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The lower bounds on the second order nonlinearity of three classes of Boolean functions with high nonlinearity |
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| Authors: | Guanghong Sun Chuankun Wu |
| Affiliation: | a The State Key Laboratory of Information Security, Institute of Software, Chinese Academy of Sciences, 4# South Fourth Street, Beijing 100190, China b The Graduate University of the Chinese Academy of Sciences, Beijing 100049, China c College of Sciences, Hohai University, Nanjing 210098, China |
| Abstract: | The rth order nonlinearity of Boolean functions is an important cryptographic criterion associated with some attacks on stream and block ciphers. It is also very useful in coding theory, since it is related to the covering radii of Reed-Muller codes. This paper tightens the lower bounds of the second order nonlinearity of three classes of Boolean functions in the form f(x)=tr(xd) in n variables, where (1) d=2m+1+3 and n=2m, or (2)  , n=2m and m is odd, or (3) d=22r+2r+1+1 and n=4r. |
| Keywords: | Boolean function Cryptography Nonlinearity Derivation Walsh coefficient Reed-Muller code |
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