7.7.1: Application of Matrices in Cryptography (Exercises)

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Sep 10, 2021
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- 7.7: Application of Matrices in Cryptography
- 7.8: Chapter Review

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SECTION 2.5 PROBLEM SET: APPLICATION OF MATRICES IN CRYPTOGRAPHY

In problems 1 - 8, the letters A to Z correspond to the numbers 1 to 26, as shown below, and a space is represented by the number 27.

$\begin{array}{lllllllllllll} \mathrm{A} & \mathrm{B} & \mathrm{C} & \mathrm{D} & \mathrm{E} & \mathrm{F} & \mathrm{G} & \mathrm{H} & \mathrm{I} & \mathrm{J} & \mathrm{K} & \mathrm{L} & \mathrm{M} \\ 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 \\ \hline \mathrm{N} & \mathrm{O} & \mathrm{P} & \mathrm{Q} & \mathrm{R} & \mathrm{S} & \mathrm{T} & \mathrm{U} & \mathrm{V} & \mathrm{W} & \mathrm{X} & \mathrm{Y} & \mathrm{Z} \\ 14 & 15 & 16 & 17 & 18 & 19 & 20 & 21 & 22 & 23 & 24 & 25 & 26 \end{array} \nonumber$

In problems 1 - 2, use the matrix $A$ , given below, to encode the given messages.

$A=\left[\begin{array}{ll} 3 & 2 \\ 1 & 1 \end{array}\right] \nonumber$

In problems 3 - 4, decode the messages that were encoded using matrix $A$ .
Make sure to consider the spaces between words, but ignore all punctuation. Add a final space if necessary.

Encode the message: WATCH OUT!

Encode the message: HELP IS ON THE WAY.

Decode the following message:

64 23 102 41 82 32 97 35 71 28 69 32

Decode the following message:

105 40 117 48 39 19 69 32 72 27 37 15 114 47

SECTION 2.5 PROBLEM SET: APPLICATION OF MATRICES IN CRYPTOGRAPHY

In problems 5 - 6, use the matrix $B$ , given below, to encode the given messages.

$\mathrm{B}=\left[\begin{array}{lll} 1 & 0 & 0 \\ 2 & 1 & 2 \\ 1 & 0 & -1 \end{array}\right] \nonumber$

In problems 7 - 8, decode the messages that were encoded using matrix $B$ .

Make sure to consider the spaces between words, but ignore all punctuation. Add a final space if necessary.

Encode the message using matrix $B$ :

LUCK IS ON YOUR SIDE.

Encode the message using matrix $B$ :

MAY THE FORCE BE WITH YOU.

Decode the following message that was encoded using matrix $B$ :

8 23 7 4 47 - 2 15 102 -12 20 58 15 27 80 18 12 74 -7

Decode the following message that was encoded using matrix $B$ :

12 69 - 3 11 53 9 5 46 -10 18 95 - 9 25 107 4 27 76 22 1 72 -26

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SECTION 2.5 PROBLEM SET: APPLICATION OF MATRICES IN CRYPTOGRAPHY

SECTION 2.5 PROBLEM SET: APPLICATION OF MATRICES IN CRYPTOGRAPHY

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