Affine Cipher.

Assume that a = 15 and b = 12 in affine cipher. What is the encryption of 8, 11, and 13 (e(8), e(11), e(13))? What is the decryption of 8, 11, and 13 (d(8), d(11), d(13))?

An obvious approach to increase the security of a symmetric algorithm is to apply the same cipher twice, i.e.: y = e_k2(e_k1(x))

As is often the case in cryptography, things are very tricky and results are often different from the expected and/ or desired ones. In this problem we show that a double encryption with the affine cipher is only as secure as single encryption! Assume two affine ciphers e_k1 = a₁x+b₁ and e_k2 = a₂x+b₂. Show that there is a single affine cipher e_k3 = a₃x+b₃ which performs exactly the same encryption (and decryption) as the combination e_k2(e_k1(x)). Find the values for a₃, b₃ when a₁ = 11, b₁ = 8 and a₂ = 17, b₂ = 12.