Resource-constrained　users　outsource　the　massive　image　data　to　the　cloud　to　reduce　storage　and　computation　overhead　locally,　but　security　and　privacy　concerns　seriously　hinder　the　applications　of　outsourced　image　processing　services.　Besides,　existing　image　processing　solutions　in　the　encrypted　domain　still　bring　high　computation　overhead,　and　even　lead　to　characteristic　loss.　To　this　end,　we　propose　a　Privacy-Preserving　Krawtchouk　Moment　(PPKM)　feature　extraction　framework　over　encrypted　image　data　by　utilizing　the　Paillier　cryptosystem.　First,　a　mathematical　framework　for　PPKM　implementation　and　image　reconstruction　is　presented　in　the　encrypted　domain.　Then,　the　detailed　expanding　factor　and　upper　bound　analysis　shows　that　plaintext　Krawtchouk　moment　and　plaintext　image　reconstruction　can　be　realized　over　encrypted　image　with　PPKM.　Furthermore,　the　computation　complexity　of　PPKM　can　be　significantly　reduced　with　the　block-based　parallel　algorithm.　Experimental　results　verify　that　the　PPKM　is　feasible　and　acceptable　in　practice　in　terms　of　image　reconstruction　capability　and　image　recognition　accuracy.　©　2020