Question

Decrypt these messages encrypted using the shift cipher $\mathbf{f}\left(p\right)\mathbf{=}\left(p+10\right)\mathbf{mod}\mathbf{26}$

a)CEBBOCXNOB XYG

b)LO WIPBSOXN

c) DSWO PYB PEX

Short answer

a) SURRENDER NOW

b) BE MY FRIEND

c) TIME FOR FUN

Step-by-step solution

Step 1

SHIFT CIPHER:

$\mathbf{f}\mathbf{\left(}\mathbf{p}\mathbf{\right)}\mathbf{=}\mathbf{(}\mathbf{p}\mathbf{+}\mathbf{10}\mathbf{)}\mathbf{mod}\mathbf{26}$

Corresponding decryption

${\mathbf{f}}^{\mathbf{-}\mathbf{1}}\mathbf{\left(}\mathbf{p}\mathbf{\right)}\mathbf{=}\mathbf{(}\mathbf{p}\mathbf{‐}\mathbf{10}\mathbf{)}\mathbf{mod}\mathbf{26}$

a) Given message: CEBBOCXNOB XYG

Let

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

241114 23 13141 23 24 6

Let us apply the decryption ${\mathbf{f}}^{\mathbf{-}\mathbf{1}}\mathbf{\left(}\mathbf{p}\mathbf{\right)}\mathbf{=}\mathbf{(}\mathbf{p}\mathbf{‐}\mathbf{10}\mathbf{)}\mathbf{mod}\mathbf{26}$

18 2017 17 4 13 3 4 17 13 14 22

Let

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

SURRENDER NOW

Step 2

b) Given message: LO WIPBSOXN

Let

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

11 14 228 15 118 14 23 13

Let us apply the decryption ${\mathbf{f}}^{\mathbf{-}\mathbf{1}}\mathbf{\left(}\mathbf{p}\mathbf{\right)}\mathbf{=}\mathbf{(}\mathbf{p}\mathbf{‐}\mathbf{10}\mathbf{)}\mathbf{mod}\mathbf{26}$

14 12 24 517 84 133

Let

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

BE MY FRIEND

Step 3

c) Given message: DSWO PYB PEX

Let

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

318 2214 15 24 1 15423

Let us apply the decryption ${\mathbf{f}}^{\mathbf{-}\mathbf{1}}\mathbf{\left(}\mathbf{p}\mathbf{\right)}\mathbf{=}\mathbf{(}\mathbf{p}\mathbf{‐}\mathbf{10}\mathbf{)}\mathbf{mod}\mathbf{26}$

98 124 51417 520 13

Let

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

TIME FOR FUN