Abstract
An irreducible polynomial is one of the main components in building an S-box with an algebraic technique approach. The selection of the precise irreducible polynomial will determine the quality of the S-box produced. One method for determining good S-box quality is strict avalanche criterion will be perfect if it has a value of 0.5. Unfortunately, in previous studies, the strict avalanche criterion value of the S-box produced still did not reach perfect value. In this paper, we will discuss S-box construction using selected irreducible polynomials. This selection is based on the number of elements of the least amount of irreducible polynomials that make it easier to construct S-box construction. There are 17 irreducible polynomials that meet these criteria. The strict avalanche criterion test results show that the irreducible polynomial p17(x) =x8 + x7 + x6 + x + 1 is the best with a perfect SAC value of 0.5. One indicator that a robust S-box is an ideal strict avalanche criterion value of 0.5
Highlights
S-box which is known as a substitution box has a function in the process of randomizing data bits [1]
A novel method was introduced in building S-box construction to get the perfect strict avalanche criterion (SAC) value
The S-box construction starts with classifying the irreducible polynomial based on the number of the least polynomial elements
Summary
S-box which is known as a substitution box has a function in the process of randomizing data bits [1]. Irreducible polynomials play an important role in making S-box construction [3]. The role of the irreducible polynomial is crucial in building a strong S-box construction [5]. One of the criteria for determining the strength of an S-box is the perfect value of the strict avalanche criterion (SAC) [1]. If there is a change in 1-bit of input, ideally there should be half of the output bit changed This means that the perfect SAC value is 0.5 [6]. The SAC value produced by the S-boxes construction that has been carried out by previous researchers is various. We will present S-boxes construction using simple irreducible polynomials. S-boxes are built based on 17 simple irreducible polynomials, i.e., p1(x), p2(x), ..., p17(x).
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