Given a summary function H$1$ : $\{0,1\}$

$2$n $->\{0,1\}$

n

$.$ This function is used in a Merkle tree of height h with input a binary sequence x$0$x$1...$ x$2$

h where each xi

is a binary sequence of size n bits. With successive applications of H$1,$ the Merkle tree can itself be thought of as a summary function H that compresses strings of size n$2$

h in

strings of size n$.$ Show that if H$1$ has difficulty finding conflicts then so does

H has difficulty finding conflicts