XTR is a novel public key system based on a method to represent elements of subgroup of a multiplicative group of a finite field. It integrates most of the advantages of RSA and ECC without any of their limitations. Recently, Lenstra et al describe an improved while conceptually more complicated method for XTR key representation and present two excellent formulas.

In this paper, an original and fundamental method for XTR public key reduction is introduced. The formulas we presented seem a little more complicated than those of Lenstra et al, however, the computation is almost the same as that of the previous method, which takes only a small number of operations in the finite field. Meanwhile, we present a fast algorithm of computing the trace, which can be used to construct XTR blind signature schemes.