Building Faster Cryptography with Carryless Multiplication in NVIDIA CUDA 13.3 | NVIDIA Technical Blog

This post details the introduction of the `clmad` PTX instruction in CUDA 13.3, providing hardware-accelerated carryless multiplication for binary extension fields on NVIDIA Ampere and newer GPUs. It demonstrates significant performance gains (up to 18.8x for GHASH on B200, 4-13x for sum-check protocols) compared to prior bitsliced implementations. The post explains the underlying mathematics of binary extension fields and provides inline PTX examples for developers integrating these optimizations into cryptographic pipelines.