Finding Preimages of Tiger Up to 23 Steps

This paper evaluates the preimage resistance of the Tiger hash function. We will propose a pseudo-preimage attack on its compression function up to 23 steps with a complexity of 2, which can be converted to a preimage attack on 23-step Tiger hash function with a complexity of 2. The memory requirement of these attacks is 2 words. Our pseudo-preimage attack on the Tiger compression function adopts the meet-in-the-middle approach. We will divide the computation of the Tiger compression function into two independent parts. This enables us to transform the target of finding a pseudo-preimage to another target of finding a collision between two independent sets of some internal state, which will reduce the complexity. In order to maximize the number of the attacked steps, we derived several properties or weaknesses in both the key schedule function and the step function of the Tiger compression function, which gives us more freedom to separate the Tiger compression function.