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Journal of Chinese Computer Systems

Security Research of BLAKE Algorithm Based on Grover Quantum Search Algorithm and Quantum Counting

Jing Sun

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

This article presents a quantum search method of Hash collision,based on the combination of Grover search algorithm and quantum counting algorithm ideas.We give a quantum circuit diagram for quantum counting on Hash collision.Then we put forward the circuit design of corresponding quantum black-box for the typical Hash function BLAKE.Finally we make a brief performance analysis about our method.

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This article presents a quantum search method of Hash collision,based on the combination of Grover search algorithm and quantum counting algorithm ideas.We give a quantum circuit diagram for quantum counting on Hash collision.Then we put forward the circuit design of corresponding quantum black-box for the typical Hash function BLAKE.Finally we make a brief performance analysis about our method.
Block cipher has some advantages such as fast,easy to achieve standardization and ease of hardware and software.It has the most extensive application in the computer communication and information system security.This article presents a parallel quantum key search model of block cipher,based on the combination of Grover search algorithm and classical parallel search ideas.Then we put forward the circuit design of corresponding quantum black-box of the typical block cipher.Finally we give a brief performance analysis.
Quantum computers have the potential to solve a number of hard problems that are believed to be almost impossible to solve by classical computers. This observation has sparked a surge of research to apply quantum algorithms against the cryptographic systems to evaluate its quantum resistance. In assessing the security strength of the cryptographic algorithms against the upcoming quantum threats, it is crucial to precisely estimate the quantum resource requirement (generally in terms of circuit depth and quantum bit count). The National Institute of Standards and Technology by the US government specified five quantum security levels so that the relative quantum strength of a given cipher can be compared to the standard ones. There have been some progress in the NIST-specified quantum security levels for the odd levels (i.e., 1, 3 and 5), following the work of Jaques et al. (Eurocrypt’20). However, levels 2 and 4, which correspond to the quantum collision finding attacks for the SHA-2 and SHA-3 hash functions, quantum attack complexities are arguably not well-studied. This is where our article fits in. In this article, we present novel techniques for optimizing the quantum circuit implementations for SHA-2 and SHA-3 algorithms in all the categories specified by NIST. After that, we evaluate the quantum circuits of target cryptographic hash functions for quantum collision search. Finally, we define the quantum attack complexity for levels 2 and 4, and comment on the security strength of the extended level. We present new concepts to optimize the quantum circuits at the component level and the architecture level.
In this note, we give a quantum algorithm that finds collisions in arbitrary τ-to-one functions after only O ( 3 √ N /τ) expected evaluations of the function. Assuming the function is given by a black box, this is more efficient than the best possible classical algorithm, even allowing probabilism. We also give a similar algorithm for finding claws in pairs of functions. Furthermore, we exhibit a space-time tradeoff for our technique. Our approach uses Grover's quantum searching algorithm in a novel way.
We study some extensions of Grover's quantum searching algorithm. First, we generalize the Grover iteration in the light of a concept called amplitude amplification. Then, we show that the quadratic speedup obtained by the quantum searching algorithm over classical brute force can still be obtained for a large family of search problems for which good classical heuristics exist. Finally, as our main result, we combine ideas from Grover's and Shor's quantum algorithms to perform approximate counting, which can be seen as an amplitude estimation process.
At present, the scale of quantum computers in the real sense is still small, and quantum simulation has become one of the important ways of quantum theory research, grover quantum search algorithm is suitable for the search problem of disordered database. Firstly, according to the implementation principle of Grover algorithm and Boolean logic relationship, the design idea of multi-objective Oracle is analyzed, based on IBMQ quantum cloud platform, the quantum circuit of Grover algorithm with multi-objective items is simulated. Based on the characteristics of Grover algorithm and the simulation process of quantum gate, the action of multiple identical quantum gates is combined to reduce the update times of probability amplitude and improve the simulation efficiency. The libquantum quantum simulator is used for experiments and the target item is successfully searched, which proves the feasibility of the optimization method and provides reference for the simulation and optimization of other quantum algorithms.
This paper develops and analyzes Grover’s quantum search algorithm in 2- and 3-qubit systems in terms of the number of gates, representation of state vectors, and state vector measurement probabilities. We designed, verified and simulated the quantum circuit using QCAD. We present a theoretical implementation of the search algorithm in different qubit systems. We may observe that our circuit design for 2-qubit systems is accurate and does not allow any error when a small error occurs in the design of a 3-qubit quantum system. it was considered to what extend given information about object of the research is used purposefully in the modeling process, as a result of mathematical analysis of Grover’s method of the quantum algorithm, i.e. it is important to provide the adequacy of the model. The results of the optimization performed with the quantum algorithm based on Grover’s method are presented.