To　reduce　the　security　implementation　cost　of　the　outsourcing　data　audit　mechanism　for　the　regenerating-coding-based　distributed　storage　systems,　an　orthogonal　algebraic　coding　method　was　put　forward　to　construct　a　lightweight　privacy-preserving　audit　scheme　based　on　linear　homomorphic　authentication.　The　homomorphic　authentication　tags　were　generated　with　the　orthogonalization　between　the　file　encoded　data　and　the　private　secret　key　vector,　and　the　privacy　protection　of　the　auditing　response　message　was　achieved　by　using　the　random　masking　that　was　constructed　by　randomizing　the　orthogonal　basis　vectors　of　the　specific　sub-vector　of　the　user＇s　secret　key.　The　work　realized　the　effective　integration　of　algebraic　coding,　privacy　protection,　and　security　auditing.　Theoretical　analysis　shows　that　the　proposed　scheme　can　realize　the　information-theoretic　security　in　the　regenerating-coding-based　storage　applications.　Compared　with　the　existing　works,　the　proposed　scheme　is　of　low　computational　complexity　and　communication　overhead,　and　better　performance　advantages.　©　2021,　Editorial　Board　of　Journal　on　Communications.　All　right　reserved.