Designs, Codes and Cryptography

, Volume 87, Issue 12, pp 3045–3062 | Cite as

Construction of resilient Boolean functions in odd variables with strictly almost optimal nonlinearity

  • Yujuan SunEmail author
  • Jiafang Zhang
  • Sugata Gangopadhyay


Construction of resilient Boolean functions in odd variables having strictly almost optimal (SAO) nonlinearity is a challenging problem in coding theory and symmetric ciphers. In this paper, we propose a new method to obtain SAO resilient Boolean functions. By combining this method with High-Meets-Low construction technique, we can obtain resilient functions with better resiliency order and currently best known nonlinearity.


Balanceness Boolean functions Nonlinearity Resiliency Symmetric cryptography 

Mathematics Subject Classification

06E30 94A60 



This study was funded by National Natural Science Foundation of China (Grant Nos. 61672414, U1604180) and National Cryptography Development Fund (Grant No. MMJJ20170113).


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Authors and Affiliations

  1. 1.State Key Laboratory of Integrated Services Networks, Xidian UniversityXi’anChina
  2. 2.State Key Laboratory of CryptologyBeijingChina
  3. 3.School of Mathematics and StatisticsHenan UniversityKaifengChina
  4. 4.Indian Institute of Technology RoorkeeRoorkeeIndia

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