edited by
11,196 views
21 votes
21 votes

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 cryptosystems, respectively are:

  1. $n(n-1)$ and $2n$
  2. $2n$ and $\dfrac{n(n - 1)}{2}$
  3. $\dfrac{n(n - 1)}{2}$ and $2n$
  4. $\dfrac{n(n - 1)}{2}$ and $n$
edited by

4 Answers

Best answer
45 votes
45 votes

For private key crypto for communication between each pair of individuals on secret key will be required, so if an individual wants to communicate with other $\text{n-1}$ individuals he should have $\text{n-1}$ secret keys,

So, the total number of secret keys for private encryption,

$=n\times (n-1)$ (If we include copies) or $n\times \dfrac{(n-1)}{2}$ (distinct keys).

For public key encryption each individual needs to have a public and private key,
so the total keys required in $2\times n$.

From the tone of the question the answer seems to be C) $\dfrac{n(n-1)}{2}$ and $2n$.

edited by
27 votes
27 votes
in private key encryption a key used for encryption as well as decryption.  so no of keys required for n individuals is same as no of communication link between any two individuals.
no links = nC2
no of keys = n*(n-1)/2

in case of Public key each sender has its own public as well as private key so no of keys are 2n..
1 votes
1 votes

For a private key encryption

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)

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.

1 votes
1 votes

For secret or symmetric key cryptography, we need a key between each pair of hosts. So, $n_{C_{2}}$ keys,

For public key cryptography, each host would have two keys — public key and private key. So, $2n$

Option C

Answer:

Related questions

29 votes
29 votes
7 answers
2