Opposite the substitution cypher is the transposition cypher. In this cypher none of the plaintext letters are changed, but, rather, they are rearranged according to a system.
The simplest form of transposition cypher is flipping the message backwards: So, "Einstein's theory of relativity states that light always travels at the same speed, regardless of an individual's frame of reference." becomes ".ecnerefer fo emarf s'laudividni na fo sseldrager ,deeps emas eht ta slevart syawla thgil taht setats ytivitaler fo yroeht s'nietsniE". (If you're lazy like I am, you can find online converters; there's also this nifty one that reverses the whole thing, words, or flips it upside down.) You can rearrange the letters in groups of a certain number and take out grammatical marks so it looks like another cypher ("ECNE REFE RFOE MARF SLAU DIVI...") or make it so it looks like another language ("Ecne refer foem arfs laudi vidni na fos sel drager...").
An example of reversed text being used in popular culture is its use in Harry Potter and the Philosopher's Stone by JK Rowling: "Erised stra ehru oyt ube cafru oyt on wohsi" appears on The Mirror of Erised.
There are other forms of transposition cyphers, however, such as the rail fence cypher and the twisted path cypher.
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The rail fence cypher breaks up the cypher by taking every-other letter and separating them. If the message is very long, it can be broken up into different sections.
Ex. AN OBJECT IN MOTION REMAINS IN MOTION UNLESS ACTED ON BY AN OUTSIDE FORCE.
If your statement is not a multiple of four, add null letters (or dummy letters) so that it is. We're in luck, though, as the above statement has sixty letters.
Then divide the text by a certain number (we're using sixteen):
AN OBJECT IN MOTION | REMAINS IN MOTION U | NLESS ACTED ON BY AN | OUTSIDE FORCE
Take the first section and separate it by every-other letter:
A O J C I M T O
N B E T N O I N
Then take the bottom letters and move them to the end of the top letters:
AOJC IMTO NBET NOIN
Repeat this for all the sections and put them together.
AOJC IMTO NBET NOIN RMIS NOIN EANI MTOU NESC EOBA LSAT DNYN OTIE OCUS DFRE
To decypher, group them in numbers of sixteen letters, and count every other:
AOJC IMTO | NBET NOIN
First group, second group
Odd numbers, even numbers
A O J C I M T O | N B E T N O I N
1 3 5 7 9 11 13 15 | 2 4 6 8 10 12 14 16
Then put them in order and repeat for each segment.
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The twisted path cypher uses an empty cell matrix. You write your message inside and take the letters from an agreed-upon path.
Ex. AN OBJECT AT REST REMAINS AT REST UNLESS ACTED ON BY AN OUTSIDE FORCE.
I'm using a seven-by-eight matrix for this, because there are fifty-six letters.
Write your letters in the manner agreed upon. This is just across from left to right.
And then take the letters from the agreed-upon path.
So, you get "ANOB JECT ERSN SECR OFED IBSE MATR ESTR TEOT UONA YASA INSA LDET CTUN."