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Hardware Acceleration for Binary Field Arithmetic in CUDA

Hardware Acceleration for Binary Field Arithmetic in CUDA

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posts
2026

This feature thread tracks the development of hardware-accelerated binary field arithmetic within NVIDIA CUDA. Initially, operations like carryless multiplication, crucial for cryptography and coding theory, were emulated with significant overhead. The introduction of the `clmad` instruction in CUDA 13.3 on Ampere and newer GPUs marks a significant advancement, providing hardware acceleration for these operations. This has led to substantial performance improvements in key cryptographic workloads like GHASH and sum-check protocols for zero-knowledge proofs, with benchmarks showing significant speedups on both high-end data center GPUs (B200) and consumer GPUs (RTX 5090).

2026

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

7/15/2026

Introduced the `clmad` PTX instruction in CUDA 13.3, providing hardware acceleration for carryless multiplication on NVIDIA Ampere and newer GPUs. Demonstrated significant performance improvements for GHASH (up to 18.8x on B200) and sum-check protocols for zero-knowledge proofs (3-13x speedup) by leveraging this new instruction, enabling faster cryptographic and coding-theoretic workloads.