To　examine　the　integrity　and　authenticity　of　an　IP　address　efficiently　and　economically,　this　paper　proposes　a　new　non　-iterative　hash　function　called　JUNA　that　is　based　on　a　multivariate　permutation　problem　and　an　anomalous　subset　product　problem　to　which　no　subexponential　time　solutions　are　found　so　far.　JUNA　includes　an　initialization　algorithm　and　a　compression　algorithm,　and　converts　a　short　message　of　n　bits　which　is　regarded　as　only　one　block　into　a　digest　of　m　bits,　where　80　＜=　m　＜=　232　and　80　＜=　m　＜=　n　＜=　4096.　The　analysis　and　proof　show　that　the　new　hash　is　one-way,　weakly　collision　-free,　and　strongly　collision-free,　and　its　security　against　existent　attacks　such　as　birthday　attack　and　meet　in　-the　-middle　attack　is　to　0(2(m)).　Moreover,　a　detailed　proof　that　the　new　hash　function　is　resistant　to　the　birthday　attack　is　given.　Compared　with　the　Chaum-Heijst-Pfitzmann　hash　based　on　a　discrete　logarithm　problem,　the　new　hash　is　lightweight,　and　thus　it　opens　a　door　to　convenience　for　utilization　of　lightweight　digital　signing　schemes.　(C)　2016　Elsevier　B.V.　All　rights　reserved.