The　preservation　of　privacy　has　become　a　widely　discussed　topic　on　the　Internet.　Encryption　is　an　approach　to　privacy;　however,　to　outsource　computing　to　an　cloud　service　without　revealing　private　information　over　encrypted　data　is　difficult.　Homomorphic　encryption　can　contribute　to　it　but　is　based　on　complicated　mathematical　structures　of　abstract　algebra.　We　propoase　a　new　scheme　for　securely　computing　the　similarity　between　binary　vectors　through　a　cloud　server.　The　scheme　is　constructed　from　ciphertext　policy　attribute　based　encryption　and　garbled　circuits　rather　than　homomorphic　encryption.　Attribute　based　encryption　provides　the　access　power,　which　is　a　necessary　primitive　in　our　scheme.　Moreover,　for　computing　over　encrypted　data,　we　rely　on　garbled　circuits　to　handle　secure　outsourcing　and　to　avoid　the　use　of　homomorphic　encryption.　©　Springer　International　Publishing　AG,　part　of　Springer　Nature　2018.