A New Non-MDS Hash Function Resisting Birthday Attack and Meet-in-the-middle Attack
This addresses the need for efficient and secure hash functions for IP address integrity and authenticity, particularly in lightweight applications, though it appears incremental as it builds on existing hash function concepts with new mathematical foundations.
The paper proposes JUNA, a new non-MDS hash function based on multivariate permutation and anomalous subset product problems, which is proven to be one-way, collision-free, and resistant to birthday and meet-in-the-middle attacks with security up to O(2^m). It is lightweight compared to existing methods like the Chaum-Heijst-Pfitzmann hash, enabling more efficient digital signing schemes.
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.