Discussion
In symmetric-key cryptography, if every person in a group of 10 people needs to communicate with every other person in another group of 10 people, how many minimum secret keys are needed ?
Answer: C
The number of keys is 100.
In symmetric-key cryptography each communicating pair needs a secret key known only to the two of them; if one key were shared by more people, any holder could read the others' messages. Every one of the 10 people in the first group talks to every one of the 10 in the second:
\[ 10 \times 10 = 100 \]
People in the same group are not said to talk to each other, so the formula n(n − 1)/2 for one group of n does not apply. A figure of 10 would give each person a single key, and 1 a single shared key, neither of which keeps pairs private. 50 matches no counting.
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