Multi-Collisions Attack in Ring Hash Structure

Ring hash structure is a new hash structure which has been introduced by Joux to strengthen the current hash structures against multi-collision attacks. In this paper, we present a cryptanalysis on Ring hash structure. We show that finding multi-collisions, i.e. 2-way collision, for a Ring hash structure is not much harder than finding such multi-collisions for ordinary MD hash structure. The complexity of our attack is approximately ( ) log n times harder than the complexity of attacks against MD structures. We employ these multi-collisions to find a D-way pre-image for this structure. We show the complexity of finding 2-way multi-collision and 2-way preimage are ( ) ( ) ( ) / 2 1 / 2 2 O k n + × × and ( ) / 2 / 2 2 2 2 n n O k n × × + × respectively. We also show that Ring structure should not be used to create a hash function of 2n-bit length, by concatenating this structure to any other hash structure of n-bit output length. We show that the time complexity of finding a collision for this concatenated structure is ( ) ( ) ( ) / 2 1 / 2 2 O k n + × × that is much smaller than ( ) 2 Ω , which is expected for a generic-birthday attack.