Implementation and Performance Evaluation of RNS Variants of the BFV Homomorphic Encryption Scheme

Badawi, Ahmad Al; Polyakov, Yuriy; Aung, Khin Mi Mi; Veeravalli, Bharadwaj; Rohloff, Kurt

doi:10.1109/tetc.2019.2902799

Cited by 78 publications

(55 citation statements)

References 24 publications

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“…They all target performing a small number of HE Mul without bootstrapping, inhibiting their applicability to a wide range of applications requiring hundreds to thousands of multiplication be performed (e.g., deep learning). GPU implementation studies [4], [7], [8], [22] do not take advantage of the algorithm's internal parallelism sufficiently, operate on only small or limited parameters, or do not consider the cost of modulo operations.…”

Section: Introductionmentioning

confidence: 99%

HEAAN Demystified: Accelerating Fully Homomorphic Encryption Through Architecture-centric Analysis and Optimization

Jung,

Lee,

Kim

et al. 2020

Preprint

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Homomorphic Encryption (HE) draws a significant attention as a privacy-preserving way for cloud computing because it allows computation on encrypted messages called ciphertexts. Among numerous HE schemes proposed, HE for Arithmetic of Approximate Numbers (HEAAN) is rapidly gaining popularity across a wide range of applications (e.g., machine learning) because it supports messages that can tolerate approximate computation with no limit on the number of arithmetic operations applicable to the corresponding ciphertexts.A critical shortcoming of HE is the high computation complexity of ciphertext arithmetic; especially, HE multiplication (HE Mul) is more than 10,000 times slower than the corresponding multiplication between unencrypted messages. This leads to a large body of HE acceleration studies, including ones exploiting FPGAs; however, those did not conduct a rigorous analysis of computational complexity and data access patterns of HE Mul. Moreover, the proposals mostly focused on designs with small parameter sizes, making it difficult to accurately estimate the performance of the HE accelerators in conducting a series of complex arithmetic operations.In this paper, we first describe how HE Mul of HEAAN is performed in a manner friendly to computer architects. Then we conduct a disciplined analysis on its computational and memoryaccess characteristics, through which we (1) extract parallelism in the key functions composing HE Mul and (2) demonstrate how to effectively map the parallelism to the popular parallel processing platforms, multicore CPUs and GPUs, by applying a series of optimization techniques such as transposing matrices and pinning data to threads. This leads to the performance improvement of HE Mul on a CPU and a GPU by 42.9× and 134.1×, respectively, over the single-thread reference HEAAN running on a CPU. The conducted analysis and optimization would set a new foundation for future HE acceleration research.

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Section: Introductionmentioning

confidence: 99%

HEAAN Demystified: Accelerating Fully Homomorphic Encryption Through Architecture-centric Analysis and Optimization

Jung,

Lee,

Kim

et al. 2020

Preprint

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“…Our work is the first to comprehensively optimize client-side HE cryptographic primitives, which is crucial in client-aided HE. Furthermore, unlike prior work targeting large, high-power GPUs [3,18,54] and FPGAs [46,59,63,70], CHOCO-TACO empirically optimizes for a small ASIC implementation, directly addressing the need for low-power, energy-efficient operation at the client device. Hardware Security.…”

Section: Related Workmentioning

confidence: 99%

Client-optimized algorithms and acceleration for encrypted compute offloading

Hagen

Lucia

2022

Proceedings of the 27th ACM International Conference on Architectural Support for Programming Languages and Operating Systems

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Homomorphic Encryption (HE) enables secure cloud offload processing on encrypted data. HE schemes are limited in the complexity and type of operations they can perform, motivating client-aided implementations that distribute computation between client (unencrypted) and server (encrypted). Prior client-aided systems optimize server performance, ignoring client costs: client-aided models put encryption and decryption on the critical path and require communicating large ciphertexts. We introduce Client-aided HE for Opaque Compute Offloading (CHOCO), a client-optimized system for encrypted offload processing. CHOCO reduces ciphertext size, reducing communication and computing costs through HE parameter minimization and through "rotational redundancy", a new HE algorithm optimization. We present Client-aided HE for Opaque Compute Offloading Through Accelerated Cryptographic Operations (CHOCO-TACO), an accelerator for HE encryption and decryption, making client-aided HE feasible for even resource-constrained clients. CHOCO supports two popular HE schemes (BFV and CKKS) and several applications, including DNNs, PageRank, KNN, and K-Means. CHOCO reduces communication by up to 2948× over prior work. With CHOCO-TACO client enc-/decryption is up to 1094× faster and uses up to 648× less energy. CCS CONCEPTS• Security and privacy → Cryptography; • Computer systems organization → Parallel architectures; • Software and its engineering → Designing software.

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“…GPU-based Acceleration. GPU is an alternative computing platform to accelerate evaluation functions [6,21,24,42,48,59]. Wang et al [59] have proposed the first GPU acceleration of FHE that targets Gentry-Halevi [34] scheme.…”

Section: Large-integer Multiplication Hardware Accelerationmentioning

confidence: 99%

“…In [58], a GPU-based implementation of BGV scheme [11] is introduced. In [6], a comprehensive study is reported for multithreaded CPU execution as well as GPU for the BFV scheme. To the best of our knowledge, there is no GPU-accelerated implementation of the CKKS scheme.…”

Section: Large-integer Multiplication Hardware Accelerationmentioning

confidence: 99%

Heax

Riazi

Laine

Pelton

et al. 2020

Proceedings of the Twenty-Fifth International Conference on Architectural Support for Programming Languages and Operating Syste

158

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With the rapid increase in cloud computing, concerns surrounding data privacy, security, and confidentiality also have been increased significantly. Not only cloud providers are susceptible to internal and external hacks, but also in some scenarios, data owners cannot outsource the computation due to privacy laws such as GDPR, HIPAA, or CCPA. Fully Homomorphic Encryption (FHE) is a groundbreaking invention in cryptography that, unlike traditional cryptosystems, enables computation on encrypted data without ever decrypting it. However, the most critical obstacle in deploying FHE at large-scale is the enormous computation overhead. In this paper, we present HEAX, a novel hardware architecture for FHE that achieves unprecedented performance improvements. HEAX leverages multiple levels of parallelism, ranging from ciphertext-level to fine-grained modular arithmetic level. Our first contribution is a new highlyparallelizable architecture for number-theoretic transform (NTT) which can be of independent interest as NTT is frequently used in many lattice-based cryptography systems. Building on top of NTT engine, we design a novel architecture for computation on homomorphically encrypted data. Our implementation on reconfigurable hardware demonstrates 164-268× performance improvement for a wide range of FHE parameters.

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Implementation and Performance Evaluation of RNS Variants of the BFV Homomorphic Encryption Scheme

Cited by 78 publications

References 24 publications

HEAAN Demystified: Accelerating Fully Homomorphic Encryption Through Architecture-centric Analysis and Optimization

HEAAN Demystified: Accelerating Fully Homomorphic Encryption Through Architecture-centric Analysis and Optimization

Client-optimized algorithms and acceleration for encrypted compute offloading

Heax

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