Suppose 6 people want to communicate with each other i.e., each person should be

Question

Suppose 6 people want to communicate with each other i.e., each person should be able to communicate with any of the other 4. The communication needs to be confidential i.e. if A is communicating with B, nobody else should be able to decipher the communication. (a) How many total keys are needed if RSA (and nothing else) is used for encrypting messages? Include both the public keys and private keys in your calculations. (b) How many total are needed if DES (and nothing else) is used for encrypting messages, and there is no key distribution center or any other trusted third party.

Explanation / Answer

There are 6 people as a group. Each person can communicate with any of other 5 persons. The communication should be confidential.

a) If they are using RSA encrypting algorithm, which is a asymmetric then, every person will have their own public(+ve) and private(-ve) keys with them. Because no person knows private keys of others, both the keys ensure confidential communication.

So, because there are 6 people in the group, they need 12 keys in total ,i.e (6 people x 2 keys) keys.

b) If we are using DES encryption algorithm, which is a symmetric then, every unique communication, i.e pair of people, will need a secret key. This unique secret key ensures communication to be confidential.

Because there are 6 people in the group, we can have 15 ways of unique communications, i.e 6C2 ways.

So, they need 15 keys in total.

But in any symmetric encryption algorithm, we will need help of key distribution centre to deliver secret key safe to the recipient. But in question they mentioned that there is no key distribution centre. So, any number of keys cannot satisfy our need, i.e confidential communication in this case.

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