 Hi, everyone. This work is entitled Superposition Meeting the Middle Attacks, Update on Fundamental Security of AES-like caching. The Meeting the Middle Attack was originally introduced to investigate the security of multiple encryption schemes. Later, the generic Meeting the Middle Attack was used to discuss pre-image resistance of block-sefer-based hash functions. Later, the Meeting the Middle idea was used to devise dedicated attacks on hash functions. In dedicated Meeting the Middle Attacks on the compression function, typically, it is difficult to find a complete partition of the message words, so the attacker only found two separate subsides of the message words. When all other words are fixed, one can split the computation into two chunks. Each chunk can be computed over values of one subset of the message word and independently from the other subset. Those message words in the subsides are called neutral words. The two chunks are typically computed forward and backward independently and end up at a common state where their results can be pairwise matched. Several advanced techniques have been proposed to find better chunk separations and to cover more wrongs. In 2011, the Meeting the Middle Pre-Image Attack was applied to AES-hashing mode. In the attack, the neutral words are directly selected from the encryption state where the key states are fixed. Using initial structure and indirect partner matching, the attack successfully covers several of AES-hashing modes. In the attack published at Eurocrypt 2021, the Meeting the Middle Attack was generalized by removing many artificial limitations and automatic search were performed over extended attack spaces. The attack configuration was formalized and translated into mixed integer linear programming models. The searching for the best attacks was reduced into solving optimization problems and their constraints in MLP. In this work, we enhanced this Meeting the Middle MLP modeling in several ways. The first point is that different from the common practice of bad-oriented decomposition of the state, we propose to use the superposition state. That is, every intermediate state is reviewed as a combination of two virtual states. Each virtual state carries one attribute propagation through linear operations independently of the other. The two virtual states are combined only by going through the nonlinear operation. A direct advantage of this representation is the preservation of the linear combinations. It opens up the possibility of new local collisions between or within the encryption and the key state. Besides, it facilitates the modeling of various ways of consolations and modeling the matching. The next point is allowing the bidirection attribute propagation and consolation. It lets the attribute be consumed and preserve the opposite propagation, but it finally benefits the original propagation because it might enable a remote consolation of impact by the add-on key or by the mixed column. Besides, it contributes to gain the degree of matching. The next point is enhancing the Meeting the Middle MLP model with guess and determine, which was not integrated into previous Meeting MLP models for automatic search. The next point is dedicated to the harsh function workflow. Due to the identity between its encryption and the key schedule, the add-on key can be moved easily around the mixed columns using an equivalent key state which is already involved in the key schedule. Moving forward, I'll stay as it was. One choice might have an advantage that the other choice at different ones says when you integrate the consideration of both choices into one model. The MLP models for searching for pre-image resistant attack can be directly transformed to search for collision attacks on harsh functions and the key recovery attacks on block ciphers. With the enhanced Meeting the Middle MLP modeling, we obtain many updates on the fundamental security of AS-like harsh functions and block ciphers, including the forced pre-image attack on seven rounds were pulled and improved pre-image and collision attacks on growth toll and AS-harsh mode and improved key recovery attacks on tickable block ciphers skinny. Thanks for your attention.