total keys in cryptography

Question

For n users , how many total  keys are  needed by using pvt key cryptography and public key cryptography respectively

a) 2n ,2n    b) n(n-1)/2  , n(n+1)/2   c)2n+2   , 2n    d) n(n-1)/2 , 2n

Comments

public key crypto---> assymetric

private key crypto ----> symmetric

Answer 1

d)

For private key cryptography, we need n(n-1)/2 keys for n users because there is a secret conversation between every 2 distinct users and hence we need ⁿC₂ keys. Whereas for public key cryptography, we need 2 keys for each user (it's private and public key) which amounts to 2n keys for n users.