Rot13 (Sed)

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A sed script implementation of a Rot13 en-/decoding filter.

[edit] theory

Rot13 shifts each element of the english alphabet forward (equivalently, backward) by 13 places. As this alphabet contains 26 letters, 26 / 13 = 2, exactly, and hence this function is an involution — like a hallway light-switch, it is its own inverse.

Question: an involution obeys the equation ff = e, where e is the identity. What are a few examples of command line filters that are projections — i.e. they are idempotent: ff = f?

Question: What is an example of a common command line filter that is both an involution and a projection?

Question: Why is it desirable for ciphers to act more like permutations, less like projections? Also, why do involutions make weak ciphers?

[edit] practice

As there are only 52 characters involved, it is easier to provide a translation table than to bother calculating offsets at runtime.

Question: Which x86 opcode implements single-byte translation tables?

Rather than use the traditional tr a-zA-Z n-za-mN-ZA-M presentation, we choose a presentation to make the involution clear.

<<rot13.sed>>=
#/bin/sed -f
y/anbocpdqerfsgthuivjwkxlymz/naobpcqdresftguhviwjxkylzm/
y/NAOBPCQDRESFTGUHVIWJXKYLZM/ANBOCPDQERFSGTHUIVJWKXLYMZ/

Question: What would a program to generate this lookup table look like? Can these strings be written as a functional expression in your favorite language?

[edit] wrapping up

Finally, we take some sample text from Rot13 (Java)

<<rot13.txt>>=
Now is the Winter of our Discontent,
Made glorious summer by this Son of Yorke:

to check that we generate the same output

% rot13.sed < rot13.txt
Abj vf gur Jvagre bs bhe Qvfpbagrag,
Znqr tybevbhf fhzzre ol guvf Fba bs Lbexr:

and that (at least for this case) we do indeed have an involution

% rot13.sed < rot13.txt | rot13.sed
Now is the Winter of our Discontent,
Made glorious summer by this Son of Yorke:
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