[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-118823-en":3,"doc-seo-118823-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},118823,962075006959,"Anda","https://ap-avatar.wpscdn.com/avatar/e0002397efbe92a78e?_k=1776741047341049297",8,"Research & Report","Learning in the Dark - Privacy-Preserving Machine Learning using Function Approximation","Machine learning adoption through cloud services increases convenience while moving sensitive data to untrusted remote providers. This work presents Learning in the Dark, a hybrid privacy-preserving machine learning approach where training uses plaintext data but inference runs directly on homomorphically encrypted ciphertexts. To support homomorphic evaluation, the method approximates nonlinear activation functions such as ReLU and Sigmoid using low-degree Chebyshev polynomials. The resulting model classifies encrypted images with high accuracy and produces outputs in a blind, privacy-preserving manner by leveraging homomorphic encryption properties.","Learning in the Dark: Privacy-Preserving Machine Learning using Function Approximation  \n1st Tanveer Khan Department of Computing Sciences Tampere University Tampere, Finland [tanveer.khan@tuni.fi](tanveer.khan@tuni.fi)  \n2nd Antonis Michalas Department of Computing Sciences Tampere University, Finland and RISE Research Institutes of Sweden [antonios.michalas@tuni.fi](antonios.michalas@tuni.fi)  \narXiv :2309 .08190v1 [ cs .CR] 15 Sep 2023  \nAbstract—Over the past few years, a tremendous growth of machine learning was brought about by a significant increase in adoption and implementation of cloud-based services. As a result, various solutions have been proposed in which the machine learning models run on a remote cloud provider and not locally on a user’s machine. However, when such a model is deployed on an untrusted cloud provider, it is of vital importance that the users’ privacy is preserved. To this end, we propose Learning in the Dark – a hybrid machine learning model in which the training phase occurs in plaintext data, but the classification of the users’ inputs is performed directly on homomorphically encrypted ciphertexts. To make our construction compatible with homomorphic encryption, we approximate the ReLU and Sigmoid activation functions using low-degree Chebyshev polynomials. This allowed us to build Learning in the Dark – a privacypreserving machine learning model that can classify encrypted images with high accuracy. Learning in the Dark preserves users’ privacy since it is capable of performing high accuracy predictions by performing computations directly on encrypted data. In addition to that, the output of Learning in the Dark is generated in a blind and therefore privacy-preserving way by utilizing the properties of homomorphic encryption.  \nIndex Terms—Activation Function, Homomorphic Encryption, Neural Networks, Polynomial Approximation, Privacy,  \nI. INTRODUCTION  \nMachine Learning (ML), specifically Deep Learning (DL), has garnered significant attention from researchers due to its solid performance in many tasks, such as speech recognition, spam detection, image classification, traffic analysis, face recognition, financial detection, and genomics prediction [1],[2], [3], [4], [5], [6] . To meet the growing demand for ML services, Cloud Service Providers (CSPs) such as Google Prediction API [7], Microsoft Azure ML [8], and Ersatz Lab [9] also offer Machine Learning as a Service (MLaaS), enabling users to train and test the ML models using the CSP infrastructure. Typically, these models involve a training phase where the model learns from a dataset and a testing phase where the model predicts outputs based on unseen inputs. Once the model is trained and deployed on the CSP, the users can use it for online prediction services. However, the adoption of MLaaS raises concerns about the privacy of data  \nThis work was funded by the Technology Innovation Institute (TII) for the project ARROWSMITH and from Horizon Europe for HARPOCRATES (101069535) .  \nbeing outsourced, in sensitive domains such as finance and healthcare [10] . There is a risk of data misuse or theft when sending data to prediction models hosted by CSPs. To address these privacy concerns, researchers proposed various methods to protect user data in MLaaS settings [11], [12], [4], [13],[14] .  \nThis work aims to demonstrate the application of Neural Network (NN) on Encrypted Data (ED) using Homomorphic Encryption (HE) . HE allows performing arithmetic operations (addition and multiplication) over ED without decryption, enabling the homomorphic evaluation of functions relying on these operations. More specifically, our focus is to evaluate the Convolution Neural Network (CNN) on ED, where most operations, except for Non-linear Activation Functions (NLAF), can be homomorphically evaluated.  \nEnabling the homomorphic evaluation of CNNs on ED has been an active area of research, with significant efforts dedicated to designing efficient support for N","cbCaiftli3XoJlWi","https://ap.wps.com/l/cbCaiftli3XoJlWi","pdf",849766,1,10,"English","en",105,"# Introduction\n## Background on Polynomial Approximations\n## Our Contribution","[{\"question\":\"How does Learning in the Dark preserve privacy in cloud inference?\",\"answer\":\"Training occurs on plaintext data, while classification is performed directly on homomorphically encrypted ciphertexts, avoiding decryption during inference.\"},{\"question\":\"Why are low-degree Chebyshev polynomials used in the model?\",\"answer\":\"They approximate the nonlinear activation functions ReLU and Sigmoid so that these functions can be evaluated under homomorphic encryption.\"},{\"question\":\"What enables evaluation of most CNN operations on encrypted data?\",\"answer\":\"Homomorphic encryption supports addition and multiplication over encrypted data, allowing linear parts of CNNs to be computed homomorphically while handling nonlinearities via polynomial approximation.\"}]","Learning in the Dark - Privacy-Preserving Machine Learning using Function Approximation | PDF",1785720462,25,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"learning-in-the-dark-privacy-preserving-machine-learning-using-function-approximation","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/learning-in-the-dark-privacy-preserving-machine-learning-using-function-approximation/118823/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-03",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"How does Learning in the Dark preserve privacy in cloud inference?","Question",{"text":75,"@type":76},"Training occurs on plaintext data, while classification is performed directly on homomorphically encrypted ciphertexts, avoiding decryption during inference.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Why are low-degree Chebyshev polynomials used in the model?",{"text":80,"@type":76},"They approximate the nonlinear activation functions ReLU and Sigmoid so that these functions can be evaluated under homomorphic encryption.",{"name":82,"@type":73,"acceptedAnswer":83},"What enables evaluation of most CNN operations on encrypted data?",{"text":84,"@type":76},"Homomorphic encryption supports addition and multiplication over encrypted data, allowing linear parts of CNNs to be computed homomorphically while handling nonlinearities via polynomial approximation.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,134],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":21,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":21,"slug":133},"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]