You are trying to cryptanalyze an affine enciphering transformation of single-le

Question

You are trying to cryptanalyze an affine enciphering transformation of single-letter message units in a 37-letter alphabet. This alphabet includes the numerals 0-9, which are labeled by themselves (i.e., by the integers 0-9). The letters A-Z have numerical equivalents 10-35, respectively, and blank=36. You intercept the ciphertext "0H7F86BB46R36270266BB9" (here the O's are the letter "oh", not the numeral zero). You know that the plaintext ends with the signature "007" (zero zero seven). What is the message?

Explanation / Answer

We have f(0) = B~11

and f(7) = 9

In Affine encryption, We know that C = f(P) = Pa + b mod <size>

where, P stands for plaintext, size is the total size of alphabet being used and C stands for Crypto text.

a and b are the coeffiecients that are used as keys for encryption and decryption.

We have to calculate the values of a and b in the following equations

f(0) = 0a+b mod 37 = 11

f(7) = 7a +b mod 37 = 9

These equations can be rewritten as

b = 11 mod 37 ------------(1)

7a + b = 9 mod 37 ------------(2);

subtracting (1) from (2), we get

7a = -2 mod 37 = 35 mod 37

=> a = 5;

from (1) , b = 11;

Now, using these values, we can find the decryption formula.

P = f-1(C) = (a-1C - a-1.b)mod 37 = (5-1C - 5-1.11) mod 37

= (15C - 15.11) mod 37 (because 5-1 mod 37 = 15)

= (15C + 20) mod 37.

Using the above formula we can decrypt the given crypto-text.

for ex. O ~ 24.

so for O the corrosponding plain text is (15*24 + 20) mod 37 = 380 mod 37 = 10 ~ A.

Similarly H ----> G, 7 -----> E and so on.

Lastly, the plaintext is "AGENT 006 IS DEAD 007".

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