This document presents a novel reversible architecture for a Linear Feedback Shift Register (LFSR) and Parallel Signature Analyzer (PSA) with applications in cryptography, quantum computing, and low power VLSI. It proposes reversible realizations of serial-in serial-out and serial-in parallel-out shift registers up to N bits and analyzes their delay, quantum cost, and garbage. The reversible LFSR and PSA architecture aim to improve on existing designs in terms of these performance metrics. Hardware requirements include a computer with a Pentium III processor, 1GB RAM, and 40GB hard disk to run Xilinx ISE 14.3 software for designing with Verilog.