sparse ternary fma — Optimize ternary arithmetic with…

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About this project

The sparse-ternary-fma library offers a powerful solution for high-performance ternary arithmetic, crucial for Fully Homomorphic Encryption (FHE) and low-precision AI. Through innovations like 2-bit encoding, sparse processing, and AVX-512 SIMD acceleration, this library significantly enhances computational efficiency and resource utilization.

Overview of sparse-ternary-fma

The sparse-ternary-fma project offers a high-performance ternary arithmetic kernel, designed specifically for applications in Fully Homomorphic Encryption (FHE) and low-precision Artificial Intelligence (AI). This C library is optimized with innovative techniques such as 2-bit encoding and AVX-512 SIMD acceleration, resulting in significant improvements in both speed and efficiency.

Problem Analysis: Addressing Performance Bottlenecks

Fully Homomorphic Encryption (FHE) has the potential to enhance secure computing, yet its widespread use has been limited due to remarkable performance challenges. In schemes like TFHE (Fully Homomorphic Encryption over the Torus), polynomial arithmetic is a computationally intensive task. The use of traditional integer representations for ternary secret keys leads to inefficient memory usage, with up to 87.5% of resources going to waste. This inefficiency impedes the creation of high-performance client-side FHE applications and constrains advancements in low-precision AI.

Key Innovations

The sparse-ternary-fma kernel introduces crucial optimizations that transform the performance landscape:

2-Bit Ternary Encoding: By implementing a compact 2-bit representation for ternary values, the kernel enhances data density, enabling the packing of 256 trits into a single 512-bit AVX-512 vector, resulting in a 4x to 16x improvement in efficiency.
Sparse Processing: This kernel leverages sparse ternary keys, which are prevalent in FHE, processing only non-zero elements and achieving speed increases that often exceed 16x for standard key distributions.
SIMD Acceleration: A hand-optimized AVX-512 implementation allows for the execution of fused multiply-add (FMA) operations on 8 coefficients concurrently, improving throughput by 2.38 times compared to scalar implementations.

Performance Validation

Performance gains achieved by the sparse-ternary-fma kernel are substantiated in the Cryptology ePrint report, detailing its benchmarks:

Metric	Improvement
Throughput	2.38x
Latency	26.12x

These results confirm the kernel's ability to boost performance across diverse applications, underscoring its potential in the realm of FHE and AI.

Vision for Open-Source Innovation

The open-source release of this kernel under the MIT license aims to accelerate client-side FHE integration and foster advancements in next-generation AI technologies. By providing this core component freely, the project encourages collaboration among developers and researchers, paving the way for transformative breakthroughs in FHE and low-precision AI.

Related Work

The sparse-ternary-fma kernel is part of the HyperFold T-Encrypt (T-Enc) architecture. For a comprehensive view of the production system containing advanced optimizations, refer to the evaluation repository.