems and future directions toward the development of practical quantum cryptographic primitives beyond key distribution, and the emergence of a broader quantum-cryptographic ecosystem.
In the paper, we define the concept of the quantum hash generator and offer design, which allows to build a large amount of different quantum hash functions. The construction is based on composition of classical ∈ -universal hash family and a given family of functions-quantum hash generator. In particular, using the relationship between ∈ -universal hash families and Freivalds fingerprinting schemas we present explicit quantum hash function and prove that this construction is optimal in the sense of number of qubits needed for construction.
Following its etymology, the term cryptography denotes the techniques used to ensure the confidentiality of information in its storage or transmission. Besides confidentiality, cryptography also encompasses other important functions such as authentication, signature, non-repudiation or secret sharing, to name just a few. The purpose of this section is to give a short introduction to classical cryptography, but only for areas that are relevant to quantum cryptography. For our purposes, we will only deal with confidentiality and authentication. The former is the most important function that quantum key distribution helps to achieve, while the latter is a requirement for quantum key distribution to work. Also, we will cover some topics on the security of classical cryptographic schemes so as to give some insight when comparing classical and quantum cryptography. The study of cryptography ranges from the analysis of cryptographic algorithms (or primitives ) to the design of a solution to a security problem. A cryptographic algorithm is a mathematical tool that provides a solution to a very specific problem and may be based on premises or on other primitives. A solution can be designed by combining primitives, and the requirements and functions of the primitives have to be combined properly. We will first review the confidentiality provided by ciphers that use the same key for both encryption and decryption, hence called secret-key ciphers . Then, we will discuss authentication techniques. Finally, we will show some aspects of public-key cryptography .