Functional encryption with application to machine learning: simple conversions from generic functions to quadratic funct
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Functional encryption with application to machine learning: simple conversions from generic functions to quadratic functions Huige Wang1,2 · Kefei Chen3,4 · Yuan Zhang5 · Yunlei Zhao2 Received: 30 September 2019 / Accepted: 19 March 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Functional encryption (FE) and predicate encryption (PE) can be utilized in deploying and executing machine learning (ML) algorithms to improve efficiency. However, most of existing FE and PE algorithms only consider generic functions. Actually, quadratic-functions-based FE and PE can be used to further reduce the computation costs significantly. In this paper, we present a functional encryption scheme for quadratic functions from those for generic functions. In our constructions, ciphertexts are associated with a pair of vectors (x, y) ∈ Znq × Zm q , private keys are associated with a quadratic function, and the decryption of ciphertexts CT(x,y) with a private key skF , where F is a n × m-dimensional matrix, recovers (x) Fy ∈ Zq . Compared with Baltico et al.’s FEs for quadratic functions (at Crypto 2017), our schemes could obtain almost the same ciphertexts size of O((n + m) log q) as their schemes (in contrast to O(n) in Baltico et al.’s schemes), and the computation for quadratic functions in our scheme does not rely on bilinear maps, while their schemes must rely on this assumption. In particular, our schemes under the standard assumptions achieve adaptive security, while Baltico et al.’s scheme only obtains selective security. Moreover, beyond the MDDH and GGM assumptions, our schemes allow for instantiations under standard assumptions such as LWE, LPN, and etc. Keywords Quadratic functions · Functional encryption · Adaptive security · Generic conversions · Machine learning
1 Introduction Applying emerging ML algorithms with the integration of cloud computing [38] in reality has already brought large benefits for people [21, 30]. For example, in cloudassisted eHealth systems [19, 36, 37], with these ML algorithms, a medical institution can train a cloud server (which is subject to a cloud service provider) to deploy ML models on the server. After that, the cloud server is able to provide healthcare services for users (e.g., patients) without requiring the participation of the medical institution. By doing so, the medical institution can outsource the healthcare services to the cloud server and enables the users to leverage the services in an efficient and convenient way. This article is part of the Topical Collection: Special Issue on Security and Privacy in Machine Learning Assisted P2P Networks Guest Editors: Hongwei Li, Rongxing Lu and Mohamed Mahmoud Huige Wang
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Despite the conveniences and benefits brought by ML algorithms, critical security and privacy concerns [14, 31] in training the cloud server [33] and requesting services from it have been raised seriously [22]. Specifically, in most ML al
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