Quantum Hash Functions Research Articles

Analysis of the amplitude form of the quantum hash function

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.

Quantum hash function based on controlled alternate lively quantum walks

Quantum hash function is an important area of interest in the field of quantum cryptography. Quantum hash function based on controlled alternate quantum walk is a mainstream branch of quantum hash functions by virtue of high efficiency and flexibility. In recent development of this kind of schemes, evolution operators determined by an input message depend on not only coin operators, but also direction-determine transforms, which usually are hard to extend. Moreover, the existing works ignore the fact that improper choice of initial parameters may cause some periodic quantum walks, and further collisions. In this paper, we propose a new quantum hash function scheme based on controlled alternate lively quantum walks with variable hash size and provide the selection criteria for coin operators. Specifically, each bit of an input message determines the magnitude of an additional long-range hop for the lively quantum walks. Statistical analysis results show excellent performance in the aspect of collision resistance, message sensitivity, diffusion and confusion property, and uniform distribution property. Our study demonstrates that a fixed coin operator, along with different shift operators, can effectively work on the design of a quantum hash function based on controlled alternate quantum walks, and shed new light on this field of quantum cryptography.

Quantum-Inspired Blockchain-Based Cybersecurity: Securing Smart Edge Utilities in IoT-Based Smart Cities

Blockchain plays a vital task in cybersecurity. With the exerted efforts for realising large-scale quantum computers, most current cryptographic mechanisms may be hacked. Accordingly, we need a quantum tool utilised for designing blockchain frameworks to have the ability to be executed in the level of digital computers and resist the probable attacks from both digital and quantum computers. Quantum walks may be utilised as a quantum-inspired model for designing new cryptographic algorithms. In this paper, we present a new authentication and encryption protocol based on quantum-inspired quantum walks (QIQW). The proposed protocol is utilized to build a blockchain framework for secure data transmission among IoT devices. Instead of using classical cryptographic hash functions, quantum hash functions based on QIQW are employed for linking blocks of the chain. The main advantages of the presented framework are helping IoT nodes to effectively share their data with other nodes and full control of their records. Security analysis demonstrates that our proposed protocol can defend against message attack and impersonation attacks, thus ensuring secure transmission of data among IoT devices.

Usefulness of Decoherence in Quantum-Walk-Based Hash Function

We study the usefulness of the broken-line-type decoherence in quantum Hash functions based on discrete-time quantum walks on a cycle. We first observe that the time-evolution of probability distribution of quantum walks on a cycle is of high sensitivity to such broken-line-type decoherence, increasing with the number of steps in the walk. Based on this observation, we further propose a quantum Hash function based on the broken-line quantum walk on a cycle. Numerical simulation and performance analyses show that decoherence can be useful to improve the performances of quantum hash functions such as better diffusion and confusion, better collision resistance and more uniform distribution of hash values in the hash space. Moreover, our results promote the practical use of quantum-walk-based hash functions in realistic situations.

Analysis of Properties of Quantum Hashing

We analyze a method of binary quantum hashing that allows one to represent binary sets as quantum states. We show that this method is very stable with respect to the recovery of preimages. Moreover, we propose heuristic approaches to small-bias sets on which the construction of quantum hash-functions is based and show that they are stable with respect to collisions.

Attacking Quantum Hashing. Protocols and Their Cryptanalysis

Quantumhash functions are similar to classical (cryptographic) hash functions and their security is guaranteed by physical laws. However, security of a primitive does not automatically mean that protocols based on this primitive are secure. We propose protocols based on quantum hash function and assess their security using Holevo entropy and recently introduced notion of quantum information cost.

Efficient Branching Programs for Quantum Hash Functions Generated by Small-Biased Sets

In the paper we consider quantum (δ, ϵ)-hash functions in so called phase form (phase quantum (δ, ϵ)-hash function). It is known that ϵ-biased sets generate phase quantum (δ, ϵ)- hash function. We show that the construction is invertible, that is, phase quantum (δ, ϵ)-hash function defines ϵ-biased sets. Next, we present an efficient (in the sense of time and qubits needed) Branching program construction for phase quantum (δ, ϵ)-hash function.

Constructing quantum Hash functions based on quantum walks on Johnson graphs

We present a quantum hash function in a quantum walk framework on Johnson graphs. In this quantum hash function, the message bit decides which coin operator, i.e., Grover operator or DFT operator, is applied on the coin at each step. Then a fixed conditional shift operator is applied to decide the movement of the walker. Compared with existing quantum-walk-based hash functions, the present hash function has a lower collision rate and quantum resource cost. It provides a clue for the construction of other cryptography protocols by introducing the quantum walk model into hash functions.

Controlled Alternate Quantum Walks based Quantum Hash Function

Through introducing controlled alternate quantum walks, we present controlled alternate quantum walks (CAQW) based quantum hash function. CAQW based quantum hash function have excellent security, outstanding statistical performance and splendid expansibility. Furthermore, due to the structure of alternate quantum walks, implementing CAQW based quantum hash function significantly reduces the resources necessary for its feasible experimental realization than implementing other quantum hash functions.

From graphs to keyed quantum hash functions

We present two new constructions of quantum hash functions: the first based on expander graphs and the second based on extractor functions and estimate the amount of randomness that is needed to construct them. We also propose a keyed quantum hash function based on extractor function that can be used in quantum message authentication codes and assess its security in a limited attacker model.

Quantum Hashing. Group approach

In this paper we consider a generalization of quantum hash functions for arbitrary groups. We show that quantum hash function exists for arbitrary abelian group. We construct a set of "good" automorphisms --- a key component of quantum hash funciton. We prove some restrictions on Hilbert space dimension and group used in quantum hash function

On the balanced quantum hashing

In the paper we define a notion of a resistant quantum hash function which combines a notion of pre-image (one-way) resistance and the notion of collision resistance. In the quantum setting one-way resistance property and collision resistance property are correlated: the “more” a quantum function is one-way resistant the “less” it is collision resistant and vice versa. 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 balanced quantum hash functions.

On the concept of cryptographic quantum hashing

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.

Quantum hashing via ∈-universal hashing constructions and classical fingerprinting

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.

Cryptographic quantum hashing

We present a version of quantum hash functions based on non-binary discrete functions. The proposed quantum procedure is ‘classical-quantum’, that is, it takes a classical bit string as an input and produces a quantum state. The resulting function has the property of a one-way function (pre-image resistance); in addition it has properties analogous to classical cryptographic hash second pre-image resistance and collision resistance. We also show that the proposed function can be naturally used in a quantum digital signature protocol.