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Quantum algorithm for Boolean Equation Solving and Quantum Algebraic Attack on Cryptosystems

Journal of Systems Science & Complexity 2022年第1期35卷 373-412页

作者： CHEN Yu-Ao GAO Xiao-Shan Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China University of Chinese Academy of Sciences Beijing 100049China

This paper presents a quantum algorithm to decide whether a Boolean equation system F has a solution and to compute one if F does have solutions with any given success *** runtime complexity of the algorithm is polynomial in the size of F and the condition number of certain Macaulay matrix associated with *** a consequence,the authors give a polynomial-time quantum algorithm for solving Boolean equation systems if their condition numbers are polynomial in the size of *** authors apply the proposed quantum algorithm to the cryptanalysis of several important cryptosystems:The stream cipher Trivum,the block cipher AES,the hash function SHA-3/Keccak,the multivariate public key cryptosystems,and show that they are secure under quantum algebraic attack only if the corresponding condition numbers are *** leads to a new criterion for designing such cryptosystems which are safe against the attack of quantum computers:The corresponding condition number.

关键词： Block cipher AES Boolean equation solving condition number hash function SHA3/Keccak hhl algorithm MPKC polynomial system solving quantum algorithm stream cipher Trivum

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Near Term Hybrid Quantum Computing Solution to the Matrix Riccati Equations

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Journal of Quantum Computing 2022年第3期4卷 135-146页

作者： Augusto Gonzalez Bonorino Malick Ndiaye Casimer DeCusatis Claremont Graduate University Claremont91711USA Marist College Poughkeepsie12601USA

The well-known Riccati differential equations play a key role in many fields,including problems in protein folding,control and stabilization,stochastic control,and cybersecurity(risk analysis and malware propaga-tion).Quantum computer algorithms have the potential to implement faster approximate solutions to the Riccati equations compared with strictly classical *** systems with many qubits are still under development,there is significant interest in developing algorithms for near-term quantum computers to determine their accuracy and *** this paper,we propose a hybrid quantum-classical algorithm,the Matrix Riccati Solver(MRS).This approach uses a transformation of variables to turn a set of nonlinear differential equation into a set of approximate linear differential equations(i.e.,second order non-constant coefficients)which can in turn be solved using a version of the Harrow-Hassidim-Lloyd(hhl)quantum algorithm for the case of Hermitian *** implement this approach using the Qiskit language and compute near-term results using a 4 qubit IBM Q System quantum *** with classical results and areas for future research are discussed.

关键词： Quantum computing matrix ricatti equations differential equations qiskit hybrid algorithm hhl algorithm

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