Similar to Problem 1.14 in the textbook: 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, results may be different from the desired ones. In this problem we show that a double encryption with the affine cipher is only as secure as a single encryption.

1. Given two affine ciphers (for the 26 letters A to Z) e_k1=a1 x +b1 and e_k2=a2 x +b2 with a1=2, b1=10 and a2=3, b2=5. Find the coefficients for the cipher e_k3=a3 x +b3 which performs exactly the same encryption (and decryption) as the combination e_k2(e_k1(x)): a3= ( ) and b3= ( ) .

2. For verification: (1) encrypt the letter K first with ek1 to get ( ) and the result with ek2: ( ) , and (2) encrypt the letter K with ek3: ( ) .

Remark: Multiple encryption is of great practical importance in the case of the Data Encryption Standard (DES), for which multiple encryption (in particular, triple encryption) does increase security considerably.