Question

Suppose that the cipher text,ERC WY JJMIRXPC EHZERGIH XIGLRSPSKC MW, MRHMWXMRKYMWLEFPI JVSQ QEKMGwas produced by encrypting a plain text message using a shift cipher. What is the original plain text.

Short answer

ANY SUFFICIENTLY ADVANCED TECHNOLOGY IS INDUSTINGUISHABLE FROM MAGIC

Step-by-step solution

Step 1

Given message:

ERC WY JJMIRXPC EHZERGIH XIGLRSPSKC MW,

MRHMWXMRKYMWLEFPI JVSQ QEKMG

SHIFT CIPHER:

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

Corresponding cipher:

role="math" localid="1668610838771" ${\mathbf{f}}^{\mathbf{-}\mathbf{1}}\mathbf{\left(}\mathbf{p}\mathbf{\right)}\mathbf{=}\mathbf{(}\mathbf{p}\mathbf{‐}\mathbf{k}\mathbf{)}\mathbf{mod}\mathbf{26}$

The most common letter in the cipher text is M

Let

role="math" localid="1668610893361" $$\begin{gathered} \mathit{A}\mathbf{=}\mathbf{0}\mathbf{,}\mathit{B}\mathbf{=}\mathbf{1}\mathbf{,}\mathit{C}\mathbf{=}\mathbf{2}\mathbf{,}\mathit{D}\mathbf{=}\mathbf{3}\mathbf{,}\mathit{E}\mathbf{=}\mathbf{4}\mathbf{,}\mathit{F}\mathbf{=}\mathbf{5}\mathbf{,}\mathit{G}\mathbf{=}\mathbf{6}\mathbf{,}\mathit{H}\mathbf{=}\mathbf{7}\mathbf{,}\mathit{I}\mathbf{=}\mathbf{8}\mathbf{,} \\ \mathit{J}\mathbf{=}\mathbf{9}\mathbf{,}\mathit{K}\mathbf{=}\mathbf{10}\mathbf{,}\mathit{L}\mathbf{=}\mathbf{11}\mathbf{,}\mathit{M}\mathbf{=}\mathbf{12}\mathbf{,}\mathit{N}\mathbf{=}\mathbf{13}\mathbf{,}\mathit{O}\mathbf{=}\mathbf{14}\mathbf{,}\mathit{P}\mathbf{=}\mathbf{15}\mathbf{,}\mathit{Q}\mathbf{=}\mathbf{16}\mathbf{,}\mathit{R}\mathbf{=}\mathbf{17}\mathbf{,}\mathit{S}\mathbf{=}\mathbf{18}\mathbf{,}\mathit{T}\mathbf{=}\mathbf{19}\mathbf{,} \\ \mathit{U}\mathbf{=}\mathbf{20}\mathbf{,}\mathit{V}\mathbf{=}\mathbf{21}\mathbf{,}\mathit{W}\mathbf{=}\mathbf{22}\mathbf{,}\mathit{X}\mathbf{=}\mathbf{23}\mathbf{,}\mathit{Y}\mathbf{=}\mathbf{24}\mathbf{,}\mathit{Z}\mathbf{=}\mathbf{25} \end{gathered}$$

$\mathbf{M}\mathbf{=}\mathbf{12}$

The most common letter in the English text is E, T, A , O, I, N, S, H and R .The description will only make sense, if the letter corresponding to M is I (you could try all common letters and decrypt the first word using the corresponding key, then you will note that only the case of I will make sense).

Let

role="math" localid="1668610884675" $$\begin{gathered} \mathit{A}\mathbf{=}\mathbf{0}\mathbf{,}\mathit{B}\mathbf{=}\mathbf{1}\mathbf{,}\mathit{C}\mathbf{=}\mathbf{2}\mathbf{,}\mathit{D}\mathbf{=}\mathbf{3}\mathbf{,}\mathit{E}\mathbf{=}\mathbf{4}\mathbf{,}\mathit{F}\mathbf{=}\mathbf{5}\mathbf{,}\mathit{G}\mathbf{=}\mathbf{6}\mathbf{,}\mathit{H}\mathbf{=}\mathbf{7}\mathbf{,}\mathit{I}\mathbf{=}\mathbf{8}\mathbf{,} \\ \mathit{J}\mathbf{=}\mathbf{9}\mathbf{,}\mathit{K}\mathbf{=}\mathbf{10}\mathbf{,}\mathit{L}\mathbf{=}\mathbf{11}\mathbf{,}\mathit{M}\mathbf{=}\mathbf{12}\mathbf{,}\mathit{N}\mathbf{=}\mathbf{13}\mathbf{,}\mathit{O}\mathbf{=}\mathbf{14}\mathbf{,}\mathit{P}\mathbf{=}\mathbf{15}\mathbf{,}\mathit{Q}\mathbf{=}\mathbf{16}\mathbf{,}\mathit{R}\mathbf{=}\mathbf{17}\mathbf{,}\mathit{S}\mathbf{=}\mathbf{18}\mathbf{,}\mathit{T}\mathbf{=}\mathbf{19}\mathbf{,} \\ \mathit{U}\mathbf{=}\mathbf{20}\mathbf{,}\mathit{V}\mathbf{=}\mathbf{21}\mathbf{,}\mathit{W}\mathbf{=}\mathbf{22}\mathbf{,}\mathit{X}\mathbf{=}\mathbf{23}\mathbf{,}\mathit{Y}\mathbf{=}\mathbf{24}\mathbf{,}\mathit{Z}\mathbf{=}\mathbf{25} \end{gathered}$$

