Week 3: GPU Programming and Parallelization

As part of my ongoing research project, I have been spending a lot of time looking for ways to optimize the performance of advanced cryptography for GPU acceleration. While our main area of interest is the acceleration of the Additive Number Theoretic Transform (ANTT) in hardware, the architecture of parallel computing is just as important. In the last few weeks, I have been looking into the way in which Graphics Processing Units (GPUs) fundamentally change the way in which calculations are carried out. A normal processor or CPU is designed to handle complex tasks quickly, though only a few at a time. A GPU, on the other hand, is designed for parallelization, with thousands of cores working together to perform simpler calculations.

The BINIUS proof system includes the ANTT, which is a complex mathematical operation required to perform calculations on massive polynomial equations. When a computational constraint is encountered, the operation required to resolve the constraint involves the execution of millions of individual arithmetic operations. While the execution of these operations is complex, the fact that they must be carried out sequentially on a normal CPU creates a bottleneck in the system. While the execution of every operation individually is computationally not possible for the complex calculations required in the BINIUS proof system, the solution to the bottleneck is the way in which GPU programming works. By restructuring the ANTT to include parallelization, the calculations required to execute the individual operations of the proof system are carried out in parallel. This effectively compresses the execution time of the operation by a great degree. By ensuring the parallelization is optimized, the hardware acceleration ensures the BINIUS system is not only secure against quantum threats in the future but also highly efficient.