Secure　outsourced　computation　is　a　key　technique　for　protecting　data　security　and　privacy　in　the　cloud.　Although　fully　homomorphic　encryption　(FHE)　enables　computations　over　encrypted　data,　it　suffers　from　high　computation　costs　in　order　to　support　an　unlimited　number　of　arithmetic　operations.　Recently,　secure　computations　based　on　interactions　of　multiple　computation　servers　and　partially　homomorphic　encryption　(PHE)　were　proposed　in　the　literature,　which　enable　an　unbound　number　of　addition　and　multiplication　operations　on　encrypted　data　more　efficiently　than　FHE　and　do　not　add　any　noise　to　encrypted　data;　however,　these　existing　solutions　are　either　limited　in　functionalities　(e.g.,　computation　on　natural　numbers　only)　or　leak　information　of　the　underlying　data.　To　tackle　these　shortcomings,　this　paper　proposes　Secure　Outsourced　Computation　on　Integers　(SOCI)　based　on　PHE　and　a　twin-server　architecture.　Compared　with　the　existing　solutions,　SOCI　supports　computations　on　encrypted　integers　(vs.　natural　numbers)　and　greatly　improves　the　security　and　correctness　of　the　computations.　Results　of　theoretical　analysis　and　experimental　evaluation　show　that　SOCI　outperforms　existing　solutions　in　computation　and　communication　efficiencies.