期刊
IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES
卷 E101A, 期 12, 页码 2397-2401出版社
IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG
DOI: 10.1587/transfun.E101.A.2397
关键词
Boolean function; second-order nonlinearity; bent function; differential uniformity
类别
资金
- NationalNatural Science Foundation of China [61872435, 61602394]
- Guangxi Key Laboratory of Cryptography and Information Security [GCIS201724]
Boolean functions used in stream ciphers and block ciphers should have high second-order nonlinearity to resist several known attacks and some potential attacks which may exist but are not yet efficient and might be improved in the future. The second-order nonlinearity of Boolean functions also plays an important role in coding theory, since its maximal value equals the covering radius of the second-order Reed-Muller code. But it is an extremely hard task to calculate and even to bound the second-order nonlinearity of Boolean functions. In this paper, we present a lower bound on the second-order nonlinearity of the generalized Maiorana-McFarland Boolean functions. As applications of our bound, we provide more simpler and direct proofs for two known lower bounds on the second-order nonlinearity of functions in the class of Maiorana-McFarland bent functions. We also derive a lower bound on the second-order nonlinearity of the functions which were conjectured bent by Canteaut and whose bentness was proved by Leander, by further employing our bound.
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