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A quantum algorithm to approximate the linear structures of Boolean functions

HONGWEI LI, LI YANG
2016 Mathematical Structures in Computer Science  
A quantum algorithm to determine approximations of linear structures of Boolean functions is presented and analysed.  ...  A proper combination of these two approaches results here to a polynomial-time approximation to the linear structures set.  ...  Acknowledgement This work was supported by the National Natural Science Foundation of China under Grant No.61173157.  ... 
doi:10.1017/s0960129516000013 fatcat:3fselvn645hmpk3r3htvlgcbx4

Quantum Half and Full Spinning Operator Based Nonlinear Confusion Component

Abdullah Alghafis
2021 IEEE Access  
The structure of a substitution box (S-box) is one of the principal ideas of the modern encryption techniques.  ...  The security of a modern encryption algorithm highly depends on its nonlinear confusion component.  ...  CATEGORIZATION OF CONFUSION COMPONENT The nonlinear confusion component is categorized into three types. 1) ONE TO ONE BOOLEAN FUNCTION A multivalued Boolean functions S is said to be one-to-one if the  ... 
doi:10.1109/access.2021.3060498 fatcat:r6qcx6uqezd4fdwjzkonm2qbde

Linear Cryptanalysis through the Lens of Clauser-Horne-Shimony-Holt Game [article]

Arpita Maitra, Ravi Anand, Suman Dutta
2021 arXiv   pre-print
Application of CHSH game in Linear Cryptanalysis is presented. Till date, the known usage of CHSH game in Quantum Cryptology is to verify the device independence of the protocols.  ...  This observation opens a new direction of research in quantum cryptography.  ...  BOOLEAN CHSH GAME FOR IMPROVING THE BIAS OF SIMON To exploit the Boolean circuit of CHSH game in SI-MON , we need to design SIMON round function in quantum domain.  ... 
arXiv:2111.01656v2 fatcat:eccxsqqeuvfj3dnamhbcefdhje

Quantum algorithms for testing and learning Boolean functions

DOMINIK FLOESS, ERIKA ANDERSSON, MARK HILLERY
2013 Mathematical Structures in Computer Science  
There are 2 n possible linear Boolean functions of n input variables; given a linear Boolean function, the Bernstein-Vazirani quantum algorithm can deterministically identify which one of these Boolean  ...  We show how the same quantum algorithm can also be used to learn which input variables any other type of Boolean function depends on.  ...  We are given a black box that evaluates Quantum algorithms for testing and learning Boolean functions 387 a Boolean function f(x 1 , x 2 , . . . x n ) that maps {0, 1} n to {0, 1}.  ... 
doi:10.1017/s0960129512000151 fatcat:dvb7juy6k5cmlihlrqvlav7lve

Three Puzzles on Mathematics, Computation, and Games [article]

Gil Kalai
2018 arXiv   pre-print
The first puzzle is to understand the amazing success of the simplex algorithm for linear programming. The second puzzle is about errors made when votes are counted during elections.  ...  The third puzzle is: are quantum computers possible?  ...  Puzzle 1: What can explain the success of the simplex algorithm? Linear programming is the problem of maximizing a linear function φ subject to a system of linear inequalities.  ... 
arXiv:1801.02602v1 fatcat:zeicivye4zhjjc6t32tyhu2pn4

Using Bernstein-Vazirani Algorithm to Attack Block Ciphers [article]

Huiqin Xie, Li Yang
2018 arXiv   pre-print
Specifically, we first present a quantum algorithm for finding the linear structures of a function.  ...  Afterwards, by observing that the linear structures of a encryption function are actually high probability differentials of it, we apply our algorithm to differential analysis and impossible differential  ...  Based on these two facts, Li and Yang present a quantum algorithm to find the linear structures of a Boolean function in [16] .  ... 
arXiv:1711.00853v3 fatcat:n53gqqa5qbdaxm6yjod3lwlene

Using Bernstein–Vazirani algorithm to attack block ciphers

Huiqin Xie, Li Yang
2018 Designs, Codes and Cryptography  
Specifically, we first present a quantum algorithm for finding the linear structures of a function.  ...  Afterwards, by observing that the linear structures of a encryption function are actually high probability differentials of it, we apply our algorithm to differential analysis and impossible differential  ...  Based on these two facts, Li and Yang present a quantum algorithm to find the linear structures of a Boolean function in [17] .  ... 
doi:10.1007/s10623-018-0510-5 fatcat:xr7j6sxqwzgudpuyilu3m356na

New advanced computing architecture for cryptography design and analysis by D-Wave quantum annealer

Xiangmin Ji, Baonan Wang, Feng Hu, Chao Wang, Huanguo Zhang
2022 Tsinghua Science and Technology  
derived from the binary structure of the integers to be factored.  ...  First, although we optimize the general quantum Hamiltonian on the basis of the structure of the multiplication table (factor up to 1 005 973), this study attempts to explore the simplification of Hamiltonian  ...  Acknowledgment This study was supported by the Special Zone Project of National Defense Innovation, the National Natural Science Foundation of China (Nos. 61572304 and 61272096), the Key Program of the  ... 
doi:10.26599/tst.2021.9010022 fatcat:3vzoo3imcrcs3o4iy2vrdtwcxu

Is Quantum Search Practical?

