Given a plaintext message, say the word "fab", first convert the letters into numbers using the following table:

a b c d e f g h i j k l m n o p q r s t u v w x y z 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27The word fab turns into the numbers 7, 2, 3. Then use the following encryption formula encrypt the numbers:

y = x

For this formula p should be a prime number bigger than the biggest number in our table above. In class we picked p = 29. The encryption exponent e must be a number between 1 and p-1 such that gcd(e, p-1) = 1. In class we picked e = 3.

To encrypt the numbers 7, 2, 3, we take the number for each letter and plug it in for x to get y.

Now, f is 7 so we compute 7

Likewise, a is 2 so we compute 2

Finally, b is 3 so we compute 3

Thus encrypting "fab" gives a ciphertext of 24, 8, 27.

Problem [1]: Encrypt the word "Hello" using the procedure described above (i.e., using the cipher described above).

You can use this web page to do the arithmetic for you.