1) Client Server Puzzles (CounterDoS.ppt and its reference papers) and Hash Chains a. Slide 8 describes four desirable properties of a basic counter DoS puzzle, and Slides 9-12 gave the main idea behind a puzzle construction that achieves these features (please see corresponding papers provided in the references if you need more details). With approximately 4-5 sentences each, explain how (X, Y)-puzzle design can achieve each of these desirable properties (remember in-class discussions explaining these in detail). Provide mathematical formulations if needed. b. In Partial Image-based Puzzles (see slides), what is the advantage of using sub-puzzles over one large puzzle, providing formulation and its rationale? c. In slide 19, we describe a new puzzle mechanism that permits the pre-computation of puzzles and puzzle sharing (i.e., the same puzzle can be used by different clients). Please elaborate on at least three design rationales (discussed in the class) that permit this feature. d. There are several trade-offs in using hash chains (in general, NOT only concerning the above case), explain THREE advantages (each 1pt) and TWO disadvantages of using hash chains.