Title: Novel Boolean functions for generating cryptographic stream ciphers

Authors: Dheeraj Kumar Sharma; Rajoo Pandey

Addresses: Department of Electronics and Communication Engineering, National Institute of Technology Kurukshetra, Kurukshetra, Haryana, India ' Department of Electronics and Communication Engineering, National Institute of Technology Kurukshetra, Kurukshetra, Haryana, India

Abstract: In this paper, two constructions of balanced Boolean functions are reported by using powers of primitive elements of Galois field of order 2ⁿ. These balanced Boolean functions are useful in generating pseudorandom stream ciphers. The lower bound of the nonlinearity which decides immunity against cryptographic attacks such as linear correlation attack is calculated. The results indicate that these Boolean functions for small number of input variables obtain greater lower bound of nonlinearity in comparison to existing Boolean functions. Moreover, algebraic degree, algebraic immunity and fast algebraic immunity which decide linear complexity and resistance to algebraic attack are also determined. It is observed that the proposed Boolean functions possess high algebraic degree, optimum algebraic immunity and good resistance to fast algebraic attack which are equivalent or better than that of other existing Boolean functions.

Keywords: Boolean function; cryptography; nonlinearity; stream ciphers; algebraic immunity; fast algebraic attack; algebraic degree; pseudorandom generator; s-box; univariate polynomial representation.

DOI: 10.1504/IJWS.2022.122958

International Journal of Web Science, 2022 Vol.3 No.3, pp.175 - 192

Received: 09 Jul 2018
Accepted: 03 Feb 2019
Published online: 19 May 2022 *

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