Blind　quantum　computation　(BQC)　studies　the　problem　of　how　a　client　with　lim-ited　quantum　computation　power　delegates　a　computing　task　to　a　quantum　server　while　keeping　his　input,　output　and　algorithm　private.　To　resist　attacks　from　the　lack　of　identity　authentication　in　BQC　protocols,　we　propose　a　multiparty　BQC　pro-tocol　with　deterministic　mutual　identity　authentication.　For　concreteness,　a　variant　of　measurement-device-independent　quantum　key　distribution　(MDI-QKD)　is　first　pre-sented,　and　based　on　this,　a　method　of　deterministically　generating　the　authentication　keys　of　the　registered　client　and　the　designated　server　is　presented　in　the　registration　phase.　Then　a　deterministic　mutual　identity　authentication　protocol　is　proposed　to　authenticate　the　identities　of　the　registered　client　and　the　designated　server　by　using　the　variant　of　MDI-QKD.　Finally,　in　the　blind　quantum　computation　phase,　the　registered　client　can　delegate　a　computing　task　to　the　designated　server.　Compared　with　existing　BQC　protocols　with　mutual　identity　authentication,　our　proposal　works　in　a　deterministic　and　efficient　way.　Furthermore,　the　proposed　mutual　identity　authentication　method　can　be　applied　in　other　quantum　cryptography　protocols,　thus　providing　a　valuable　way　for　the　construction　of　multiparty　quantum　communication　protocols　with　identity　authentication.　(c)　2022　Elsevier　B.V.　All　rights　reserved.