Question

Decrypt these messages that were encrypted using the Caesar cipher.

a) EOXH MHDQV

b) WHVW WRGDB

c) HDW GLP VXP

Short answer

a) EOXH MHDQV = BLUE JEANS

b) WHVW WRGDB = TEST TODAY

c) HDW GLP VXP = EATDIM SUM

Step-by-step solution

Step 1

Caesar cipher:

$\mathbf{f}\mathbf{\left(}\mathbf{p}\mathbf{\right)}\mathbf{=}\left(p+3\right)\mathbf{mod}\mathbf{}\mathbf{26}$

Corresponding decryption:

role="math" localid="1668604516763" $f^{-1}\left(p\right)=\left(p-3\right)mod26$

Step 2

(a) Given message: EOXH MHDQV

$$\begin{gathered} \mathbf{Let}\mathbf{}\mathit{A}\mathbf{=}\mathbf{0}\mathbf{,}\mathit{B}\mathbf{=}\mathbf{1}\mathbf{,}\mathit{C}\mathbf{=}\mathbf{2}\mathbf{,}\mathit{D}\mathbf{=}\mathbf{3}\mathbf{,}\mathit{E}\mathbf{=}\mathbf{4}\mathbf{,}\mathit{F}\mathbf{=}\mathbf{5}\mathbf{,}\mathit{G}\mathbf{=}\mathbf{6}\mathbf{,}\mathit{H}\mathbf{=}\mathbf{7}\mathbf{,}\mathit{I}\mathbf{=}\mathbf{8}\mathbf{,}\mathit{J}\mathbf{=}\mathbf{9}\mathbf{,}\mathit{K}\mathbf{=}\mathbf{10}\mathbf{,}\mathit{L}\mathbf{=}\mathbf{11}\mathbf{,}\mathit{M}\mathbf{=}\mathbf{12}\mathbf{,}\mathit{N}\mathbf{=}\mathbf{13}\mathbf{,} \\ \mathit{O}\mathbf{=}\mathbf{14}\mathbf{,}\mathit{P}\mathbf{=}\mathbf{15}\mathbf{,}\mathit{Q}\mathbf{=}\mathbf{16}\mathbf{,}\mathit{R}\mathbf{=}\mathbf{17}\mathbf{,}\mathit{S}\mathbf{=}\mathbf{18}\mathbf{,}\mathit{T}\mathbf{=}\mathbf{19}\mathbf{,}\mathit{U}\mathbf{=}\mathbf{20}\mathbf{,}\mathit{V}\mathbf{=}\mathbf{21}\mathbf{,}\mathit{W}\mathbf{=}\mathbf{22}\mathbf{,}\mathit{X}\mathbf{=}\mathbf{23}\mathbf{,}\mathit{Y}\mathbf{=}\mathbf{24}\mathbf{,}\mathit{Z}\mathbf{=}\mathbf{25} \end{gathered}$$

414237 12731621

Let us apply the decryption : $f^{-1}\left(p\right)=\left(p-3\right)mod26$

111204 9401318

$$\begin{gathered} \mathbf{Let}\mathbf{}\mathit{A}\mathbf{=}\mathbf{0}\mathbf{,}\mathit{B}\mathbf{=}\mathbf{1}\mathbf{,}\mathit{C}\mathbf{=}\mathbf{2}\mathbf{,}\mathit{D}\mathbf{=}\mathbf{3}\mathbf{,}\mathit{E}\mathbf{=}\mathbf{4}\mathbf{,}\mathit{F}\mathbf{=}\mathbf{5}\mathbf{,}\mathit{G}\mathbf{=}\mathbf{6}\mathbf{,}\mathit{H}\mathbf{=}\mathbf{7}\mathbf{,}\mathit{I}\mathbf{=}\mathbf{8}\mathbf{,}\mathit{J}\mathbf{=}\mathbf{9}\mathbf{,}\mathit{K}\mathbf{=}\mathbf{10}\mathbf{,}\mathit{L}\mathbf{=}\mathbf{11}\mathbf{,}\mathit{M}\mathbf{=}\mathbf{12}\mathbf{,}\mathit{N}\mathbf{=}\mathbf{13}\mathbf{,} \\ \mathit{O}\mathbf{=}\mathbf{14}\mathbf{,}\mathit{P}\mathbf{=}\mathbf{15}\mathbf{,}\mathit{Q}\mathbf{=}\mathbf{16}\mathbf{,}\mathit{R}\mathbf{=}\mathbf{17}\mathbf{,}\mathit{S}\mathbf{=}\mathbf{18}\mathbf{,}\mathit{T}\mathbf{=}\mathbf{19}\mathbf{,}\mathit{U}\mathbf{=}\mathbf{20}\mathbf{,}\mathit{V}\mathbf{=}\mathbf{21}\mathbf{,}\mathit{W}\mathbf{=}\mathbf{22}\mathbf{,}\mathit{X}\mathbf{=}\mathbf{23}\mathbf{,}\mathit{Y}\mathbf{=}\mathbf{24}\mathbf{,}\mathit{Z}\mathbf{=}\mathbf{25} \end{gathered}$$

