Reverse the Polarity
Befunge

Whoa, that was a job, even with the editor I made for this challenge. Here's what I got, a nice 11x12 block:

v$,g6&lt;6g,$v
v,$ _^_ $,v
1W&gt;v\B\v&gt;L1
~T+:1E1:-O~
+F00-F-02L+
&gt;:|6gUg6|:&gt;
{a@&gt;^N^&gt;@z`
&gt;1+|@G$| +&gt;
:^9&lt; E&lt;  ^1
~&gt;7^@_,#:&gt;:
 xD&gt;65 ^=P~
v,-\+**&lt;  v


It does a couple of things, sadly only for lowercase letters.

What it does

When run normally, it performs a Caesar cipher on the input.

abcxyz      -&gt; bcdyza
exampletext -&gt; fybnqmfufyu


When flipped horizontally, it reverses said cipher. This is the requirement for the challenge, but it doesn't end here.

bcdyza      -&gt; abcxyz
fybnqmfufyu -&gt; exampletext


When flipped vertically, it ciphers input with a reverse alphabet. This can be considered the opposite approach to the Caesar cipher.

abcxyz      -&gt; zyxcba
exampletext -&gt; vcznkovgvcg


Finally, when rotated 180 degrees, it reverses input. I have a feeling it has to be a reverse of something (hint: the input).

abcxyz      -&gt; zyxcba
exampletext -&gt; txetelpmaxe


How it works

The block basically consists of four semi-overlapping algorithms.

Caesar cipher encoder

v$,g6&lt;
v,$ _^
1 &gt;v\
~ +:1
+ 00-
&gt;:|6g
{a@&gt;^


Caesar cipher decoder (flipped horizontally)

v$,g6&lt;
v,$ _^
1 &gt;v\
~ -:1
+ 20-
&gt;:|6g
`z@&gt;^


Reverse alphabet cipher (flipped vertically)

v,-\+**&lt;
   &gt;65 ^
~&gt;7^
:^9&lt;
&gt;1+|@
   &gt;^


Text reverser (rotated 180 degrees)

v  &lt;
~      
:&gt;:#,_@
1^  &lt;
&gt;+ |$
   &gt;^