Second order collision for the 42-step reduced DHA-256 hash function

• Analyze the security of DHA-256 hash function with respect to the second order differential attacks.
• Produce a practical distinguisher for 42-step-reduced DHA-256 compression function and provide an example for a colliding quartet.
• Propose a strengthening tweak to the message scheduling algorithm.

At the Cryptographic Hash Workshop hosted by NIST in 2005, Lee et al. proposed the DHA-256 (Double Hash Algorithm-256) hash function. The design of DHA-256 builds upon the design of SHA-256, but introduces additional strengthening features such as optimizing the message expansion and step function against local collision attacks. Previously, DHA-256 was analyzed by J. Zhong and X. Lai, who presented a preimage attack on 35 steps of the compression function with complexity 2239.6. In addition, the IAIK Krypto Group provided evidence that there exists a 9-step local collision for the DHA-256 compression function with probability higher than previously predicted. In this paper, we analyze DHA-256 in the context of higher order differential attacks. In particular, we provide a practical distinguisher for 42 out of 64 steps and give an example of a colliding quartet to validate our results.