Quantum Algorithms for Cryptographically Significant Boolean Functions: An IBMQ Experience

Boolean functions are important building blocks in cryptography for their wide application in both stream and block cipher systems. For cryptanalysis of such systems one tries to find out linear functions that are correlated to the Boolean functions used in the crypto system. Let $f$ be an $n$ -variable Boolean function and its Walsh spectra is denoted by $W_f(ω)$ at the point $ω\in \{0, 1\}^n$ . The Boolean function is available in the form of an oracle. We like to find an $ω$ such that $W_f(ω) \neq 0$ as this will provide one of the linear functions which are correlated to $f$ . We show that the quantum algorithm proposed by Deutsch and Jozsa (1992) solves the above mentioned problem in constant time. However, the best known classical algorithm to solve this problem requires exponential time in $n$ . We also analyse certain classes of cryptographically significant Boolean functions and highlight how the basic Deutsch-Jozsa algorithm performs on them.Boolean functions are important building blocks in cryptography for their wide application in both stream and block cipher systems. For cryptanalysis of such systems one tries to find out linear functions that are correlated to the Boolean functions used in the crypto system. Let $f$ be an $n$-variable Boolean function and its Walsh spectra is denoted by $W_f(ω)$ at the point $ω\in \{0, 1\}^n$. The Boolean function is available in the form of an oracle. We like to find an $ω$ such that $W_f(ω) \neq 0$ as this will provide one of the linear functions which are correlated to $f$. We show that the quantum algorithm proposed by Deutsch and Jozsa (1992) solves the above mentioned problem in constant time. However, the best known classical algorithm to solve this problem requires exponential time in $n$. We also analyse certain classes of cryptographically significant Boolean functions and highlight how the basic Deutsch-Jozsa algorithm performs on them.

arXiv:quant-ph/0410042Oct 6, 20044 citations

Quantum computation and cryptography: an overview

Manuel Calixto

Natural ComputingAug 14, 20089 citations

Quantum computing: A cryptographic perspective

Fang Song

Jun 17, 20131 citation

THE DEUTSCH–JOZSA ALGORITHM REVISITED IN THE DOMAIN OF CRYPTOGRAPHICALLY SIGNIFICANT BOOLEAN FUNCTIONS

Subhamoy Maitra, PARTHA MUKHOPADHYAY

Boolean functions are important building blocks in cryptography for their wide application in both stream and block cipher systems. For cryptanalysis of such systems, one tries to find out linear functions that are correlated to the Boolean functions used in the crypto system. Let f be an n-variable Boolean function and its Walsh spectra is denoted by Wf(ω) at the point ω ∈ {0, 1}n. The Boolean function is available in the form of an oracle. We like to find a ω such that Wf(ω) ≠ 0 as this will provide one of the linear functions which are correlated to f. We show that the quantum algorithm proposed by Deutsch and Jozsa7 solves this problem in constant time. However, the best known classical algorithm to solve the problem requires exponential time in n. We also analyze certain classes of cryptographically significant Boolean functions and highlight how the basic Deutsch–Jozsa algorithm performs on them.Boolean functions are important building blocks in cryptography for their wide application in both stream and block cipher systems. For cryptanalysis of such systems, one tries to find out linear functions that are correlated to the Boolean functions used in the crypto system. Let f be an n-variable Boolean function and its Walsh spectra is denoted by Wf(ω) at the point ω ∈ {0, 1}n. The Boolean function is available in the form of an oracle. We like to find a ω such that Wf(ω) ≠ 0 as this will provide one of the linear functions which are correlated to f. We show that the quantum algorithm proposed by Deutsch and Jozsa7 solves this problem in constant time. However, the best known classical algorithm to solve the problem requires exponential time in n. We also analyze certain classes of cryptographically significant Boolean functions and highlight how the basic Deutsch–Jozsa algorithm performs on them.

International Journal of Quantum InformationMay 31, 200513 citations

f

be an

n

-variable Boolean function and its Walsh spectra is denoted by

W_f(ω)

at the point

ω\in \{0, 1\}^n

. The Boolean function is available in the form of an oracle. We like to find an

ω

such that

W_f(ω) \neq 0

as this will provide one of the linear functions which are correlated to

f

. We show that the quantum algorithm proposed by Deutsch and Jozsa (1992) solves the above mentioned problem in constant time. However, the best known classical algorithm to solve this problem requires exponential time in

n

. We also analyse certain classes of cryptographically significant Boolean functions and highlight how the basic Deutsch-Jozsa algorithm performs on them.