Originally, the Nostradamus attack, also known as chosen target forced prefix preimage attack, was introduced by Kelsey and Kohno in [KeKo06] and applied on strengthened Merkle-Damgard (MD) iterative hash functions. In this work we adapt the attack for the particular case of tree based hash functions. The new Nostradamus attack on tree hash functions differs mainly in the precomputation step from the original attack on the MD construction but has approximately the same complexity (as MD) in its offline, online and memory requirements.
Moreover, we develop a simple long message second preimage attack on tree hash functions and adapt a TMD methods to decrease the computation.