L0 Norm Optimization in Scrambled Sparse Representation Domain and Its Application to EtC System

Takayuki NAKACHI  Hitoshi KIYA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E103-A   No.12   pp.1589-1598
Publication Date: 2020/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.2020SMP0027
Type of Manuscript: Special Section PAPER (Special Section on Smart Multimedia & Communication Systems)
Category: Cryptography and Information Security
sparse coding,  secure computation,  orthogonal matching pursuit (OMP),  random unitary transform,  EtC system,  

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In this paper, we propose L0 norm optimization in a scrambled sparse representation domain and its application to an Encryption-then-Compression (EtC) system. We design a random unitary transform that conserves L0 norm isometry. The resulting encryption method provides a practical orthogonal matching pursuit (OMP) algorithm that allows computation in the encrypted domain. We prove that the proposed method theoretically has exactly the same estimation performance as the nonencrypted variant of the OMP algorithm. In addition, we demonstrate the security strength of the proposed secure sparse representation when applied to the EtC system. Even if the dictionary information is leaked, the proposed scheme protects the privacy information of observed signals.