Abstract: Authentication encryption algorithm is a symmetric key encryption scheme. Provide confidentiality and data integrity during encryption. Mk-3 algorithm is an authentication encryption algorithm based on simplified duplex sponge structure, which supports private customization. And mk-3 algorithm is the first algorithm using 16 bit S-box. The S-box used in the algorithm is constructed by multiplicative inverse element on finite field and affine transformation. While ensuring algebraic security, this design can also reduce hardware implementation resources through isomorphic mapping transformation over finite fields. At present, the implementation scheme of mk-3 algorithm S-box hardware still has great room for improvement. In this scheme, the polynomial basis is used to construct a finite field GF(2¹⁶), and the inverse operation on is transformed into a composite field GF((2⁸)²). The scheme searches and evaluates the linear Boolean functions transformed by two fields, including 16 affine equivalent isomorphic matrices. On this basis, the implementation results of multiplication, inversion and square multiplication based on irreducible polynomials in composite field GF((2⁸)²) are also given. This scheme adopts three basic logic gates: AND gate, XOR gate and NOT gate. And adapt to all gate circuit processes. Compared with the current optimal S-box hardware implementation of mk-3 algorithm, the scheme in this paper reduces the circuit area by at least 58.3%. From the perspective of FPGA simulation, the scheme in this paper reduces the table lookup resources by at least 47.5%.