Question: Please explain the answer completely. Thank you. Alice can use a binary Merkle tree to commit to a set of elements S = {T1 ,

Please explain the answer completely. Thank you.

Alice can use a binary Merkle tree to commit to a set of elements S = {T1 , , Tn } so that later she can prove to Bob that some Ti is in S using a proof containing at most log2n hash values ( is the ceiling function that rounds up a number, e.g. 3.1 = 4). The hash value for every non-leaf node is computed is the hash of the concatenation of the values of its children.

Generalizing this idea, suppose S contains n elements. What is the minimum number of Merkle tree nodes that proves to Bob that some Ti is in S, as a function of n and k?

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