a) In our lecture we discussed how Alice can use a binary Merkle tree to commit to a set of messages S = {m₁, M₂, M3,..., mg) by providing Bob with one commitment value which is the Merkle root. Later she can prove to Bob that some m, is in S by sending him an authentication path containing at most [log₂ n] values. Now consider that Alice decided to do the same but using ternary Merkle trees where every non-leaf node has three children (instead of 2). The hash value for every non-leaf node is computed as the hash of the concatenation of the values of its children. i) ii) Suppose S= {m₁, M₂, M3,..., mg). Explain how Alice computes a one commitment value to all the messages in S using the above described ternary Merkle tree. You may use pictorial illustration. Explain how Alice later proves to Bob that m4 is in the set S which is committed to in the previous step. iii) iv) Consider generalizing the problem of accumulator commitments using ternary Merkle trees where S contains n messages. What is the size of the authentication path that proves that some mi is in S as a function of n? For a very large n, is the authentication path using a ternary Merkle tree shorter or longer than when using a binary Merkle tree? Please explain.