Improvements for Finding Impossible Differentials of Block Cipher Structures

Algorithm 3

The algorithm for checking an impossible differential.

input: A differential pair and the system

output: A boolean flag indicates if is an impossible differential

(1) is the augmented matrix of ;

(2) is the dimension variable vector;

(3) is the map of constraints of ;

(4) flagfalse;

(5) indextrue;

(6) Initialize every variable in according to and the constraints in ;

(7) while  index  do

(8) UpdateMatrix (, ) // Update    according to  ;

  Transform    into the reduced-row-echelon form by Gauss-Jordan Elimination  

(9) ReducedRowEchelon ();

(10) if   has no solution then

(11) flagtrue;

(12) break;

(13) else

(14) index false;

(15) count 0;

(16) for     to  1 do

(17) Row of ;

(18) if the sum of the first elements of is 1 then

(19) the index of the element in ;

(20) the last element of ; // the solution of the  th  variable in  

(21)   update the variable vector    with    and return true if there is

no contradiction and return false otherwise.

(22) UpdateVector (, , , );

(23) if   is false then

(24) flag true;

(25) return flag;

(26) else

(27) index true;

(28) end

(29) end

(30) end

(31) end

(32) end

(33) return  flag;