A circuit area optimization of MK-3 S-box

AbstractIn MILCOM 2015, Kelly et al. proposed the authentication encryption algorithm MK-3, which applied the 16-bit S-box. This paper aims to implement the 16-bit S-box with less circuit area. First, we classified the irreducible polynomials over$$\mathbb {F}_{2^n}$$F2ninto three kinds. Then we compared the logic gates required for multiplication over the finite field constructed by the three types of irreducible polynomials. According to the comparison result, we constructed the composite fields,$$\mathbb {F}_{(2^4)^2}$$F(24)2and$$\mathbb {F}_{(2^8)^2}$$F(28)2. Based on the isomorphism of finite fields, the operations over$$\mathbb {F}_{2^{16}}$$F216can be conducted over$$\mathbb {F}_{(2^8)^2}$$F(28)2. Similarly, elements over$$\mathbb {F}_{2^8}$$F28can be mapped to the corresponding elements over$$\mathbb {F}_{(2^4)^2}$$F(24)2. Next, the SAT solver was used to optimize the operations over smaller field$$\mathbb {F}_{2^4}$$F24. At last, the architecture of the optimized MK-3 S-box was worked out. Compared with the implementation proposed by the original designer, the circuit area of the MK-3 S-box in this paper is reduced by at least 55.9%.