## 5 Results and Analysis  
On AES, we found that linear cryptanalysis attacks are possible on rounds one and two only. Attacks are impossible on rounds three and above. The main building block that makes rounds one and two possible for linear cryptanalysis attacks is the S-Box. The S-Box of AES is 8 \(\times\) 8, meaning that it has 8 inputs and 8 outputs. We found that it is easy to construct a LAT table using the AES S-Box. The LAT of the AES S-Box is a table of 2\({}^{8}\)\(\times\) 2\({}^{8}\) matrixes with probability entities for guessing a key. We wrote a C++ program to construct the LAT of the AES S-Box. We confirmed that it is possible to attack the AES algorithm using LAT after analyzing the procedure. To block linear attack, we mapped GF (**232**) and its long irreducible polynomial to obtain a new S-Box with 32-bit output. The new S-Box for AES was constructed. We tried to construct the LAT of a new S-Box, which is supposed to be a 2\({}^{8}\)\(\times\) 2\({}^{32}\) matrix. That is a 256 \(\times\) 4,294,967,296 matrix. We found that it is infeasible to construct the LAT of a new AES S-Box with an output of 32 bits because of the maximum size allocation. We tried to use array **232** = 4,294,967,296 size, and we found that we also have to include input 2\({}^{8}\) = 256. The program for constructing LAT on a new S-Box crashed before LAT was constructed due to a lack of memory. The computation of **232** needs more than 2\({}^{64}\) memory allocations, which is impossible. [PERSON] et al. [37] (p. 121) also confirmed that it is infeasible to construct a probability table (like LAT) for a 32-bit output S-Box because it needs a memory of 2\({}^{64}\), which is impossible. To achieve probabilities of guessing a key from a 32-bit output, S-Box is impossible [38] (p. 9). 32-bit S-Boxes are robust to linear cryptanalysis attacks due to the cost of computing LAT due to the memory required [39] (p. 179). Therefore, we managed to block and prevent LAT construction using GF (**232**) and its long irreducible polynomial. GF (**232**) and long irreducible polynomials always yield 32-bit output when applied to S-Box or any building block of an algorithm. No LAT, no linear cryptanalysis attack. Therefore, we managed to secure AES against the linear cryptanalysis attack. For Blowfish, the linear cryptanalysis attack was performed on P-arrays rather than S-boxes. S-Boxes of Blowfish already have 32-bit output, so attackers avoided S-Boxes and attacked P-array because P-array is weakly generated [26]. P-array is generated from PI ratio = 22/7; all digits are taken from the string of P1 [26] (p. 21). We applied GF (**232**) and the long irreducible polynomial to the P-array, and we tried to do the linear cryptanalysis attack using the same steps used on [26]. We found it to be impossible because we destroyed the weakness of the P-array and the nature of the PI derivation, which was the advantage of the attacker in running the linear cryptanalysis attack easily. We found that CAST already has 32-bit out S-Boxes; attackers reduced output CAST S-Boxes [45]. We applied GF (**232**) and a long irreducible polynomial to the original 32-bit output S-Boxes and tried to apply a linear cryptanalysis attack. We found that it was impossible to guess the key. We found that RC5 and MMB have no S-Boxes. We used the new AES S-Box on RC5 and MMB to block linear cryptanalysis attacks since the new AES S-Box has already been developed and proven to be strong against linear cryptanalysis attacks. For the rest of the algorithms, like DES, CAMELLIA, SERPENT, etc., we applied GF (**232**) and its irreducible polynomial. We found that all are resistant to linear cryptanalysis attacks due to the memory required to construct LAT. No LAT, no linear cryptanalysis attack. We rewrote all ten algorithms with new components mapped to GF (**232**) and long irreducible polynomials. We tested whether all ten algorithms were encrypting and decrypting with new 32-bit output components. All were working according to our expectations.