# GATE | Gate IT 2008 | Question 68

The total number of keys required for a set of n individuals to be able to communicate with each other using secret key and public key crypto-systems, respectively are:
(A) n(n-1) and 2n
(B) 2n and ((n(n – 1))/2)
(C) ((n(n – 1))/2) and 2n
(D) ((n(n – 1))/2) and n

Explanation:
If there are 2 individuals then total number of distinct keys for communication will be 1 Similarly for 3 individuals we will need 2 distinct keys. Like ways for n users we will need n-1 keys So, total number of keys will be

1+2+3+…n-1 = (n (n-1)/2)

Now for a public key encryption scheme every individual will have two keys one public key and one private key.
Therefore, for n individuals to communicate we will have 2* n keys
Hence, the correct answer will be ((n(n – 1))/2) and 2n.

This solution is contributed by Namita Singh.

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