Institutional Repository UIN Sunan Kalijaga YogyakartaMODIFIKASI S-BOX PADA ALGORITMA KRIPTOGRAFI AES MENGGUNAKAN POLINOMIAL IRREDUSIBEL ALTERNATIF ATAS LAPANGAN HINGGA GF(28)NIM.: 22106010071Hizbullah NajihanauthorThis research investigates the modification of the finite field structure of GF(28) in the Advanced Encryption Standard (AES) by replacing the standard irreducible polynomial with an alternative irreducible polynomial. The objectives of this research are to analyze the method for determining degree-8 irreducible polynomials over Z2, examine the algebraic structure of the finite field GF(28) constructed from the quotient rings Z2[x]/⟨m(x)⟩ and Z2[x]/⟨f(x)⟩, and analyze the effect of changing the defining irreducible polynomial on the cryptographic metrics of the S-Box. This research employs a literature study and theoretical analysis in pure algebra using a deductive approach. The results demonstrate that the alternative irreducible polynomial is irreducible over Z2 and generates the maximal ideal ⟨f(x)⟩, so that the quotient ring Z2[x]/⟨f(x)⟩ forms the finite field GF(28). Furthermore, there exists an isomorphism establishing the algebraic equivalence between the constructions of GF(28) obtained from the standard irreducible polynomial and the alternative irreducible polynomial. The resulting S-Box achieves cryptographic metrics of NL = 112, AD = 7, and DU = 4, while satisfying the Strict Avalanche Criterion (SAC), which are equivalent to those of the standard AES S-Box. Therefore, replacing the irreducible polynomial in AES does not degrade the cryptographic quality of the algorithm and provides opportunities for exploring alternative algebraic structures in modern cryptographic design.510 Mathematics (Matematika)2026-08-12UIN SUNAN KALIJAGA YOGYAKARTA;FAKULTAS SAINS DAN TEKNOLOGIThesis

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