THE FACTORIZATION OF X255 – 1 IN Z2[X]

Adrian Atanasiu () and Bogdan Ghimiș ()
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Adrian Atanasiu: University of Bucharest, Bucharest, Romania
Bogdan Ghimiș: University of Bucharest, Bucharest, Romania

Journal of Information Systems & Operations Management, 2018, vol. 12, issue 2, 257-264

Abstract: AES (Rijndael) is considered the most prolific and widely used ([2]) encryption algorithm and it has deep roots in Galois field theory. The mathematical operations that occur are done in a special finite field – GF(28) that is obtained by factorizing Z2[X] over the polinomial 1 + X + X3 + X4 + X8. We have been wondering why that polynomial has been chosen and if there are some hidden proprieties of that polynomial that other’s don’t have. In this paper, we are going to look into the structure of GF(28) and try to find some answers regarding this choice made by the authors of AES.

Date: 2018
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