Science:Math Exam Resources/Courses/MATH312/December 2010/Question 06/Statement

Recall that an affine cryptosystem with encryption key $\displaystyle K_{E}=(26,a,b)$ and decryption key $\displaystyle K_{D}=(26,c,d)$ works as follows. Each letter is assigned a numerical value, in alphabetical order:

$\displaystyle A\mapsto 0,B\mapsto 1,...,Z\mapsto 25$

These numbers are then viewed modulo 26: They are encrypted by the formula

$\displaystyle x\to y\equiv ax+b\mod {26}$

and decrypted by the formula

$\displaystyle y\to x\equiv cy+d\mod {26}$

It is known that the most frequently occurring letter in the English language is E (with numerical value 4) and the second most frequently occurring letter is T (with numerical value 19). Suppose these letters are encoded as F (numerical value 5) and G (numerical value 6), respectively.

(a) Find the encryption key $\displaystyle K_{E}$

(b) Find the decryption key $\displaystyle K_{D}$