The Deutsch-Jozsa algorithm revisited in the domain of cryptographically significant boolean functions
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 (w) at the point w is an element of {0, 1}(n). The Boolean function is available in the form of an oracle. We like to find a w such that W-f (w) not equal 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(7) 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 walsh spectra quantum algorithms query complexity