CUDA 13.3 Brings Hardware Carryless Multiplication to GPUs

NVIDIA CUDA 13.3 introduces clmad, a new PTX instruction that finally gives GPUs hardware-accelerated carryless multiplication on Ampere and newer architectures (SM 80+). x86 CPUs have had this primitive via PCLMULQDQ for over 15 years, but GPU developers previously had to rely on slower workarounds like bitsliced circuits.

Benchmarks show substantial gains: GHASH, the integrity hash inside AES-GCM, reaches ~6.3 TB/s on the B200 — near DRAM read bandwidth and up to 18.8x faster than the prior bitsliced approach. The RTX 5090 sees a 2x throughput improvement, hitting ~1,300 GB/s. The sum-check protocol, a core primitive in zero-knowledge proving systems, gains 4-13x speedups over GF(2^128).

The impact extends well beyond AES-GCM: carryless multiplication underlies CRC and Reed-Solomon codes used in storage and telecom, BCH codes for flash memory, quantum stabilizer codes, several post-quantum schemes, and the binary-field arithmetic powering modern ZK systems like Binius. For every already-deployed Ampere-or-later GPU, this changes the cost calculus for a wide swath of cryptographic and coding-theoretic workloads.