BLUE JEANS

Step 3

(b) Given message: WHVW WRGDB

$$\begin{gathered} \mathbf{Let}\mathbf{}\mathit{A}\mathbf{=}\mathbf{0}\mathbf{,}\mathit{B}\mathbf{=}\mathbf{1}\mathbf{,}\mathit{C}\mathbf{=}\mathbf{2}\mathbf{,}\mathit{D}\mathbf{=}\mathbf{3}\mathbf{,}\mathit{E}\mathbf{=}\mathbf{4}\mathbf{,}\mathit{F}\mathbf{=}\mathbf{5}\mathbf{,}\mathit{G}\mathbf{=}\mathbf{6}\mathbf{,}\mathit{H}\mathbf{=}\mathbf{7}\mathbf{,}\mathit{I}\mathbf{=}\mathbf{8}\mathbf{,}\mathit{J}\mathbf{=}\mathbf{9}\mathbf{,}\mathit{K}\mathbf{=}\mathbf{10}\mathbf{,}\mathit{L}\mathbf{=}\mathbf{11}\mathbf{,}\mathit{M}\mathbf{=}\mathbf{12}\mathbf{,}\mathit{N}\mathbf{=}\mathbf{13}\mathbf{,} \\ \mathit{O}\mathbf{=}\mathbf{14}\mathbf{,}\mathit{P}\mathbf{=}\mathbf{15}\mathbf{,}\mathit{Q}\mathbf{=}\mathbf{16}\mathbf{,}\mathit{R}\mathbf{=}\mathbf{17}\mathbf{,}\mathit{S}\mathbf{=}\mathbf{18}\mathbf{,}\mathit{T}\mathbf{=}\mathbf{19}\mathbf{,}\mathit{U}\mathbf{=}\mathbf{20}\mathbf{,}\mathit{V}\mathbf{=}\mathbf{21}\mathbf{,}\mathit{W}\mathbf{=}\mathbf{22}\mathbf{,}\mathit{X}\mathbf{=}\mathbf{23}\mathbf{,}\mathit{Y}\mathbf{=}\mathbf{24}\mathbf{,}\mathit{Z}\mathbf{=}\mathbf{25} \end{gathered}$$

2272122 2217631

Let us apply the decryption : $f^{-1}\left(p\right)=\left(p-3\right)mod26$

$$\begin{gathered} \mathbf{Let}\mathbf{}\mathit{A}\mathbf{=}\mathbf{0}\mathbf{,}\mathit{B}\mathbf{=}\mathbf{1}\mathbf{,}\mathit{C}\mathbf{=}\mathbf{2}\mathbf{,}\mathit{D}\mathbf{=}\mathbf{3}\mathbf{,}\mathit{E}\mathbf{=}\mathbf{4}\mathbf{,}\mathit{F}\mathbf{=}\mathbf{5}\mathbf{,}\mathit{G}\mathbf{=}\mathbf{6}\mathbf{,}\mathit{H}\mathbf{=}\mathbf{7}\mathbf{,}\mathit{I}\mathbf{=}\mathbf{8}\mathbf{,}\mathit{J}\mathbf{=}\mathbf{9}\mathbf{,}\mathit{K}\mathbf{=}\mathbf{10}\mathbf{,}\mathit{L}\mathbf{=}\mathbf{11}\mathbf{,}\mathit{M}\mathbf{=}\mathbf{12}\mathbf{,}\mathit{N}\mathbf{=}\mathbf{13}\mathbf{,} \\ \mathit{O}\mathbf{=}\mathbf{14}\mathbf{,}\mathit{P}\mathbf{=}\mathbf{15}\mathbf{,}\mathit{Q}\mathbf{=}\mathbf{16}\mathbf{,}\mathit{R}\mathbf{=}\mathbf{17}\mathbf{,}\mathit{S}\mathbf{=}\mathbf{18}\mathbf{,}\mathit{T}\mathbf{=}\mathbf{19}\mathbf{,}\mathit{U}\mathbf{=}\mathbf{20}\mathbf{,}\mathit{V}\mathbf{=}\mathbf{21}\mathbf{,}\mathit{W}\mathbf{=}\mathbf{22}\mathbf{,}\mathit{X}\mathbf{=}\mathbf{23}\mathbf{,}\mathit{Y}\mathbf{=}\mathbf{24}\mathbf{,}\mathit{Z}\mathbf{=}\mathbf{25} \end{gathered}$$

