 This is a short presentation for our paper, an analysis of the algebraic group model. My name is Hongsheng Zhou, and this is a joint work with Jonathan Katz and Sun Zhai. Group-based cryptography received lots of attention since the famous result by Define Hermann. Security of a cryptographic scheme can be based on Honey's assumption relative to a group. We must know that these assumptions are already related to some concrete encoding of the group elements, including the matter. Unfortunately, we do not know how to prove any unconditional Honey's result relative to any concrete group encoding. Thus, researchers start to consider restricted class of algorithms. Generic algorithms and the generic group model were introduced. In the generic group model, we can prove unconditional Honey's results. Later, algebraic algorithms and the algebra group model were introduced. In the 2018 paper, among many results, the authors claim that a generic reduction between two problems in the algebra group model implies a generic reduction between these problems in the generic group model. In our paper, we show a count example to the claim in the 2018 paper. And the count example is called a binary encoding game. More issues of the algebra group model can be found in our paper.