For the last couple of decades, multiple-valued logic (MVL) such as ternary logic styles has attracted considerable attention. MVL circuits can reduce the number of operations necessary to implement a particular mathematical function and further have an advantage in terms of reduced area. Carbon nanotube field effect transistors (CNFETs) are being extensively studied as possible successors to Silicon MOSFETs. Implementable CNTFET circuits have operational characteristics to approach the advantage of using MVL in voltage mode. In this paper through using “carbon nanotube field effect transistor” characteristics we present efficient galois field operations. Consequently, the simulation denouements demonstrate the efficient circuit parameters such as chip area, delay, power and power delay product.