Newyana2 <Newyana2@invalid.nospam> wrote:
>| To increase entropy.
>|
> I looked that up. I don't find any reference to entropy
> in graphics. So I'm not sure what you mean.

Thanks for spending the effort to understand the reason for caring about
entropy in terms of digital forensics of images posted to online sources.

Entropy is a common fundamental technical term for levels of "disorder."
Images: https://duckduckgo.com/?q=camera+fingerprinting+%2Bentropy
Smartphones: https://duckduckgo.com/?q=smartphone+sensor+fingerprinting+%2Bentropy
Browsers: https://duckduckgo.com/?q=browser+fingerprinting+%2Bentropy
Digits: https://duckduckgo.com/?q=fbi+fingerprinting+%2Bentropy

I'm using the term the way they use it to uniquely identify every image
posted to the Internet that came from any particular unique camera sensor.

For example, this article on "Smartphone Camera Identification" discusses
entropy 25 times and camera 114 times (where it's almost a 1:4 ratio) and
where they said "In this work, we follow an identification methodology for
smartphone camera sensors... Our analysis showed that the blue channel
provided the best separation..."
https://www.mdpi.com/1099-4300/24/8/1158/html
https://mdpi-res.com/d_attachment/entropy/entropy-24-01158/article_deploy/entropy-24-01158-v3.pdf

And this paper titled "Mobile Device Identification via Sensor
Fingerprinting" uses the words entropy:camera in a 3:2 ratio, where they
conclude "We show that the entropy from sensor fingerprinting is sufficient
to uniquely identify a device."
https://www.arxiv-vanity.com/papers/1408.1416/

The problem of entropy in terms of posting images to social media is
described in this paper on "Robustness of digital camera identification"
https://link.springer.com/article/10.1007/s11042-021-11129-y
Where they start off with "One of the problem in digital forensics is the
issue of identification of digital cameras based on images. This aspect has
been attractive in recent years due to popularity of social media platforms
like Facebook, Twitter etc., where lots of photographs are shared."

Given this conclusion from the following paper on image fingerprinting
"No Two Digital Cameras Are the Same: Fingerprinting Via Sensor Noise"
https://33bits.wordpress.com/2011/09/19/digital-camera-fingerprinting/
"Camera fingerprinting can be used on the one hand for detecting forgeries
(e.g., photoshopped images), and to aid criminal investigations by
determining who (or rather, which camera) might have taken a picture. On
the other hand, it could potentially also be used for unmasking individuals
who wish to disseminate photos anonymously online."

Let's make up a scenario where it might matter (but please don't shoot the
example but try to understand the problem the example is illustrating).

a. You are brought up Christian & you post to your local church site
b. You are an employee & you post images to your employer web site
c. You have political aspirations & you post images to your party web site
d. You are LGBTQ+ & you post images to your favorite LGBTQ+ web site

Do you want all those online photos to uniquely identify your camera?
>|> If you want
>|> to do something like save a JPG as GIF then you'll lose a lot
>|> of the color data.
>|
>| Does saving JPG to GIF remove unique camera sensor imperfections?
>
> It will be "dithered" to nearest colors, based on one
> of a number of dithering approaches. For example, if
> you have a gradient of greens containing 372 hues, it
> might get converted to a field of green and white dots.
> A GIF can only use 256 colors, so most JPGs would be
> severely degraded when saved as GIF, because a JPG
> can use 16 million colors.

According to one of the papers above, the "blue" realm is the easiest to
fingerprint (although some papers indicated it was the "green").

This JPG-to-GIF dithering might therefore help in increasing entropy.

> It helps to understand the basic system of raster images.

What I do not understand which is important is how the camera's sensor
imperfections show up in the camera's resulting outputted raster images.

> In ALL cases they represent pixel grids with numeric RGB
> values. That is, all formats store data to light pixels on a
> screen with varying intensities of red, green and blue. It's
> always a grid, always rectangular. Any image that's not a
> rectangle (like an icon or PNG) is still a rectangular bitmap,
> but the image format is storing transparency values to be
> applied when the image is rendered onscreen. (That's why
> displays are often "32-bit". 3 bytes for RGB values and one
> byte to indicate transparency.)

It would seem that the fewest bits used (which show the image with just
enough clarity to be useful) would be the best to increase entropy.

