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\section*{1}
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\subsection*{1.1}
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key: JDQLWBSNZM
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w1: MONISTICAL
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w2: APHRODITES
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\subsection*{1.2}
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The first step was to load all the words from the word list into a tree, where each depth of the tree corresponds with an $i$th letter of the word. The branches that come off each node correspond to the next letter of the word.i.e.
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Would generate a tree that looks like:
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$$() ->{a->{a, b}, b->{a}}$$
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$$()\to(a\to(a, b), b\to(a))$$
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Since the words were encrypted with the same key, that means if we were to generate a possible key, that key would need to decrypt both ciphertexts such that when the tree is navigated we navigate to nodes that exist. If the key results in a path in the tree that does not exist, then we can disregard that answer as a possible key and continue with the possible next key.
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Once you find a key that is the same length as the cipher text, we know that we found the right key.
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