Security and Communication Networks

Research Article

A Key Selected S-Box Mechanism and Its Investigation in Modern Block Cipher Design

Table 6

The combined bias distribution (CBD) table of the key selected S-box.
Input maskOutput mask
(8, 4)(0, 4)(0, 4)(0, 4)(0, 4)(0, 4)(0, 4)(0, 4)(0, 4)(0, 4)(0, 4)(0, 4)(0, 4)(0, 4)(0, 4)(0, 4)
(0,4)(−4,1)(0, 1)(−2,2)(−2,1)(0,4)(−2,2)(−2,1)(−2,1)(−2,3)(−2,3)(−4,1)(−2,2)(−2,1)(−2,1)(−2,1)
 (−2,1)(+2,3)(0,1)(0,3) (0,1)(0,1)(0,2)(+4,1)(0,1)(−2,1)(0,1)(0,1)(0,1)(0,1)
 (0,2) (+4,1)  (+4,1)(+2,2)(+2,1)  (+2,1)(+2,1)(+2,1)(+2,1)(+2,2)
(0,4)(−2,1)(−4,1)(−2,1(−2,2)(−2,1)(−2,1)(0,2)(−2,1)(−2,1)(−2,1)(−2,1)(−2,1)(−4,1)(−4,1)(−4,1)
 (0,3)(−2,1) (0,1)(0,2)(0,1)(+2,1)(0,1)(0,1)(0,2)(0,2)(0,2)(0,3)(−2,1)(−2,1)
  (0,2)(0,2)(+2,1)(+2,1)(+2,1)(+4,1)(+2,1)(+2,2)(+4,1)(+2,1)(+4,1) (0,1)(0,1)
   (+2,1)  (+4,1) (+4,1)     (+2,1)(+4,1)
(0,4)(−2,1)(−2,2)(−2,1)(−2,2)(−2,1)(0,2)(−2,2)(−2,1)(−4,1)(0,2)(−2,2)(−4,1)(−2,1)(−4,1)(−4,1)
 (0,2)(+2,2)(0,2)(0,2)(0,2)(+2,2)(0,1)(0,1)(0,2)(+2,2)(+2,2)(−2,2)(0,2)(−2,1)(0,1)
 (+2,1) (+2,1) (+2,1) (+4,1)(+2,1)(+4,1)  (0,1)(+2,1)(+2,1)(+2,2)
        (+4,1)     (+4,1) 
(0,4)(−2,2)(0,3)(−2,2)(−2,1)(−4,1)(−2,2)(−2,1)(−2,1)(−2,1)(−2,1)(−4,1)(−2,1)(−4,1)(0,3)(0,3)
 (0,1)(+2,1)(0,1)(0,2)(−2,2)(0,1)(+2,3)(+2,2)(0,1)(0,2)(0,1)(0,1)(0,1)(+2,1)(+2,1)
 (+4,1) (+2,1)(+4,1)(+2,1)(+4,1) (+4,1)(+2,2)(+2,1)(+2,2)(+2,1)(+2,2)  
(0,4)(−2,1)(−2,2)(−2,1)(−4,1)(−4,1)(−2,2)(−4,1)(0,2)(−4,1)(0,2)(−2,1)(−2,2)(−4,1)(−4,1)(−2,1)
 (0,3)(0,2)(0,3)(−2,1)(−2,2)(0,1)(0,1)(+2,1)(0,3)(+2,1)(0,2)(0,1)(−2,1)(0,2)(0,2)
    (0,1)(+2,1)(+4,1)(+2,1)(+4,1) (+4,1)(+2,1)(+2,1)(0,1)(+2,1)(+2,1)
    (+2,1)  (+4,1)     (+2,1)  
(0,4)(−4,1)(−4,1)(−2,1)(−4,1)(0,3)(−2,1)(−2,1)(−2,2)(−4,1)(−2,3)(−4,1)(−2,1)(−2,2)(−2,2)(−4,1)
 (+2,3)(−2,1)(0,1)(−2,1)(+2,1)(0,2)(0,1)(0,1)(0,3)(+4,1)(0,1)(0,3)(0,1)(0,1)(−2,1)
  (0,1)(+2,2)(0,1) (+2,1)(+2,2)(+2,1)  (+2,2) (+4,1)(+2,1)(0,1)
  (+2,1) (+2,1)          (+2,1)
(0,4)(0,1)(−2,2)(−4,1)(−2,1)(−4,1)(−2,2)(−4,1)(0,1)(−4,1)(−4,1)(−2,2)(−2,2)(−4,1)(0,3)(0,3)
 (+2,2)(0,1)(−2,2)(0,3)(−2,1)(+2,2)(−2,2)(+2,3)(−2,1)(0,3)(0,1)(+2,2)(−2,1)(+2,1)(+2,1)
