### Cryptographically Significant Boolean Functions: Construction and Analysis in Terms of Algebraic Immunity [chapter]

Deepak Kumar Dalai, Kishan Chand Gupta, Subhamoy Maitra
<span title="">2005</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Algebraic attack has recently become an important tool in cryptanalysing different stream and block cipher systems. A Boolean function, when used in some cryptosystem, should be designed properly to resist this kind of attack. The cryptographic property of a Boolean function, that resists algebraic attack, is known as Algebraic Immunity (AI). So far, the attempt in designing Boolean functions with required algebraic immunity was only ad-hoc, i.e., the functions were designed keeping in mind the
more &raquo; ... other cryptographic criteria, and then it has been checked whether it can provide good algebraic immunity too. For the first time, in this paper, we present a construction method to generate Boolean functions on n variables with highest possible algebraic immunity n 2 . Such a function can be used in conjunction with (using direct sum) functions having other cryptographic properties. In a different direction we identify that functions, having low degree subfunctions, are weak in terms of algebraic immunity and analyse some existing constructions from this viewpoint.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11502760_7">doi:10.1007/11502760_7</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/eq5nx5qexjgjpg7pf7pu5wgvti">fatcat:eq5nx5qexjgjpg7pf7pu5wgvti</a> </span>
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