Algebraic Cryptanalysis Scheme of AES-256 Using Gröbner Basis

Algorithm 2

Algebraic cryptanalysis algorithm of AES-256.

(1)   list the equation system of AES-256 algorithm;

(2)  select a known plaintext and ciphertext pair, and substitute it into the equation system;

(3)  construct Gröbner basis Ggrelex of the ideal relative to degree lexicographical order using the method in Section 5.1;

(4)  judge the solution structure of the Gröbner basis. Because the equation system contains the field equation, the equation

    is finite or no solution.

(5)  if and only if Ggrelex = (1) then

(6)   the equation system is no solution;

(7)   if it is no solution, then

(8)    select another plaintext and ciphertext pair to return to Step (3);

(9)   else continue;

(10)      end if

(11)  end if

(12) convert degree lexicographical Gröbner basis Ggrelex to lexicographical Gröbner basis Glex by using FGLM algorithm;

(13) solve the key variables;

(14) verify the correctness of key by applying plaintext, ciphertext and key to AES-256 algorithm;

(15) return the key value;