## 3 Theoretical Background of Our Novel Approach  
In this study, the proposed procedure (novel approach), which is believed to cater to less probability, give a big table of LAT, and bring confusion to the attacker, is the Galois Field of highest order, which will yield 32 output bits compared to the minimum output bits of known S-Boxes. [PERSON] et al. [9] (p. 21) indicated that the S-Boxes with more output bits provide high security. In cryptography, the size of the S-Box is defined using input bits (let us say the number of input bits is N) and output bits (let us say the number of output bits is N). Figure 3: Tracing the entire cryptographic algorithm to obtain a key [5]. of output bits is M); therefore, the size of the S-Box is NxM. In this proposal, the highest chosen order of Galois Field is \(\bf{2^{32}}\). A Galois Field of order \(\bf{2^{32}}\) is mathematically represented by **GF (\(\bf{2^{32}}\))**; this means that the size of an S-Box constructed by **GF (\(\bf{2^{32}}\))** will be Nx32 (that is, N input bits and 32 output bits). Most algorithms used on IoT (like AES, BLOWFISH, CAMELLIA, CAST, CLEFIA, DES, MMB, RC5, SERPENT, and SKIPJACK) have S-Boxes that have fewer output bits than 32, making them vulnerable to attackers [9]. [PERSON] et al. [9] (p. 21) indicated that the S-Boxes with fewer output bits provide less security. The size of tables like LAT is determined by the size of the S-Box. For example, if the simplified DES S-Box size is 4 \(\times\) 4, then the LAT size will have 16 columns \(\times\) 16 rows, which is calculated as \(\bf{2^{4}}\)\(\times\) 2\({}^{4}\). Refer to Table 4. Therefore, an S-Box of 32 \(\times\) 32, for example, will give a LAT of the size of \(\bf{2^{32}}\)\(\times\)\(\bf{2^{32}}\), which is 4,294,967,296 (number of columns) \(\times\) 4,294,967,296 (number of rows). With this increase in events, the attacker is believed to have low chances or probability of guessing a key [15]. This is also supported by statistical theory (the probability of guessing a head from a coin is 1/2 and the probability of guessing a space ace from a deck card is 1/(56)) [16; 17]. With the size (\(\bf{2^{32}}\) = 4,294,967,296) probability table, attackers will need extra time (or struggle) to construct and analyze tables such as LAT, unlike before when the size of an S-Box was 4 \(\times\) 4. After the construction of an S-Box of Nx32 using **GF (\(\bf{2^{32}}\))** and a high irreducible polynomial, where N and 32 are the number of input and output bits, respectively, the developer can even construct an S-Box of 4 \(\times\) 32, 6 \(\times\) 32, 8 \(\times\) 32, and 16 \(\times\) 32 by extracting entities from the original Nx32 S-Box [9; 10; 11; 12; 13; 14; 15; 16; 17]. If N = 4, 6, 8, or 16, a new S-Box of 4 \(\times\) 32, 6 \(\times\) 32, 8 \(\times\) 32, and 16 \(\times\) 32 constructed by GF (\(\bf{2^{32}}\)), respectively, would give complicated probability tables of LAT of 2\({}^{4}\)\(\times\)\(\bf{2^{32}}\), 2\({}^{6}\)\(\times\)\(\bf{2^{32}}\), 2\({}^{8}\)\(\times\)\(\bf{2^{32}}\), and 2\({}^{16}\)\(\times\)\(\bf{2^{32}}\), respectively. The number of rows still needed to construct LAT will be \(\bf{2^{32}}\) = 4,294,967,296. The other aspect is driven from a statistical point of view: if the entities of the event are greater, it is more difficult to guess an entity to be true. Therefore, using a higher-order Galois Field, the probability of guessing the key will be too low, unlike before when the size of an S-Box was 4 \(\times\) 4. Little has been achieved to reconstruct, replace, and strengthen the S-Boxes of ten cryptographic algorithms, which are commonly used on the IoT. In this proposal, reconstruction of algorithms is going to be performed, and reconstruction of small output S-Boxes to 32-bit output is going to be developed using **GF (\(\bf{2^{32}}\))**. The proposed procedure to construct a strong algorithm is based on Galois Field theory.