The objective of the proposed research is to explore cryptosystem design using Composite Mersenne Product Registers (CMPRs) as a scalable alternative to nonlinear feedback shift registers (NLFSRs), which remain limited to small sizes and lack general construction methods. CMPRs concatenate Mersenne Product Registers (MPRs) through nonlinear interconnections, producing long cycle structures while retaining hardware efficiency and cryptographic resilience. Preliminary work demonstrated CMPR-based pseudorandom generators and stream ciphers, with ASIC and FPGA results showing competitive or improved area, power, and security compared to the NLFSR-based cryptosystems in the prior work, such as TRIVIUM, Grain-128AEADv2, and Espresso. Building on these results, the proposed research will extend CMPRs to other cryptosystems, including hash functions, message authentication codes, and block ciphers using sponge construction-based frameworks. The overarching goal is to provide a lightweight, mathematically grounded primitive that scales to modern cryptographic requirements while remaining efficient for use in constrained hardware systems.