With　the　emergence　of　intelligent　terminals,　the　Content-Based　ImageRetrieval　(CBIR)　technique　has　attractedmuch　attention　frommany　areas　(i.e.,　cloud　computing,　social　networking　services,　etc.).　Although　existing　privacy-preserving　CBIR　schemes　can　guarantee　image　privacy　while　supporting　image　retrieval,　these　schemes　still　have　inherent　defects　(i.e.,　low　search　accuracy,　low　search　efficiency,　key　leakage,　etc.).　To　address　these　challenging　issues,　in　this　article　we　provide　a　similarity　Search　for　Encrypted　Images　in　secure　cloud　computing　(called　SEI).　First,　the　feature　descriptors　extracted　by　the　Convolutional　Neural　Network　(CNN)　model　are　used　to　improve　search　accuracy.　Next,　an　encrypted　hierarchical　index　tree　by　usingK-means　clustering　based　on　Affinity　Propagation　(AP)　clustering　is　devised,　which　can　improve　search　efficiency.　Then,　a　limited　key-leakage　k-NearestNeighbor　(kNN)　algorithmis　proposed　to　protect　key　frombeing　completely　leaked　to　untrusted　image　users.　Finally,　SEI　is　extended　to　further　prevent　image　users＇　search　information　from　being　exposed　to　the　cloud　server.　Our　formal　security　analysis　proves　that　SEI　can　protect　image　privacy　as　well　as　key　privacy.　Our　empirical　experiments　using　a　real-world　dataset　illustrate　the　higher　search　accuracy　and　efficiency　of　SEI.