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Optimal annihilator immunity with suboptimal bound of other properties

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Abstract

In this paper we present constructions of Boolean functions based on the basic theory of annihilator immunity and bent functions. These constructions provide functions with the maximum possible annihilator immunity, and the nonlinearity and resiliency of the functions can also be calculated with specific cases. Here we have also described certain properties of Boolean functions that are necessary for resistance against algebraic and fast algebraic attacks. Annihilator immunity, nonlinearity and resiliency are important properties of a Boolean function to resist these attacks. There was no systematic attempt made to construct Boolean functions with maximum annihilator immunity that have good bound of nonlinearity and resiliency. We have constructed two different classes of desired Boolean functions through our newly developed method based on multiobjective optimization method(NSGA-II). In the first class, we have constructed bent functions(optimal nonlinearity) with sub-optimal bound of annihilator immunity while in other, Boolean functions having optimal bound of annihilator immunity with good bound of nonlinearity were developed. Our problem was multiobjective(nonlinearity, annihilator immunity and resiliency), hence a heuristic multiobjective optimization technique(NSGA-II) was used.

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  1. Department of Mathematics, University of Delhi, Delhi, Delhi, 110021, India

    Rajni Goyal

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  1. Rajni Goyal
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Correspondence to Rajni Goyal.

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Goyal, R. Optimal annihilator immunity with suboptimal bound of other properties. Int J Syst Assur Eng Manag 9, 1159–1164 (2018). https://doi.org/10.1007/s13198-018-0722-0

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  • DOI: https://doi.org/10.1007/s13198-018-0722-0

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