$\mathbf{I}\mathbf{=}\mathbf{8}$

The constantk is then the difference between the two numerical values of the two letters:

$\mathbf{k}\mathbf{=}\mathbf{}\mathbf{"}\mathbf{M}\mathbf{"\; -\; "}\mathbf{l}\mathbf{"\; =}\mathbf{12}\mathbf{-}\mathbf{8}\mathbf{=}\mathbf{4}$

Step 2

Given message:

ERC WY JJMIRXPC EHZERGIH XIGLRSPSKC MW,

MRHMWXMRKYMWLEFPI JVSQ QEKMG

Let

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

$$\begin{gathered} \mathbf{4172222499126128172315247251768723861117181518102} \\ \mathbf{1222121771222231217102412221145158921181616410126} \end{gathered}$$

Let us apply the decryption role="math" localid="1668610855235" ${\mathbf{f}}^{\mathbf{-}\mathbf{1}}\mathbf{\left(}\mathbf{p}\mathbf{\right)}\mathbf{=}\mathbf{(}\mathbf{p}\mathbf{‐}\mathbf{4}\mathbf{)}\mathbf{mod}\mathbf{26}$

$$\begin{gathered} \mathbf{01324182055828413191124032101324319427131411624} \\ \mathbf{8188133818198136208187011145171412120682} \end{gathered}$$

Let

role="math" localid="1668610866391" $$\begin{gathered} \mathit{A}\mathbf{=}\mathbf{0}\mathbf{,}\mathit{B}\mathbf{=}\mathbf{1}\mathbf{,}\mathit{C}\mathbf{=}\mathbf{2}\mathbf{,}\mathit{D}\mathbf{=}\mathbf{3}\mathbf{,}\mathit{E}\mathbf{=}\mathbf{4}\mathbf{,}\mathit{F}\mathbf{=}\mathbf{5}\mathbf{,}\mathit{G}\mathbf{=}\mathbf{6}\mathbf{,}\mathit{H}\mathbf{=}\mathbf{7}\mathbf{,}\mathit{I}\mathbf{=}\mathbf{8}\mathbf{,} \\ \mathit{J}\mathbf{=}\mathbf{9}\mathbf{,}\mathit{K}\mathbf{=}\mathbf{10}\mathbf{,}\mathit{L}\mathbf{=}\mathbf{11}\mathbf{,}\mathit{M}\mathbf{=}\mathbf{12}\mathbf{,}\mathit{N}\mathbf{=}\mathbf{13}\mathbf{,}\mathit{O}\mathbf{=}\mathbf{14}\mathbf{,}\mathit{P}\mathbf{=}\mathbf{15}\mathbf{,}\mathit{Q}\mathbf{=}\mathbf{16}\mathbf{,}\mathit{R}\mathbf{=}\mathbf{17}\mathbf{,}\mathit{S}\mathbf{=}\mathbf{18}\mathbf{,}\mathit{T}\mathbf{=}\mathbf{19}\mathbf{,} \\ \mathit{U}\mathbf{=}\mathbf{20}\mathbf{,}\mathit{V}\mathbf{=}\mathbf{21}\mathbf{,}\mathit{W}\mathbf{=}\mathbf{22}\mathbf{,}\mathit{X}\mathbf{=}\mathbf{23}\mathbf{,}\mathit{Y}\mathbf{=}\mathbf{24}\mathbf{,}\mathit{Z}\mathbf{=}\mathbf{25} \end{gathered}$$

ANY SUFFICIENTLY ADVANCED TECHNOLOGY IS INDUSTINGUISHABLE FROM MAGIC