Privacy-Preserving Computations of Predictive Medical Models with Minimax Approximation and Non-Adjacent Form

• Published in: Financial Cryptography and Data Security Vol. 10323; pp. 53 - 74
• Main Authors: Cheon, Jung Hee, Jeong, Jinhyuck, Lee, Joohee, Lee, Keewoo
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2017; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Cloud service; Healthcare; Homomorphic encryption; Minimax approximation; Non-Adjacent Form; Predictive analysis
• ISBN: 3319702777; 9783319702773
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-319-70278-0_4

In 2014, Bos et al. introduced a cloud service scenario to provide private predictive analyses on encrypted medical data, and gave a proof of concept implementation by utilizing homomorphic encryption (HE) scheme. In their implementation, they needed to approximate an analytic predictive model to a polynomial, using Taylor approximations. However, their approach could not reach a satisfactory compromise so that they just restricted the pool of data to guarantee suitable accuracy. In this paper, we suggest and implement a new efficient approach to provide the service using minimax approximation and Non-Adjacent Form (NAF) encoding. With our method, it is possible to remove the limitation of input range and reduce maximum errors, allowing faster analyses than the previous work. Moreover, we prove that the NAF encoding allows us to use more efficient parameters than the binary encoding used in the previous work or balaced base-B encoding. For comparison with the previous work, we present implementation results using HElib. Our implementation gives a prediction with 7-bit precision (of maximal error 0.0044) for having a heart attack, and makes the prediction in 0.5 s on a single laptop. We also implement the private healthcare service analyzing a Cox Proportional Hazard Model for the first time.