G.F. Viamontes, I.L. Markov, J.P. Hayes
2005 Computing in science & engineering (Print)  
consists of applying quantum gates to quantum states, but because the input to the algorithm might be normal classical bits (or nonquantum), it only affects the selection of quantum gates.  ...  The authors show that several commonly suggested applications of Grover's quantum search algorithm fail to offer computational improvements over the best conventional algorithms.  ...  Acknowledgments This work is supported in part by DARPA, the US National Science Foundation, and a US Department of Energy High-Performance Computer Science graduate fellowship.  ... 
doi:10.1109/mcse.2005.53 fatcat:m4fcd2q3dveotme3pf6qkjhwmi

Tunable Quantum Neural Networks for Boolean Functions [article]

Viet Pham Ngoc, Herbert Wiklicky
2020 arXiv   pre-print
We use this construction to introduce the idea of a generic quantum circuit whose gates can be tuned to learn any Boolean functions.  ...  This ability arises from the correspondence that exists between a Boolean function and a particular quantum circuit made out of multi-controlled NOT gates.  ...  between the algebraic normal form of a Boolean function and the quantum circuit able to compute this function over the ancillary qubit.  ... 
arXiv:2003.14122v2 fatcat:ksrxuda3sngdpal2y2ousc5fv4

The Power of Discrete Quantum Theories [article]

Andrew J. Hanson, Gerardo Ortiz, Amr Sabry, Jeremiah Willcock
2011 arXiv   pre-print
We explore the implications of restricting the framework of quantum theory and quantum computation to finite fields.  ...  Quantum theories over these fields retain the notion of unitaries and --- for particular problem sizes --- allow the same algorithms as conventional quantum theory.  ...  We would like to thank J. R. Busemeyer, J. M. Dunn, A. Lumsdaine, and L. S. Moss for many inspiring discussions. We acknowledge support from Indiana University's Institute for Advanced Study.  ... 
arXiv:1104.1630v1 fatcat:ml5fcvfypvcc3d4jwujdapavfu

Polynomial unconstrained binary optimisation inspired by optical simulation [article]

Dmitry A. Chermoshentsev, Aleksei O. Malyshev, Egor S. Tiunov, Douglas Mendoza, Alán Aspuru-Guzik, Aleksey K. Fedorov, Alexander I. Lvovsky
2021 arXiv   pre-print
The application of our algorithm to quantum chemistry sheds light on the shortcomings of approximating the electronic structure problem by a PUBO problem, which, in turn, puts into question the applicability  ...  We benchmark the proposed algorithm against existing PUBO algorithms on the extended Sherrington-Kirkpatrick model and random third-degree polynomial pseudo-Boolean functions, and observe its superior  ...  The part on quantum chemistry is also partially supported by Nissan Research (QUBO analysis). D.A. acknowledges Nikita Stroev for fruitful discussions.  ... 
arXiv:2106.13167v1 fatcat:svquaeousfegfavyncgfxiol3q

Algorithms for Boolean Function Query Properties [article]

Scott Aaronson
2001 arXiv   pre-print
We also give a subexponential-time algorithm for the space-bounded quantum query complexity of a Boolean function.  ...  These algorithms are based on new insights into the structure of Boolean functions that may be of independent interest.  ...  Andris Ambainis and an anonymous reviewer for comments and corrections, Wim van Dam for a simplification in Section 7, and Peter Bro Miltersen for correspondence.  ... 
arXiv:cs/0107010v1 fatcat:7ep5k6hrzbhtxlj7ely2tpv3qi

Algorithms for Boolean Function Query Properties

Scott Aaronson
2003 SIAM journal on computing (Print)  
-A notion of a 'tree decomposition' of a Boolean function, proof that the decomposition is unique, and an O(N log 2 3 log N ) algorithm for finding it.  ...  We investigate efficient algorithms for computing Boolean function properties relevant to query complexity.  ...  Quantum Query Complexity. The quantum query complexity of a Boolean function f is the minimum number of oracle queries needed by a quantum computer to evaluate f .  ... 
doi:10.1137/s0097539700379644 fatcat:styjketzxve6zgbl4ns3yysmum

Quantum impossible differential and truncated differential cryptanalysis [article]

Huiqin Xie, Li Yang
2018 arXiv   pre-print
Based on the fact that Bernstein-Vazirani algorithm can be used to find the linear structures of Boolean functions, we propose two quantum algorithms that can be used to find high-probability truncated  ...  Thus, in order to accurately evaluate the security of symmetric primitives in the post-quantum world, it is significant to improve classical cryptanalytic methods using quantum algorithms.  ...  He first runs Algorithm 1 to obtain the approximate linear structures of each F j , then chooses a vector that is common approximate linear structure of multiple component functions F ′ j s as the input  ... 
arXiv:1712.06997v2 fatcat:egopwr524fhxteqqxupjzz3jrm
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