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IGA : An Improved Genetic Algorithm to Construct Weightwise (Almost) Perfectly Balanced Boolean Functions with High Weightwise Nonlinearity

Published: 10 July 2023 Publication History

Abstract

The Boolean functions satisfying secure properties on the restricted sets of inputs are studied recently due to their importance in the framework of the FLIP stream cipher. However, finding Boolean functions with optimal cryptographic properties is an open research problem in the cryptographic community. This paper presents an Improved Genetic Algorithm (IGA) with the directed changes that keep the weightwise balancedness of Boolean functions. A cross-protection strategy is proposed to ensure that the offspring has the same weightwise balancedness characteristics of the parents while implementing crossover. Then, a large number of weightwise (almost) perfectly balanced (W(A)PB) functions with a good nonlinearity profile are obtained based on IGA. Finally, we make comparisons between our constructions and relevant works. The comparisons show that IGA has a significant advantage for reaching the W(A)PB functions with high weightwise nonlinearity. Moreover, it is the first time to obtain the 8-variable WPB functions with the weightwise nonlinearity of 28 in the restricted sets of inputs with Hamming weight of 4, and list the statistical indicators of the weightwise nonlinearity for W(A)PB functions for input size n = 9, 10.

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Cited By

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  • (2024)$$\mathcal {S}_0$$-equivalence classes, a new direction to find better weightwise perfectly balanced functions, and moreCryptography and Communications10.1007/s12095-024-00719-w16:6(1211-1234)Online publication date: 14-May-2024
  • (2024)Look into the Mirror: Evolving Self-dual Bent Boolean FunctionsGenetic Programming10.1007/978-3-031-56957-9_10(161-175)Online publication date: 3-Apr-2024

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  1. IGA : An Improved Genetic Algorithm to Construct Weightwise (Almost) Perfectly Balanced Boolean Functions with High Weightwise Nonlinearity

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      cover image ACM Conferences
      ASIA CCS '23: Proceedings of the 2023 ACM Asia Conference on Computer and Communications Security
      July 2023
      1066 pages
      ISBN:9798400700989
      DOI:10.1145/3579856
      Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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      Published: 10 July 2023

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      Author Tags

      1. Boolean function
      2. Genetic algorithm
      3. Nonlinearity
      4. Weightwise (almost) perfectly balancedness

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      View all
      • (2024)$$\mathcal {S}_0$$-equivalence classes, a new direction to find better weightwise perfectly balanced functions, and moreCryptography and Communications10.1007/s12095-024-00719-w16:6(1211-1234)Online publication date: 14-May-2024
      • (2024)Look into the Mirror: Evolving Self-dual Bent Boolean FunctionsGenetic Programming10.1007/978-3-031-56957-9_10(161-175)Online publication date: 3-Apr-2024

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