An obvious approach to increase the security of a symmetric algorithm is to

apply the same cipher twice, i$.$e$.$:

y $=$ ek$2($ek$1($x$))$

As is often the case in cryptography, things are very tricky and results are often dif$-$

ferent 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 ek$1=$ a$1$x $+$ b$1$ and ek$2=$ a$2$x $+$ b$2.$