Faster Cryptography with Carryless Multiplication in NVIDIA CUDA 13.3
New clmad instruction accelerates cryptographic operations on GPUs.
1The 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.
2What'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.
3GHASH 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.
4Zero-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.
5Other 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.
6Binary 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.
7Using 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.
8Future 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.