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Private sequential function computation

Tahmasebi, B ; Sharif University of Technology | 2019

387 Viewed
  1. Type of Document: Article
  2. DOI: 10.1109/ISIT.2019.8849524
  3. Publisher: Institute of Electrical and Electronics Engineers Inc , 2019
  4. Abstract:
  5. In this paper, we introduce the problem of private sequential function computation, where a user wishes to compute a composition of a sequence of K linear functions, in a specific order, for an arbitrary input. The user does not run these computations locally, rather it exploits the existence of N non-colluding servers, each can compute any of the K functions on any given input. However, the user does not want to reveal any information about the desired order of computations to the servers. For this problem, we study the capacity, defined as the supremum of the number of desired computations, normalized by the number of computations done at the servers, subject to the privacy constraint. In particular, we show that the capacity satisfies left( {1 - rac{1}{N}} ight)/left( {1 - rac{1}{{max left( {K,N} ight)}}} ight) leq C leq 1. For the achievability, we show that the user can retrieve the desired order of computations, by choosing a proper order of inquiries among different servers, while keeping the order of computations for each server fixed, irrespective of the desired order of computations. © 2019 IEEE
  6. Keywords:
  7. Information theory ; Achievability ; Arbitrary inputs ; K-function ; Linear functions ; Privacy constraints ; Sequential functions ; Specific ordering ; Supremum ; Computation theory
  8. Source: 2019 IEEE International Symposium on Information Theory, ISIT 2019, 7 July 2019 through 12 July 2019 ; Volume 2019-July , 2019 , Pages 1667-1671 ; 21578095 (ISSN); 9781538692912 (ISBN)
  9. URL: https://ieeexplore.ieee.org/abstract/document/8849524