The scalability and privacy of modern blockchain technologies rely on Zero-Knowledge Proofs (ZKPs), which are protocols that allow a prover to verify the truth of a statement while revealing as little information as possible about the statement. Currently, the mathematics used for these proofs rely on Elliptic Curve Cryptography (ECC), the industry standard for the security of the modern internet. However, ECC can be broken using Shor’s Algorithm, an algorithm that can only be run on quantum computers. This makes quantum computing, which is expected to become widespread in the 2030s, a threat to modern internet security. Anticipating this threat, cryptographers have come up with different protocols that do not need ECC. One such protocol is BINIUS, a proof system that operates over binary fields rather than the large prime fields used in ECC. However, the practical speed of BINIUS is currently by its reliance on the computationally expensive Additive Number Theoretic Transform (ANTT). By optimizing memory access patterns and exploiting the parallelism of GPUs, this project aims to find if hardware-aware optimizations on GPUs can significantly speed up the state-of-the-art implementation of the ANTT.