Construct a Play fair matrix with the key “Trust” and encrypt themessage “Be confident in yourself”.

Sure, here's how you can construct a Playfair matrix with the key "Trust" and encrypt the message "Be confident in yourself".

Step 1: Preparing the Key The key is "Trust". We remove any duplicate letters from it, which gives us "Trus".

Step 2: Constructing the Playfair Matrix We construct a 5x5 matrix and fill it with the letters of the key first, and then the rest of the alphabet (excluding 'j' because 'i' and 'j' are considered the same in this cipher). The matrix looks like this:

T R U S A B C D E F G H I K L M N O P Q V W X Y Z

Step 3: Preparing the Message The message is "Be confident in yourself". We remove spaces and convert it to uppercase, which gives us "BECONFIDENTINYOURSELF". We then split it into pairs of letters. If a pair has the same letter twice, we insert an 'X' between them. If there's a single letter left at the end, we add an 'X' to it. This gives us: "BE CO NF ID EN TI NY OU RS EL FX".

Step 4: Encrypting the Message We encrypt each pair of letters using the Playfair matrix. If the letters are in the same row, we replace them with the letters to their right (wrapping around to the start of the row if necessary). If they're in the same column, we replace them with the letters below them (wrapping around to the top if necessary). If they're in different rows and columns, we replace them with the letters in their own row but in the column of the other letter. This gives us the encrypted message: "AB UC NG HD EN TI NY OU RS EL FX".

Please note that the Playfair cipher is case-insensitive and doesn't handle numbers or special characters.