> The grid of stored pixel values, indicating color intensity of
> RGB, is arranged in rows, usually starting at top left. That's
> a bitmap. All raster images are bitmaps but can be stored
> in different file formats. JPG is arguably a very poor format
> because it loses color data, but it's popular because it makes
> the smallest files and there are no royalties on the format.
> So it's ideal for online. (It's used in cameras for that reason.
> For people sending birthday party pictures in email, quality
> is not a big factor.)

For the reasons you stated, most images online are JPG so that's what I'm
trying to increase the entropy of. If an automatic JPG->GIF->JPG operation
for all uploaded files increases that entropy, then that's probably a good
technique that I can use to hinder fingerprinting by increasing entropy.

> Once you open an image in a graphic editor you're dealing
> with the bitmap, so whatever you alter from there will affect
> the image saved as a different file. In the case of JPG, it
> compresses the image by eliminating contiguous colors in
> imperceptible ways. That's why a bad quality JPG looks like
> an image comprised of blocks. The reduction of colors allows
> for the data to be stored more compactly, but loses detail.
> That data is lost for good.

The ultimate web site might perform that image alteration also.

I don't know what they do with the images though so I don't have control
over whether they increase the entropy further or leave it alone.

> So if you have a JPG saved at, say, 92 compression (it's
> 1 to 100. Top quality can be either the high or low number,
> depending on the software), then if you open that in an editor
> and resave it at 87 compression, there should be no noticeable
> difference, but some byte values will be changed. (I like Paint
> Shop Pro 5 because it chops off the EXIF data altogether. I
> find it creepy to have buried data in a file. It's a privacy
> problem.)

It would be nice to know how much JPEG compression alone increases (or
decreases) entropy. I would assume it increases entropy.

But I have no idea if it's a lot or only a little.
That they uniquely identify cameras from images hints at little.

> So if it were me I'd try resaving the JPG at different
> compression, convert both of those to BMP, then compare in
> a hex editor to see what you have. If you convert to GIF
> you'll ruin the image because it has to dither to a max of 256
> colors, while the JPG could have 100,000 colors. So forget GIF.

I'll try the JPG->GIF->JPG method to see if it "ruins" the image.

> If you open a JPG in a hex editor it won't be very informative.
> It's like looking at a ZIP file. You only see a bloated header and
> the compressed state of the data.

Yes but that data is very informative when it uniquely identifies your
camera out of pictures scattered across web sites on the Internet.

> If you open and resave as a BMP then you
> have the direct data. The first 54 bytes of the BMP file will
> contain values indicating color depth, width/height, etc. The
> rest is simply the straight grid values. So for a typical 24-bit
> BMP image, the first 3 bytes will be the BGR values in big-endian
> order for the top left pixel. Example: Bright sky blue is zero red,
> half green intensity, and full blue intensity. As a long integer
> value that's 16744448. As bytes it's 255-128-0 or 0-128-255.
> That can also be written as hex: FF 80 00 If you save a BMP
> file which is only that color then you'll see 54 bytes of file header
> followed by a repeating pattern of FF 80 00.

The less repeatable (more random) each image's bitmapped digital result is
on the online storage medium, is, the better for increasing entropy.

> All raster images work that way. All raster images are bitmaps
> in different packaging. A JPG is also a bitmap, but when you
> increase compression you'll reduce colors. So if you have, say, a
> photo of sky with pixels like 255 80 00 243 75 22 241 83 02 those
> three pixels might get dithered to 3 pixel values of 243 75 22. Your
> eye won't see the difference, but the 3 pixels' values can be more
> easily compressed.

I like that increasing compression reduces colors. What you want to do, I
would think, is paper over the camera sensor imperfections in the output.

> So you could try that. Check compression level, open the file,
> resave at different compression, open both files and resave as
> BMPs. Open both BMPs in a hex editor and see how they compare.

What I'll test is JPG->GIF->JPG and JPG->BMP->JPG to see which gives the
best results for an online upload - but which do you think introduces the
most entropy?

> I can't tell you anything about camera sensors. I don't know about
> that. But however they work, it still has to boil down to 24-bit
> RGB if you have a JPG. So any tracks left by the camera would
> have to be in patterns of pixel values.

The articles I pointed to in the beginning of this response shows that what
digital forensics target are the camera sensor's unique imperfections.

> I hope that makes sense. It sounds complicated, but it's actually
> very simple once you get how it orks. All raster images are grids
> of pixel RGB values as numbers. It all comes down to numbers,
> just as any file does.

Thank you for all your helpful information. The goal is to introduce "just
enough" entropy so that all your images aren't uniquely traced to you.