1941819 19143025

TEST TODAY

Step 4

(c) Given message: HDW GLP VXP

$$\begin{gathered} \mathbf{Let}\mathbf{}\mathit{A}\mathbf{=}\mathbf{0}\mathbf{,}\mathit{B}\mathbf{=}\mathbf{1}\mathbf{,}\mathit{C}\mathbf{=}\mathbf{2}\mathbf{,}\mathit{D}\mathbf{=}\mathbf{3}\mathbf{,}\mathit{E}\mathbf{=}\mathbf{4}\mathbf{,}\mathit{F}\mathbf{=}\mathbf{5}\mathbf{,}\mathit{G}\mathbf{=}\mathbf{6}\mathbf{,}\mathit{H}\mathbf{=}\mathbf{7}\mathbf{,}\mathit{I}\mathbf{=}\mathbf{8}\mathbf{,}\mathit{J}\mathbf{=}\mathbf{9}\mathbf{,}\mathit{K}\mathbf{=}\mathbf{10}\mathbf{,}\mathit{L}\mathbf{=}\mathbf{11}\mathbf{,}\mathit{M}\mathbf{=}\mathbf{12}\mathbf{,}\mathit{N}\mathbf{=}\mathbf{13}\mathbf{,} \\ \mathit{O}\mathbf{=}\mathbf{14}\mathbf{,}\mathit{P}\mathbf{=}\mathbf{15}\mathbf{,}\mathit{Q}\mathbf{=}\mathbf{16}\mathbf{,}\mathit{R}\mathbf{=}\mathbf{17}\mathbf{,}\mathit{S}\mathbf{=}\mathbf{18}\mathbf{,}\mathit{T}\mathbf{=}\mathbf{19}\mathbf{,}\mathit{U}\mathbf{=}\mathbf{20}\mathbf{,}\mathit{V}\mathbf{=}\mathbf{21}\mathbf{,}\mathit{W}\mathbf{=}\mathbf{22}\mathbf{,}\mathit{X}\mathbf{=}\mathbf{23}\mathbf{,}\mathit{Y}\mathbf{=}\mathbf{24}\mathbf{,}\mathit{Z}\mathbf{=}\mathbf{25} \end{gathered}$$

7322 61115 212315

Let us apply the decryption : $f^{-1}\left(p\right)=\left(p-3\right)mod26$

4019 3812 182012

$$\begin{gathered} \mathbf{Let}\mathbf{}\mathit{A}\mathbf{=}\mathbf{0}\mathbf{,}\mathit{B}\mathbf{=}\mathbf{1}\mathbf{,}\mathit{C}\mathbf{=}\mathbf{2}\mathbf{,}\mathit{D}\mathbf{=}\mathbf{3}\mathbf{,}\mathit{E}\mathbf{=}\mathbf{4}\mathbf{,}\mathit{F}\mathbf{=}\mathbf{5}\mathbf{,}\mathit{G}\mathbf{=}\mathbf{6}\mathbf{,}\mathit{H}\mathbf{=}\mathbf{7}\mathbf{,}\mathit{I}\mathbf{=}\mathbf{8}\mathbf{,}\mathit{J}\mathbf{=}\mathbf{9}\mathbf{,}\mathit{K}\mathbf{=}\mathbf{10}\mathbf{,}\mathit{L}\mathbf{=}\mathbf{11}\mathbf{,}\mathit{M}\mathbf{=}\mathbf{12}\mathbf{,}\mathit{N}\mathbf{=}\mathbf{13}\mathbf{,} \\ \mathit{O}\mathbf{=}\mathbf{14}\mathbf{,}\mathit{P}\mathbf{=}\mathbf{15}\mathbf{,}\mathit{Q}\mathbf{=}\mathbf{16}\mathbf{,}\mathit{R}\mathbf{=}\mathbf{17}\mathbf{,}\mathit{S}\mathbf{=}\mathbf{18}\mathbf{,}\mathit{T}\mathbf{=}\mathbf{19}\mathbf{,}\mathit{U}\mathbf{=}\mathbf{20}\mathbf{,}\mathit{V}\mathbf{=}\mathbf{21}\mathbf{,}\mathit{W}\mathbf{=}\mathbf{22}\mathbf{,}\mathit{X}\mathbf{=}\mathbf{23}\mathbf{,}\mathit{Y}\mathbf{=}\mathbf{24}\mathbf{,}\mathit{Z}\mathbf{=}\mathbf{25} \end{gathered}$$

EATDIM SUM