scholarly journals Balanced 2p-variable rotation symmetric Boolean functions with optimal algebraic immunity

2016 ◽  
Vol 215 ◽  
pp. 20-30 ◽  
Author(s):  
Lei Sun ◽  
Fang-Wei Fu
Keyword(s):  
Boolean Functions ◽  
Algebraic Immunity ◽  
Symmetric Boolean Functions ◽  
Rotation Symmetric ◽  
Rotation Symmetric Boolean Functions

Some Cryptographic Properties of Rotation Symmetric Boolean Functions

2013 ◽  
Vol 321-324 ◽  
pp. 2704-2707 ◽  
Author(s):  
Jing Lian Huang ◽  
Chun Ling Zhang ◽  
Ya Jing Liu
Keyword(s):  
Internal Structure ◽  
Boolean Functions ◽  
Structural Features ◽  
Algebraic Immunity ◽  
Third Order ◽  
Symmetric Boolean Functions ◽  
Analytic Combinatorics ◽  
The Third ◽  
Rotation Symmetric ◽  
Rotation Symmetric Boolean Functions

Using the derivative of H Boolean functions and the e-derivativedefined by the authors as the research tools, we go deep into the internal structure of the Booleanfunction values​​, additionally,by the methods of cascade calculations and analytic combinatorics, cryptographic properties such as structural features, existence,balance and algebraic immunity of rotation symmetric H Boolean functions withdiffusibility are studied. Then we get the results that the Second Order rotation symmetric Boolean functionsare H Boolean functions,andthe results to the issues such asthe balance and algebraic immunity of rotation symmetric H Boolean functionsand the existence of the Third Order symmetric H Boolean functions are also be established.

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