4 research outputs found
Numerical Method for Comparison on Homomorphically Encrypted Numbers
We propose a new method to compare numbers which are encrypted by Homomorphic Encryption (HE).
Previously, comparison and min/max functions were evaluated using Boolean functions where input numbers are encrypted bit-wisely. However, the bit-wise encryption methods require relatively expensive computation of basic arithmetic operations such as addition and multiplication.
In this paper, we introduce iterative algorithms that approximately compute the min/max and comparison operations of several numbers which are encrypted word-wisely. From the concrete error analyses, we show that our min/max and comparison algorithms have and computational complexity to obtain approximate values within an error rate , while the previous minimax polynomial approximation method requires the exponential complexity and , respectively.
We also show the (sub-)optimality of our min/max and comparison algorithms in terms of asymptotic computational complexity among polynomial evaluations to obtain approximate min/max and comparison results. Our comparison algorithm is extended to several applications such as computing the top- elements and counting numbers over the threshold in encrypted state.
Our new method enables word-wise HEs to enjoy comparable performance in practice with bit-wise HEs for comparison operations while showing much better performance on polynomial operations. Computing an approximate maximum value of any two -bit integers encrypted by HEAAN, up to error , takes only milliseconds in amortized running time, which is comparable to the result based on bit-wise HEs
Privacy-Preserving Machine Learning with Fully Homomorphic Encryption for Deep Neural Network
Fully homomorphic encryption (FHE) is one of the prospective tools for
privacypreserving machine learning (PPML), and several PPML models have been
proposed based on various FHE schemes and approaches. Although the FHE schemes
are known as suitable tools to implement PPML models, previous PPML models on
FHE encrypted data are limited to only simple and non-standard types of machine
learning models. These non-standard machine learning models are not proven
efficient and accurate with more practical and advanced datasets. Previous PPML
schemes replace non-arithmetic activation functions with simple arithmetic
functions instead of adopting approximation methods and do not use
bootstrapping, which enables continuous homomorphic evaluations. Thus, they
could not use standard activation functions and could not employ a large number
of layers. The maximum classification accuracy of the existing PPML model with
the FHE for the CIFAR-10 dataset was only 77% until now. In this work, we
firstly implement the standard ResNet-20 model with the RNS-CKKS FHE with
bootstrapping and verify the implemented model with the CIFAR-10 dataset and
the plaintext model parameters. Instead of replacing the non-arithmetic
functions with the simple arithmetic function, we use state-of-the-art
approximation methods to evaluate these non-arithmetic functions, such as the
ReLU, with sufficient precision [1]. Further, for the first time, we use the
bootstrapping technique of the RNS-CKKS scheme in the proposed model, which
enables us to evaluate a deep learning model on the encrypted data. We
numerically verify that the proposed model with the CIFAR-10 dataset shows
98.67% identical results to the original ResNet-20 model with non-encrypted
data. The classification accuracy of the proposed model is 90.67%, which is
pretty close to that of the original ResNet-20 CNN model...Comment: 12 pages, 4 figure
PEGASUS: Bridging Polynomial and Non-polynomial Evaluations in Homomorphic Encryption
Homomorphic encryption (HE) is considered as one of the most important primitives for privacy-preserving applications.
However, an efficient approach to evaluate both polynomial and non-polynomial functions on encrypted data is still absent,
which hinders the deployment of HE to real-life applications. To address this issue, we propose a practical framework PEGASUS.
PEGASUS can efficiently switch back and forth between a packed CKKS ciphertext and FHEW ciphertexts without decryption,
allowing us to evaluate arithmetic functions efficiently on the CKKS side, and to evaluate look-up tables on FHEW ciphertexts.
Our FHEW ! CKKS conversion algorithm is more practical than the existing methods. We improve the computational
complexity from linear to sublinear. Moreover, the size of our conversion key is significantly smaller, e.g., reduced from 80
gigabytes to 12 megabytes. We present extensive benchmarks of PEGASUS, including sigmoid/ReLU/min/max/division, sorting
and max-pooling. To further demonstrate the capability of PEGASUS, we developed two more applications. The first one is a
private decision tree evaluation whose communication cost is about two orders of magnitude smaller than the previous HE-based approaches. The second one is a secure K-means clustering that is able to run on thousands of encrypted samples in minutes that outperforms the best existing system by 14 – 20. To the best of our knowledge, this is the first work that supports
practical K-means clustering using HE in a single server setting