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(Solved): Question 1. Encryption of German messages in WWII could be boiled down to transformations of a 26\ti ...
Question 1. Encryption of German messages in WWII could be boiled down to transformations of a
26\times 26identity matrix (a row for each letter) that encoded a message, which could then be decoded with a 'key'. We will take a similar, yet less-sophisticated approach, which assigns each letter a vector with two components:
^(')=[[0],[0]],^(')a^(')=[[0],[1]],^(')b^(')=[[0],[2]],dots, 'z' =[[2],[6]].The
2\times 2matrix
Aencrypts this code by left multiplying each letter's associated vector by
A. For example, if
Ais given by
A=[[3,1],[2,1]]we could encrypt the letter 'a' with matrix-vector multiplication:
encrypted 'a' =[[3,1],[2,1]][[0],[1]]=[[1],[1]]For us, the matrix
Ais the 'key' and an accompanying
2\times nmatrix is an encrypted message, where
nis the number of characters in the message. Decipher the following message
[[2,16,10,0,4,17,18,8,14,10,0,18,19,0,11,4,2],[4,40,25,0,10,42,45,20,35,25,0,45,47,0,27,9,4]]if the key is given as
A=[[1,2],[2,5]]