Kupyna　is　an　AES-like　hash　function　that　has　been　confirmed　as　the　Ukrainian　hash　standard　DSTU　7564:2014　in　2015.　In　this　paper,　we　present　some　preimage　attacks　and　collision　attacks　on　Kupyna.　We　combine　guess-and-determine　and　MITM　methods,　using　a　MILP-based　MITM　attack　tool,　to　apply　them　to　the　Kupyna　hash　cryptographic　algorithm.　We　improve　the　preimage　attack　on　6-round　Kupyna-256　(OT),　increasing　the　complexity　from　the　previous　best　attack　complexity　of　2240　to　2224.　Additionally,　we　also　propose,　for　the　first　time,　collision　attacks　on　6-round　Kupyna-256　(OT)　and　8-round　Kupyna-512　(OT),　with　complexities　of　2116　and　2444　respectively.　©　2023　ACM.