Comments on "Outsourcing Eigen-Decomposition and Singular Value Decomposition of Large Matrix to a Public Cloud"

The outsourcing protocols for Eigen-Decomposition (ED) and Singular Value Decomposition (SVD) proposed by Zhou and Li (2016) offer intriguing advancements but are susceptible to malicious behavior by cloud entities. Our investigation identifies a critical vulnerability in the verification scheme utilized by Zhou and Li, where a malicious cloud can deceive the client by providing incorrect results that pass the verification step undetected. This paper not only demonstrates this vulnerability through a detailed attack scenario but also proposes an enhanced verification method to fortify the protocols against such malicious activities, ensuring the integrity and reliability of the schemes proposed by Zhou and Li.