Affine Cipher Conversion for "Joe Cusack"

Using the keys a = 5 and b = 8 with the mapping A = 0, B = 1, …, Z = 25 (spaces remain unchanged), we convert "Joe Cusack" as follows:

Step 1: Map Letters to Numbers

• J → 9
• O → 14
• E → 4
• (space remains a space)
• C → 2
• U → 20
• S → 18
• A → 0
• C → 2
• K → 10

Step 2: Encrypt Each Number

The encryption function is: E(x) = (5x + 8) mod 26

"Joe"

For J (9):
E(9) = (5 * 9 + 8) mod 26
     = 53 mod 26
     = 1   → B

For O (14):
E(14) = (5 * 14 + 8) mod 26
      = 78 mod 26
      = 0   → A

For E (4):
E(4) = (5 * 4 + 8) mod 26
     = 28 mod 26
     = 2   → C
  

"Joe" converts to "BAC".

"Cusack"

For C (2):
E(2) = (5 * 2 + 8) mod 26
     = 18 mod 26
     = 18  → S

For U (20):
E(20) = (5 * 20 + 8) mod 26
      = 108 mod 26
      = 4   → E

For S (18):
E(18) = (5 * 18 + 8) mod 26
      = 98 mod 26
      = 20  → U

For A (0):
E(0) = (5 * 0 + 8) mod 26
     = 8 mod 26
     = 8   → I

For C (2):
E(2) = (5 * 2 + 8) mod 26
     = 18 mod 26
     = 18  → S

For K (10):
E(10) = (5 * 10 + 8) mod 26
      = 58 mod 26
      = 6   → G
  

"Cusack" converts to "SEUISG".

Final Result

The plaintext "Joe Cusack" encrypts to "BAC SEUISG" using the Affine Cipher with \(a = 5\) and \(b = 8\).