consider a group of 30 people who wish to establish pair-wise secure communications using symmetric-key cryptography. How many KEYS need to be exchanged in total?

30 keys

Explanation:

Symmetric-key cryptography is a method of encryption where only one key is needed to encrypt and decrypt the data transmitted from the source to the destination.

The source uses the key to encrypt the data, sends the encrypted data and the encryption key to the destination. The destination uses the key to decrypt the encrypted data.

So, each workstation requires one key to send as the source and one to receive from the source as the destination.

Therefore, the paired secure connection between 30 people needs a total of 30 keys.