
Mathematicians Encrypt Images Using Mathematics of Sudoku - ColinWright
http://www.technologyreview.com/view/428639/mathematicians-encrypt-images-using-mathematics/
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jcromartie
This seems silly. They "use Sudoku to tackle a different problem--how to
encrypt images before sending them".

You know what else works for encrypting images before sending them? Any other
encryption algorithm.

Who cares if your "encrypted" image is still an image? Doesn't that kind of
defeat the point of encryption? It's obviously just a scrambled image, leaving
only the question of what the unscrambled image is. If someone was planning on
sending illegal or sensitive images with this, you could probably still easily
guess what the nature of the original image was.

It's not like steganography where you don't know there's a message there, or
normal encryption where you have no guess as to what produced the cyphertext
or what the payload is.

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altrego99
Yes - I couldn't believe it when I read the article. This is like - "Create
any random permutation matrix. Use it to permute all the pixels. Done."

Or, use any encryption algorithm and set the key to be your Sudoku grid.

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jgrahamc
I'm not sure why the authors are concentrating on 'Sudoku' (which would
perhaps better be called a Latin square in this context) because I can't see
that they need the property that each 'number' appears once per row and
column.

If they want in place image scrambling using grids, can't they just generate a
random grid that mixes up the pixels in a square from any (x,y) to some other
(x',y') in the same square? They can still arrange for this to be a bijection,
it's trivial.

Perhaps they could Google 'permutation matrix'.

The interesting thing is how you generate the grids, and for that to be secure
you'd need some cryptographic method. In which case you might just as well
encrypt in the first place.

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Dn_Ab
I'm certain that the Sudoku part is a hook, to bring in more viewers and then
keep them for a bit. And although the site is called technology review, it is
basically just a general audience site so concepts like permutation matrix
would be lost on the audience and massacred by the time pressed journalists.
This comes down to a trade off.

You want to draw people in and show them how cool modern tech is, but if you
make it too much like a lecture you don't reach as many people. I think this
trade off is okay, people who are attracted and care will unlearn and those
who don't care will forget but still have a general idea of science as
awesome. E.g. I used to read NewScientist although now I see much of it is
garbage. That stuff can't be _much_ more damaging than non-hard scifi and
comics IMO. The only site that makes me angry is ScienceDaily and not for
their horrid site design.

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swordswinger12
Color me extremely skeptical until I see a rigorous security proof. Fun little
schemes like this are a dime a dozen, and often are essentially useless for
any real application.

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NLips
FTA: "Wu and co make no claims about its potential security but there is
clearly room for further exploration here. "

~~~
swordswinger12
They need to be more careful about using the word 'cryptography' then. Sure,
crypto people and informed laypersons know this is hopelessly insecure, but
all it takes is one overzealous intern implementing this in a banking
application to cause a huge problem.

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NLips
The only word I see is "encrypt", but regardless, this IS cryptography -
converting to a code. You can encrypt with a Ceaser cipher, though it's not
terribly secure.

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aneth4
Since a sudoku puzzle implies it's solution, it is a highly compress(able)
representation of the solution. I wonder if it might be possible to leverage
this sort of rule based matrix to improve compression algorithms, or if
compression algorithms are already more optimal than this.

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breckinloggins
That was my thought as well (see my comment elsewhere in the thread). I wonder
if this could be used as some kind of fixed sparsity encoding?

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switch33
I'm no expert but just an thought:

A sodoku puzzle(requiring only 17 digits for an unique solution) which has an
single solution isn't exactly useful for compression.

How I am thinking about this? The article states:

"And since for a 256 x 256 image, there are at least 256!=2^1684 possible
Sudoku matrices, it's not easy for an adversary to hit on the solution by
accident or even by brute force. "

Compression would make sense if the number of puzzles was something like 1684,
but it is here 2^1684!! Which is quite a lot and to be decoded would be even
worse than the image itself.

The sodoku puzzle's compression would not be of any practical use not only
because they give the data more problems to account for but also because the
data would need to be interpreted.

Also anything that uses encryption generally does the complete opposite of
compression.

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aneth4
For sure it increases the computational power required to decompress, but that
does not preclude its usefulness. Sometimes computation is cheap and bandwidth
is expensive, as perhaps when sending messages to distant stars.

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joshlegs
This is really cool to me. But it makes sense. It just uses a unique numbering
system. I suppose instead of adding a new tens or thousands placeholder to
increase the number, you just add a new grid reference. Pretty cool really.

edit: I guess it's basically a base-9 numbering method, yes?

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mistercow
If I'm understanding the technique correctly, it seems very likely that you
could use statistical properties of natural images to guess at partial
unscramblings, progressively rebuilding the image in far better than brute
force time.

~~~
breckinloggins
A bit of Googling also reveals that some Sudoku puzzles are invertible, so it
sounds like in addition to this problem, you'd better pick your sudoku
solution carefully, as it might be possible to recover the key if the number
of candidate images is small.

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Jacobi
One could exploit the continuity of the image regions. (The similarity of
neighbors in intensity and colors). Also the output is an image with the same
histogram ...

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borplk
Wow this is quite stupid for this application. When I read the title I thought
along the lines of compression by 'solving' the sudoku.

