Optimizing Key Switching for Homomorphic Encryption Through Dataflow Analysis and Transformation

Khái niệm cốt lõi

Optimizing the dataflow of the hybrid key switching (HKS) algorithm, a crucial step in homomorphic encryption, can significantly reduce off-chip data movement and on-chip memory requirements without compromising performance.

Tóm tắt

The paper presents three distinct dataflows for the HKS algorithm in homomorphic encryption (HE): Max-Parallel (MP), Digit-Centric (DC), and Output-Centric (OC).
The key insights are:

The OC dataflow can significantly compress the intermediate state of HKS while maintaining high parallelism, leading to substantial reductions in off-chip data movement and on-chip memory requirements.
Streaming the evaluation keys (evks) from off-chip memory, instead of storing them on-chip, can save 12.25x on-chip SRAM with a minimal performance penalty using the OC dataflow.
Compared to the naive MP implementation, the OC dataflow can achieve up to 4.16x speedup and save 3.3x off-chip bandwidth.
Increasing the computational throughput of the accelerator further enhances the performance benefits of the OC dataflow.
The authors evaluate the three dataflows on the RPU, a vector processor tailored for ring processing algorithms including HE. They consider different off-chip bandwidth and computational throughput configurations to understand the trade-offs.

Thống kê

A single HKS execution can involve hundreds of NTTs, hundreds of MBs of input and output data, nearly 500MB of constant evks, and up to 1GB of intermediate data.
The OC dataflow can save 12.25x on-chip SRAM by streaming evks compared to storing them on-chip.
The OC dataflow can save up to 3.3x off-chip bandwidth compared to the naive MP implementation while achieving the same performance.

Trích dẫn

"Our key insight is that with the OC dataflow, the intermediate state of HKS can be significantly compressed while maintaining high parallelism to utilize computational units."
"With OC, we demonstrate up to 4.16× speedup over the MP dataflow and show how OC can save 12.25× on-chip SRAM by streaming keys for minimal performance penalty."

Thông tin chi tiết chính được chắt lọc từ

CiFlow: Dataflow Analysis and Optimization of Key Switching for Homomorphic Encryption

by Negar Neda,A... lúc arxiv.org 04-16-2024

https://arxiv.org/pdf/2311.01598.pdf

Yêu cầu sâu hơn

How can the proposed dataflow optimizations be extended to other homomorphic encryption schemes beyond CKKS

The dataflow optimizations proposed in the paper for CKKS homomorphic encryption can be extended to other homomorphic encryption schemes by considering the specific operations and data dependencies unique to each scheme. The key idea is to analyze the dataflow of the encryption scheme, identify opportunities for data reuse and minimize off-chip data movement, and optimize the sequence of operations to maximize computational efficiency. By understanding the key operations and data dependencies of different homomorphic encryption schemes, similar dataflow analysis techniques can be applied to improve performance.

What are the potential trade-offs between on-chip memory, off-chip bandwidth, and computational throughput for real-world HE applications beyond the benchmarks considered in this work

In real-world HE applications, the trade-offs between on-chip memory, off-chip bandwidth, and computational throughput play a crucial role in determining the overall performance and efficiency of the system.

On-Chip Memory: Increasing on-chip memory allows for more data to be stored locally, reducing the need for frequent off-chip data transfers. However, larger on-chip memory may come at the cost of increased chip area and power consumption.

Off-Chip Bandwidth: Higher off-chip bandwidth enables faster data transfers between on-chip and off-chip memory, reducing latency and improving overall system performance. However, high off-chip bandwidth requirements can lead to increased power consumption and complexity in the memory subsystem.

Computational Throughput: Higher computational throughput allows for faster processing of data, reducing the overall execution time of cryptographic algorithms. However, increasing computational throughput may also lead to higher power consumption and heat generation in the system.
The optimal balance between these factors depends on the specific requirements of the HE application, such as the size of the data being processed, the complexity of the encryption scheme, and the desired level of performance. Real-world HE applications may need to carefully consider these trade-offs to achieve the best balance between on-chip memory, off-chip bandwidth, and computational throughput for efficient and effective operation.

Can the dataflow optimization techniques presented in this paper be applied to improve the performance of other complex cryptographic algorithms beyond homomorphic encryption

The dataflow optimization techniques presented in the paper can be applied to improve the performance of other complex cryptographic algorithms beyond homomorphic encryption. By analyzing the data dependencies, identifying opportunities for data reuse, and optimizing the sequence of operations, similar dataflow optimizations can be implemented for other cryptographic algorithms.
For example, in symmetric key encryption algorithms like AES, optimizing the dataflow to minimize off-chip data movement and maximize computational efficiency can lead to improved performance. By carefully analyzing the data dependencies and computational requirements of the algorithm, researchers can develop tailored dataflow optimizations to enhance the efficiency of symmetric key encryption.
Similarly, in digital signature algorithms like RSA or ECC, dataflow analysis can help identify bottlenecks in the computation process and optimize the sequence of operations to reduce latency and improve overall performance. By applying similar dataflow optimization techniques as presented in the paper, researchers can enhance the efficiency of digital signature algorithms and other complex cryptographic operations.