A Practical Limit of Security Proof in the Ideal Cipher Model : Possibility of Using the Constant As a Trapdoor In Several Double Block Length Hash Functions

Recently, Shoichi Hirose [2] proposed several double block length (DBL) hash functions. Each DBL hash function uses a constant which has a role to make the DBL hash function collision-resistant in the ideal cipher model. However, we have to instantiate a block cipher. In this paper, we show that the constant may be used as a trapdoor to help a attacker to find a collision easily. In case of 256-bit output size, we can find a collision with the complexity 2. This is a gap between the security of the DBL hash function in the ideal cipher model and the security of the DBL hash function based on any block cipher.