 (+4,1)(+2,1)(+2,1) (0,2) (0,1) (+2,2) (+4,1) (0,1)  
(0,4)(−2,1)(−2,2)(−2,2)(0,1)(0,2)(−2,2)(−2,2)(0,1)(0,3)(−2,2)(−2,2)(−2,1)(−4,1)(−4,1)(0,2)
 (0,2)(+2,2)(0,1)(+2,2)(+2,2)(0,2)(0,1)(+2,2)(+4,1)(0,2)(+2,2)(0,1)(−2,1)(−2,1)(+2,2)
 (+2,1) (+4,1)(+4,1)  (+4,1)(+4,1)   (+2,1)(0,1)(0,1) 
(0,4)(−4,1)(0,3)(−4,1)(−2,1)(−4,1)(−2,1)(−4,1)(−2,2)(−2,2)(−4,1)(−2,1)(−2,1)(−2,1)(0,2)(−4,1)
 (−2,1)(+2,1)(0,3)(0,2)(−2,2)(0,1)(0,1)(0,2)(0,1)(−2,1)(0,2)(0,2)(0,2)(+2,2)(−2,1)
 (0,2)  (+4,1)(0,1)(+2,1)(+2,1) (+2,1)(+2,2)(+2,1)(+4,1)(+2,1) (0,2)
      (+4,1)(+4,1)        
(0,4)(−4,1)(−4,1)(−4,1)(0,2)(−4,1)(−2,2)(−2,1)(0,4)(−2,3)(−4,1)(−2,2)(−4,1)(0,2)(−2,1)(0,2)
 (−2,1)(−2,2)(0,1)(+2,1)(−2,1)(+2,2)(0,3) (0,1)(−2,2)(0,2)(−2,1)(+2,2)(+2,3)(+2,1)
 (+2,2)(+2,1)(+2,2)(+4,1)(0,1)    (+2,1) (0,2)  (+4,1)
     (+2,1)          
(0,4)(−2,2)(0,3)(−2,1)(−2,2)(−4,1)(−2,1)(−2,1)(−4,1)(−4,1)(−2,1)(−4,1)(−4,1)(−2,1)(−2,2)(−2,2)
 (0,1)(+4,1)(0,1)(0,1)(0,1)(0,2)(0,2)(−2,1)(0,3)(0,1)(0,3)(−2,2)(0,2)(0,2)(0,2)
 (+4,1) (+2,1)(+4,1)(+2,2)(+2,1)(+2,1)(0,1) (+2,1) (0,1)(+2,1)  
   (+4,1)    (+2,1) (+4,1)     
(0,4)(−2,1)(−4,1)(0,2)(−4,1)(0,1)(0,2)(−2,2)(−2,1)(−2,2)(0,2)(0,1)(0,1)(−4,1)(0,2)(−2,2)
 (0,2)(−2,2)(+2,1)(+2,3)(+2,3)(+2,2)(0,2)(+2,2)(0,1)(+2,2)(+2,2)(+2,2)(0,3)(+2,1)(0,1)
 (+2,1)(+2,1)(+4,1)    (+4,1)(+2,1) (+4,1)(+4,1) (+4,1)(+2,1)
(0,4)(−2,2)(−2,2)(−2,1)(−2,1)(−2,2)(0,3)(−2,1)(−2,1)(−4,1)(−2,3)(−2,1)(−2,1)(−4,1)(−2,1)(−4,1)
 (0,1)(0,1)(0,1)(0,2)(+2,1)(+4,1)(0,1)(0,1)(0,3)(0,1)(0,2)(0,1)(−2,2)(+2,2)(0,2)
 (+2,1)(+4,1)(+2,2)(+2,1)(+4,1) (+2,2)(+2,2)  (+2,1)(+2,2)(0,1)(+4,1)(+4,1)
(0,4)(−4,1)(−2,1)(−2,1)(−4,1)(−2,2)(−2,1)(−2,3)(−2,1)(0,3)(−2,3)(−4,1)(0,1)(0,4)(−2,2)(−2,1)
 (−2,2)(0,1)(0,1)(0,3)(0,1)(0,1)(0,1)(0,1)(+4,1)(+4,1)(−2,1)(+2,3) (0,1)(0,1)
 (+2,1)(+2,1)(+2,2) (+2,1)(+2,1) (+2,2)  (0,1)  (+2,1)(+2,1)
  (+4,1)   (+4,1)    (+2,1)   (+4,1)
(0,4)(−2,2)(−4,1)(−4,1)(−2,1)(−2,2)(−4,1)(−2,1)(−4,1)(−2,1)(−2,2)(0,2)(−2,1)(−2,1)(0,1)(−4,1)
 (+2,2)(−2,1)(−2,1)(0,2)(+2,1)(−2,1)(0,2)(0,2)(0,1)(0,2)(+2,2)(0,2)(0,1)(+2,3)(0,2)
  (0,2)(+2,2)(+4,1)(+4,1)(0,1)(+2,1)(+2,1)(+2,2)  (+2,1)(+2,1) (+2,1)
      (+2,1)      (+4,1)