In　some　actual　network　such　as　electronic　voting　system,　in　order　to　count　the　number　of　the　participants,　the　voters　cannot　deny　taking　part　in　a　certain　voting　activity　but　the　voters　need　deny　the　content　of　the　voting.　However　the　proposed　quantum　deniable　authentication　protocols　cannot　meet　the　above　specific　needs.　Hence　a　restricted　quantum　deniable　authentication　protocol　based　on　asymmetric　quantum　cryptography　is　proposed　in　this　paper.　Utilizing　single-qubit　rotations　and　one-way　functions,　this　protocol　can　provide　that　the　voter　can　deny　the　content　of　the　sent　message,　but　cannot　deny　taking　part　in　electronic　voting.　Compared　with　our　previous　schemes,　this　new　scheme　has　the　remarkable　advantages.　Finally,　security　analysis　results　show　that　this　protocol　satisfies　the　basic　security　requirements　of　restricted　deniable　authentication　protocol　such　as　completeness,　restricted　deniability　and　no-counterfeiting.　(C)　2017　Elsevier　GmbH.　All　rights　reserved.