With　the　development　of　cloud　computing,　an　increasing　number　of　resource-constrained　image　owners　tend　to　store　their　images　in　the　cloud　and　rely　on　image　retrieval　services　to　obtain　the　images　they　desire.　However,　the　security　of　the　cloud　cannot　be　fully　guaranteed.　To　ensure　image　security　while　achieving　good　retrieval　performance,　we　have　designed　a　retrievable　image　encryption　algorithm　based　on　linear　fitting　and　orthogonal　transformation.　This　algorithm　first　generates　encryption　and　feature　extraction　domains　through　orthogonal　decomposition,　and　then　applies　a　modified　ResNet50　network　for　feature　extraction　in　the　feature　extraction　domain.　The　encryption　process　employs　an　improved　affine　transformation　based　on　linear　fitting,　where　part　of　the　fitting　values　comes　from　the　original　image　data　and　the　other　part　comes　from　data　generated　by　a　chaotic　system.　Additionally,　to　simplify　the　measurement　of　feature　similarity　in　the　cloud,　we　have　designed　a　hierarchical　feature　index　tree　to　narrow　the　retrieval　scope,　thereby　reducing　retrieval　complexity.　Experimental　results　show　that　the　proposed　algorithm　effectively　protects　image　privacy　and　achieves　high　retrieval　accuracy.　The　F-score　reached　6.7634%　on　the　Ghim10k　dataset　and　25.514%　on　the　Corel　1K　dataset,　significantly　improving　upon　traditional　methods.　This　algorithm　has　potential　application　value　in　the　fields　of　secure　image　storage　and　efficient　retrieval　in　the　cloud.