If protocol has fast operations and short key length, it can be efficient user authentication protocol. Lenstra and Verheul proposed XTR. XTR have short key length and fast computing speed. Therefore, this can be used usefully in complex arithmetic. In this paper, to design efficient user authentication protocol we used a subgroup of Galois Field to problem domain. Proposed protocol does not use GF(p⁶) that is existent finite field, and uses GF(p²) that is subgroup and solves problem. XTR-ElGamal based user authentication protocol reduced bit number that is required when exchange key by doing with upside. Also, proposed protocol provided easy calculation and execution by reducing required overhead when calculate. In this paper, we designed authentication protocol with y_i = g^b.psup 2(i-1)//ㆍv mol q, 1(equation omitted) 3 that is required to do user authentication.