# Faster Cryptography with Carryless Multiplication in NVIDIA CUDA 13.3 New clmad instruction accelerates cryptographic operations on GPUs. - **Source:** [Nvidia Developer Blog](https://developer.nvidia.com/blog) - **Published:** 2026-07-15 - **Topic:** [Data & AI](https://brifing.si/c/data-ai) - **Original article:** - **On Brifing:** https://brifing.si/s/ed68eb5a-e831-4b0e-936a-7a7c3dd388e3 ## The Importance of Carryless Multiplication Carryless multiplication is a cornerstone of modern cryptography, used in AES-GCM, error-correcting codes, and zero-knowledge proof systems. NVIDIA CUDA 13.3 introduces the clmad instruction, hardware-accelerating this operation on GPUs. ## What's New in CUDA 13.3 NVIDIA's CUDA 13.3 adds a new PTX instruction called clmad, providing hardware-level support for carryless multiplication on Ampere and later GPUs. This significantly boosts performance in cryptographic workloads. ## GHASH Performance GHASH is the integrity verification mechanism in AES-GCM. With clmad, GHASH throughput reaches ~6.3 TB/s on NVIDIA B200 GPUs—an 18.8x speedup over previous methods, nearing DRAM read bandwidth. ## Zero-Knowledge Proof Systems Carryless multiplication underpins zero-knowledge proof systems. CUDA 13.3 accelerates the sum-check protocol over GF(2^128) by 4–13×, a major advantage for privacy-focused applications. ## Other Applications Beyond AES-GCM, carryless multiplication is used in CRC, Reed-Solomon codes, BCH codes, quantum stabilizer codes, and post-quantum cryptography. GPU hardware acceleration reshapes the cost structure for these workloads. ## Binary Extension Fields Binary extension fields like GF(2^n) are widely used in cryptography. Addition is XOR, while multiplication relies on carryless operations. The clmad instruction in CUDA 13.3 enables efficient computation of these operations on GPUs. ## Using the clmad Instruction The clmad instruction performs carryless multiplication of two 64-bit inputs into a 128-bit result. Its .hi and .lo variants compute the upper and lower halves, respectively. This can be extended to larger fields using algorithms like Karatsuba. ## Future Implications NVIDIA's hardware support for carryless multiplication is a significant step for cryptographic applications. Data centers, VPNs, and privacy systems will benefit greatly. CUDA 13.3 opens new possibilities for developers. ## Sources covering this story - https://developer.nvidia.com/blog/building-faster-cryptography-with-carryless-multiplication-in-nvidia-cuda-13-3/ — --- _Summary written by Brifing from the original reporting. Copyright in the original article belongs to its publisher; read the full piece at the link above._