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A New Non-MDS Hash Function Resisting Birthday Attack and Meet-in-the-middle Attack
To examine the integrity and authenticity of an IP address efficiently and
economically, this paper proposes a new non-Merkle-Damgard 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-the- middle attack is to O(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.Comment: 18 Page