In　the　image　outsourcing　system,　image　privacy　is　still　an　increasing　concern　since　the　cloud　service　provider　and　image　owners　are　not　in　the　same　trusted　domain.　The　most　straightforward　method　for　guaranteeing　image　privacy　is　to　leverage　cryptographic　tools,　but　traditional　cryptographic　tools　make　feature　extraction　algorithms　useless.　To　this　end,　we　propose　a　privacy-preserving　feature　extraction　scheme　for　Legendre　circularly　orthogonal　moment,　which　is　a　novel　global　feature　descriptor　and　can　be　used　for　image　analysis.　We　first　develop　a　novel　feature　descriptor,　which　is　one　of　the　circularly　orthogonal　moments　and　termed　as　Legendre　Circularly　Orthogonal　Moment　(LCOM).　Then,　we　present　a　mathematical　framework　for　implementing　Privacy-preserving　Legendre　Circularly　Orthogonal　Moment　(PLCOM)　by　combining　LCOM　and　somewhat　homomorphic　encryption,　and　implement　the　image　reconstruction　in　the　encrypted　domain　based　on　PLCOM.　Besides,　the　detailed　theoretical　analysis　of　message　space　and　expanding　factor　generated　by　the　quantitative　technology　shows　that　LCOM　and　image　reconstruction　in　the　plaintext　domain　can　be　realized　with　the　aid　of　PLCOM.　Finally,　experimental　results　verify　that　the　PLCOM＇s　performance　in　terms　of　image　reconstruction　capability　and　image　recognition　accuracy　is　acceptable.　(C)　2019　Elsevier　Inc.　All　rights　reserved.