Signal　processing　in　the　encrypted　domain　has　become　a　hot　research　topic,　which　enable　signal　processing　tasks　in　a　secure　and　privacy-preserving　manner.　Taken　the　fact　that　SURF　(Speeded　Up　Robust　Feature)　has　been　widely　utilized　in　various　applications　into　account,　SURF　feature　extraction　method　in　the　encrypted　domain　has　been　proposed　in　this　paper.　Because　all　steps　must　be　implemented　in　the　encrypted　domain,　Paillier　homomorphic　encryption　method　is　adopted.　Experimental　results　demonstrate　that　the　number　and　location　of　SURF　features　extracted　from　the　encrypted　data　are　the　same　as　those　from　the　plaintext　data.　And　the　error　between　the　descriptors　obtained　from　the　plaintext　data　and　the　encrypted　data　is　only　0.0002932%.　We　also　provide　security　analysis　and　complexity　analysis.　The　proposed　method　can　be　used　in　the　encrypted　domain　based　applications,　such　as　secure　image　processing　and　image　retrieval.