{"paper":{"title":"Constructing Boolean Functions With Potential Optimal Algebraic Immunity Based on Additive Decompositions of Finite Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CR","authors_text":"Baofeng Wu, Dongdai Lin, Qingfang Jin, Zhuojun Liu","submitted_at":"2014-01-26T01:49:10Z","abstract_excerpt":"We propose a general approach to construct cryptographic significant Boolean functions of $(r+1)m$ variables based on the additive decomposition $\\mathbb{F}_{2^{rm}}\\times\\mathbb{F}_{2^m}$ of the finite field $\\mathbb{F}_{2^{(r+1)m}}$, where $r$ is odd and $m\\geq3$. A class of unbalanced functions are constructed first via this approach, which coincides with a variant of the unbalanced class of generalized Tu-Deng functions in the case $r=1$. This class of functions have high algebraic degree, but their algebraic immunity does not exceeds $m$, which is impossible to be optimal when $r>1$. By m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6604","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}