Counting equivalence classes for monomial rotation symmetric Boolean functions with prime dimension

2015 ◽  
Vol 8 (1) ◽  
pp. 67-81 ◽  
Author(s):  
Thomas W. Cusick ◽  
Pantelimon Stănică
Keyword(s):  
Boolean Functions ◽  
Equivalence Classes ◽  
Symmetric Boolean Functions ◽  
Rotation Symmetric ◽  
Rotation Symmetric Boolean Functions ◽  
Prime Dimension

Affine equivalence of monomial rotation symmetric Boolean functions: A Pólya’s theorem approach

2016 ◽  
Vol 10 (3-4) ◽  
Author(s):  
Thomas W. Cusick ◽  
K. V. Lakshmy ◽  
M. Sethumadhavan
Keyword(s):  
Boolean Functions ◽  
Affine Transformation ◽  
Equivalence Classes ◽  
Affine Equivalence ◽  
Symmetric Boolean Functions ◽  
Rotation Symmetric ◽  
Long Time ◽  
Input Variables ◽  
Large Groups ◽  
Rotation Symmetric Boolean Functions

AbstractTwo Boolean functions are affine equivalent if one can be obtained from the other by applying an affine transformation to the input variables. For a long time, there have been efforts to investigate the affine equivalence of Boolean functions. Due to the complexity of the general problem, only affine equivalence under certain groups of permutations is usually considered. Boolean functions which are invariant under the action of cyclic rotation of the input variables are known as rotation symmetric (RS) Boolean functions. Due to their speed of computation and the prospect of being good cryptographic Boolean functions, this class of Boolean functions has received a lot of attention from cryptographic researchers. In this paper, we study affine equivalence for the simplest rotation symmetric Boolean functions, called MRS functions, which are generated by the cyclic permutations of a single monomial. Using Pólya’s enumeration theorem, we compute the number of equivalence classes, under certain large groups of permutations, for these MRS functions in any number

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