Precise Approximation of Convolutional Neural Networks for Homomorphically Encrypted Data

Lee, Jung-Hyun; Lee, Eunsang; Lee, Dong Kun; Kim, Yongjune; Kim, Young‐Sik; No, Jong-Seon

doi:10.48550/arxiv.2105.10879

Cited by 8 publications

(10 citation statements)

References 15 publications

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“…It is worth noting that there is usually a significant accuracy penalty for this optimization (Garimella et al, 2021). Another recent work shows that to achieve reasonable accuracy on the ImageNet-1k dataset (Deng et al, 2009), a polynomial activation function must be of degree 29 needed (Lee et al, 2021). DELPHI and SAFENet partially substituted some of a network's ReLUs with low-degree polynomials assuming a baseline model is provided as input.…”

Section: Categorization Of Pi Methodsmentioning

confidence: 99%

CryptoNite: Revealing the Pitfalls of End-to-End Private Inference at Scale

Garimella¹,

Jha²,

Ghodsi³

et al. 2021

Preprint

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The privacy concerns of providing deep learning inference as a service have underscored the need for private inference (PI) protocols that protect users' data and the service provider's model using cryptographic methods. Recently proposed PI protocols have achieved significant reductions in PI latency by moving the computationally heavy homomorphic encryption (HE) parts to an offline/pre-compute phase. Paired with recent optimizations that tailor networks for PI, these protocols have achieved performance levels that are tantalizingly close to being practical. In this paper, we conduct a rigorous end-to-end characterization of PI protocols and optimization techniques and find that the current understanding of PI performance is overly optimistic. Specifically, we find that offline storage costs of garbled circuits (GC), a key cryptographic protocol used in PI, on user/client devices are prohibitively high and force much of the expensive offline HE computation to the online phase, resulting in a 10-1000× increase to PI latency. We propose a modified PI protocol that significantly reduces client-side storage costs for a small increase in online latency. Evaluated end-to-end, the modified protocol outperforms current protocols by reducing the mean PI latency by 4× for ResNet18 on TinyImageNet. We conclude with a discussion of several recently proposed PI optimizations in light of the findings and note many actually increase PI latency when evaluated from an end-to-end perspective.

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Section: Categorization Of Pi Methodsmentioning

confidence: 99%

CryptoNite: Revealing the Pitfalls of End-to-End Private Inference at Scale

Garimella¹,

Jha²,

Ghodsi³

et al. 2021

Preprint

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“…The lack of non-linear functions introduces other difficulties. For example, the ReLU activation function must be approximated using a high-degree polynomial [47]. As a result, faithfully replicating deep neural networks in FHE, as done by a recent ResNet implementation [48], comes at a high compute cost.…”

Section: Fhe Interfacementioning

confidence: 99%

CraterLake

Samardzic

Feldmann

Krastev

et al. 2022

Proceedings of the 49th Annual International Symposium on Computer Architecture

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Fully Homomorphic Encryption (FHE) enables offloading computation to untrusted servers with cryptographic privacy. Despite its attractive security, FHE is not yet widely adopted due to its prohibitive overheads, about 10,000× over unencrypted computation. Recent FHE accelerators have made strides to bridge this performance gap. Unfortunately, prior accelerators only work well for simple programs, but become inefficient for complex programs, which bring additional costs and challenges.We present CraterLake, the first FHE accelerator that enables FHE programs of unbounded size (i.e., unbounded multiplicative depth). Such computations require very large ciphertexts (tens of MBs each) and different algorithms that prior work does not support well. To tackle this challenge, CraterLake introduces a new hardware architecture that efficiently scales to very large ciphertexts, novel functional units to accelerate key kernels, and new algorithms and compiler techniques to reduce data movement.We evaluate CraterLake on deep FHE programs, including deep neural networks like ResNet and LSTMs, where prior work takes minutes to hours per inference on a CPU. CraterLake outperforms a CPU by gmean 4,600× and the best prior FHE accelerator by 11.2× under similar area and power budgets. These speeds enable realtime performance on unbounded FHE programs for the first time. CCS CONCEPTS• Computer systems organization → Parallel architectures; • Security and privacy → Cryptography.

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“…In addition, authors in [17] proposed a method to approximate the ReLU function precisely using the approximation…”

Section: Application To Min/max and Relu Functionmentioning

confidence: 99%

“…This comparison operation is widely used in various real-world applications, including machine learning algorithms such as support-vector machines, cluster analysis, and gradient boosting [15], [16]. The max function and the rectified linear unit (ReLU) function are other essential nonarithmetic operations that are widely used in deep learning applications [17], [18]. These three non-arithmetic operations can all be implemented using the sign function sgn(x), that is,…”

Section: Introductionmentioning

confidence: 99%

Optimization of Homomorphic Comparison Algorithm on RNS-CKKS Scheme

Lee

Kim

et al. 2022

IEEE Access

Self Cite

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Since the sign function can be used to implement the comparison operation, max function, and rectified linear unit (ReLU) function, several studies have been conducted to efficiently evaluate the sign function in the Cheon-Kim-Kim-Song (CKKS) scheme, one of the most promising fully homomorphic encryption schemes. Recently, Lee et al. (IEEE Trans. Depend. Sec. Comp.) proposed a practically optimal approximation method of sign function on the CKKS scheme using a composition of minimax approximate polynomials. In addition, Lee et al. proposed a polynomial-time algorithm that finds degrees of component polynomials minimizing the number of non-scalar multiplications for homomorphic comparison/max/ReLU functions. However, homomorphic comparison/max/ReLU functions using Lee et al.'s approximation method have not been successfully implemented on the residue number system variant CKKS (RNS-CKKS) scheme. In addition, the degrees of component polynomials found by Lee et al.'s algorithm are not optimized for the RNS-CKKS scheme because the algorithm does not consider that the running time of non-scalar multiplication depends much on the ciphertext level in the RNS-CKKS scheme. In this paper, we propose a fast algorithm for inverse minimax approximation error, a subroutine required to find the optimal set of degrees of component polynomials. This proposed algorithm makes it possible to find the optimal set of degrees of component polynomials with higher degrees than the previous study. In addition, we propose a method to find the degrees of component polynomials optimized for the RNS-CKKS scheme using the proposed algorithm for inverse minimax approximation error. We successfully implement the homomorphic comparison, max function, and ReLU function algorithms on the RNS-CKKS scheme with a low comparison failure rate (< 2 −15 ) and provide the various parameter sets according to the precision parameter α. We reduce the depth consumption of the homomorphic comparison, max function, and ReLU function algorithms by one depth for several α. In addition, the numerical analysis demonstrates that the homomorphic comparison, max function, and ReLU function algorithms using the degrees of component polynomials found by the proposed algorithm reduce running time by 6%, 7%, and 6% on average compared with those using the degrees of component polynomials found by Lee et al.'s algorithm, respectively.INDEX TERMS Cheon-Kim-Kim-Song (CKKS) scheme, fully homomorphic encryption (FHE), homomorphic comparison operation, minimax approximate polynomial, Remez algorithm, residue number system variant CKKS (RNS-CKKS) scheme.

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Precise Approximation of Convolutional Neural Networks for Homomorphically Encrypted Data

Cited by 8 publications

References 15 publications

CryptoNite: Revealing the Pitfalls of End-to-End Private Inference at Scale

CryptoNite: Revealing the Pitfalls of End-to-End Private Inference at Scale

CraterLake

Optimization of Homomorphic Comparison Algorithm on RNS-CKKS Scheme

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