To examine the integrity and authenticity of an IP address efficiently and economically, this paper proposes a new non-Merkle-Damgård structural (non-MDS) 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-themiddle attack is to O(2). 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.