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Say I have a $26\times 26$ matrix $M$, each column$C_i$ of which contains the numbers from 1 to 26 in a random order. To encrypt a word, I take the first letter (e.g., b), convert it to its index $i$ (here, 2) and take the $i$th element of column $C_i$ for the first letter. Let's say that b becomes d. Then I take the fourth column $C_4$ (because $d$ is the fourth letter), convert the second letter to its index $j$ and encode it with the $j$th element of $C_4$, and so one.

Example with four letters $a,b,c,d$: take

$$ M=\begin{bmatrix} 2 & 2 & 4 & 3 \\ 3 & 3 & 1 & 4 \\ 1 & 4 & 3 & 2 \\ 4 & 1 & 2 & 1\end{bmatrix} $$

to encrypt $bacd$: the first letter, $b$, has index $2$, so it will be coded by ${C_{1}}(2)=3$, so $c$. For the second letter, we use $C_3$; $a$ has index 1 so it becomes $C_3(1)=4$, that is, $d$ and the next letter will be coded with $C_4$. $c$ has index $3$ so becomes $C_4(3)=2$, so $b$ and the next letter will be coded with $C_2$. $d$ has index $4$ so becomes $C_2(4)=1$, so $a$. Finally, $bacd$ becomes $cdba$.

My question is, is this method known (certainly!) and does it have a name? One advantage is that is avoids simple statistical analysis on the frequency of letters.

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This is a form of polyalphabetic substitution cipher. I'm not aware of this particular method having a name.

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