This paper presents two new hardware designs of the WG-128 cipher, one for the multiple output version (MOWG), and the other for the single output version (WG), based on type-II optimal normal basis (ONB) representation. The proposed MOWG design uses signal reuse techniques to reduce hardware cost in the MOWG transformation, while it increases the speed by eliminating the inverters from the critical path. This is accomplished through reconstructing the Key and Initial Vector (IV) loading Algorithm (KIA) and the feedback polynomial of the Linear Feedback Shift Register (LFSR). The proposed WG design uses properties of the trace function to optimize the hardware cost in the WG transformation. The ASIC and FPGA implementations of the proposed designs show that their areas and power consumptions outperform the existing implementations of the WG cipher.