Final answer:
To construct a Playfair matrix with the key 'largest', start by removing duplicates from the key to get 'larget,' create a 5x5 matrix, and fill it with the unique key letters followed by the rest of the alphabet, excluding 'J'. The completed matrix helps in encrypting and decrypting messages in the Playfair cipher.
Step-by-step explanation:
To construct a Playfair matrix with the key 'largest', you first need to understand that the Playfair cipher is a cryptographic technique that was used historically for securing communications. In constructing the matrix, you eliminate any duplicate letters from the key and then fill in the rest of the matrix with the remaining letters of the alphabet in order. This excludes the letter 'J' which is traditionally combined with 'I'.
- Write the key 'largest' and remove any duplicate letters to get 'larget'.
- Construct a 5x5 matrix.
- Fill in the matrix with the letters of 'larget' followed by the rest of the alphabet (excluding 'J'). The matrix should look like this:
L A R G E
T B C D F
H I/K M N O
P Q S U V
W X Y Z
In a Playfair cipher, you would use this matrix to encrypt and decrypt messages by breaking them into digrams (pairs of two letters) and following a set of rules to substitute these pairs with others according to their positions in the matrix.