The Substitution box (S-Box) forms the core building block of any hardware implementation of the Advanced Encryption Standard (AES) algorithm as it is a non-linear structure requiring multiplicative inversion. This paper presents a full custom CMOS design of S-Box/Inversion S-Box (Inv S-Box) with low power GF (28) Galois Field inversions based on polynomial basis, using composite field arithmetic. The S-Box/Inv S-Box utilizes a novel low power 2-input XOR gate with only six devices to achieve a compact module implemented in 65nm IBM CMOS technology. The area of the core circuit is only about 288μm2 as a result of this transistor level optimization. The hardware cost of the S-Box/Inv S-Box is about 158 logic gates equivalent to 948 transistors with a critical path propagation delay of 7.322ns enabling a throughput of 130 Mega-SubBytes per second. This design indicates a power dissipation of only around 0.09μW using a 0.8V supply voltage, and, is suitable for applications such as RFID tags and smart cards which require low power consumption with a small silicon die. The proposed implementation compares favorably with other existing S-Box designs.