4.4 Application: Cryptography
A cryptogram is a message written according to a secret code. (The Greek Word
kryptos means hidden and the Greek word gramma means letter.) The following
technique uses matrices to encode and decode messages.
First assign a number to each letter in the alphabet with 0 assigned to a blank space.
ENCODING A MESSAGE
3#
&2
Use A = $
! to encode the message GET HELP.
% ' 1 ' 2"
Uncoded Row Matrix *
Encoding Matrix A = Coded Row Matrix
DECODING A MESSAGE : The recipient would use A-1 to decode the message.
Coded Row Matrix * Decoding Matrix A-1
= Uncoded Row Matrix
4.4 Application: Cryptography
! 1%
1 '&
"3
Use the inverse of A = $
# !2
to decode this message:
-4, 3, -23, 12, -26, 13, 15, -5, 31, -5, -38, 19, -21, 12, 20, 0, 75, -25
Coded Row Matrix * Decoding Matrix A-1
!1
Use the inverse of A = ## 0
#" 0
1
1
2
= Uncoded Row Matrix
1$
1 && to decode this message:
3 &%
12, 65, 87, 5, 29, 41, 15, 43, 50, 0, 29, 43, 4, 36, 52, 18, 71, 90, 16, 57, 75
Coded Row Matrix * Decoding Matrix A-1
= Uncoded Row Matrix
3#
&2
Use Use A = $
! to encode a message and send it over to a friend. Your
% ' 1 ' 2"
friend should decode the message using A-1
HOMEWORK: P. 228 #40-48 ALL