Visual Cryptography

#Visual #Cryptography

So here’s me and I’m going hiking I’m having a good ol time and I seen this really cool plant and I have to take a picture of it in black and white of course the plant doesn’t look like that though looks a little more like this I’m

Thinking wow what a cool picture so I decided to share it with my friend who tells me Matt you should totally put this on the Internet I tell her someone could totally steal this image from me and claim it as their own no worries she says I have this

Top-secret algorithm to help you out the concern that I expressed to my friend Cece is quite realistic today we’re constantly sharing images on the Internet and it is important for us to claim ownership of our content so I open the top-secret algorithm and discover two concepts visual cryptography and

Sampling distribution of the means visual cryptography is a scheme to hide a secret image using any number of shadow images called shares so I choose this smiley face image to be my secret image because I am so happy about the picture that I took while hiking my

Secret image is a binary image meaning it only contains either black or white values nothing in between when I break my image up into shares they alone don’t look like anything but when layered atop one another the secret image is revealed this particular algorithm generates shares using these two simple patterns if we

Layer the same pattern with itself we can see through half of this 2×2 region however if we layer a pausing patterns with one another light is blocked in this region now this is great because the shares can be printed on transparencies once the shares are aligned the secret image is revealed in

Person it is also possible to print the shares on a regular printer paper but it is more difficult to reveal the secret image this way so the trick to this algorithm is the method in which we come up with these shares because I want to protect my plant picture I simply use

Data from my plant picture and the concept of sampling distribution of the means to generate the first share or master share I begin by finding the mean or average value of my image I then choose a pseudo random sample from this image which is say 50 random pixels and

Then compute the mean of the sample if the sample is less than the image mean I use this pattern and if the samples mean is greater than the image mean I use this pattern I continue with more sense of 50 random pixels until I have generated the

Master share this next step is where my secret smiley face image comes into play this image could easily be a company’s logo or contain copyright information about the image as long as it’s a binary black or white image we’re good I run through the image again but I need

To choose the same pseudo-random sets of points that I chose before this is achieved with a numeric key that dictates the pseudo-random order while it statistically appears random a given key will always choose the same seemingly random pixel locations I continue choosing sample means to

Compare the mean of the image and add an additional comparison with a secret image until I have generated a second-chair called an ownership share the ownership share can now be combined with the master share to reveal the secret image I give the ownership share to a trusted neutral party in the event

Of a dispute if my image was stolen I could generate a new master share from the stolen image printed out obtain the ownership share from the neutral party and reveal my secret image in order for this to work I would also need the numeric key for the pseudo-random number

Generator to ensure that the same points on the suspect image were chosen to generate the new master share if the numeric key was wrong or the suspect image wasn’t really stolen the new master share layered on top of the ownership share would not reveal the secret image well this is wonderful I

Say I’m glad I could help CC replies so does this really work if someone steals my image and manipulates it I’m glad you asked she says this technique is effective against many alterations I decided to test this for myself I alter my image in ten different ways and generate new

Master shares for each alteration to see if I can still recover my smiley face watermark I’ll do this analysis using computers rather than printing new master shares for a controlled assessment I use two metrics to assess the attacks on my original image I first use peak signal-to-noise ratio or psnr

To assess how different the modified image is ideally this number should be small and less than 30 this indicates a seriously altered image to assess the quality of my newly generated watermark I’ll used normalized correlation a simple percentage to see how alike two images are I’d like this

Number to be really high a normalized correlation of a hundred percent would indicate an identical pair of images in other words if the smiley face is visible the algorithm is successful I’ll first take my original image and blur it just like this removing the high frequency information from the image

Despite this pretty severe blur the watermark is still recoverable though the watermark is quite noisy the smiley face is still detectable and I could still claim this blurry image as my own now I’ll go the other way and sharpen the image which results in an increase of contrast along edges this

Modification is numerically less severe than blurring and sure enough the watermark can still be regenerated and the algorithm stands up to sharpening perhaps the image in question is a brightened version of my original image while this is a noisier attack than blurring or sharpening the watermark is still regenerated more clearly this is

Because changing the brightness of the image shifts the mean of the image uniformly with all of the values in the image sure enough with the darkened image we can expect similar results for the same reason regenerating the watermark is a bit more successful with this darkened image it is likely that

Brightening the image clipped some of the image content resulting in an adverse effect on the image mean this darkened image however does not appear to be as crushed as the brightened image was clipped now the image is geometrically altered when cropping the image the cropped region was filled with

The mean of the available values so that the cropped area would not skew the watermarks regeneration despite real values being completely absent from the modified image again the smiley face is still visible rotating the image on the other hand proved to be a bit of a challenge for this algorithm

The watermark regenerated from the rotated image there’s no resemblance to the original watermark however if time is taken to register the rotated image back to its original position the rotated image more closely resembles a cropped image and the watermark can be successfully regenerated a lot of images shared

Online are severely compressed will now see if the watermark can be regenerated from the image sent through JPEG compression JPEG is a lossy compression scheme which works by removing high frequency information from an image this image closely resembles the original and sure enough the watermark is easily generate able the

Introduction of noise to the original image did prove to be a bit problematic for this algorithm since noise is typically random it is therefore uncorrelated with the values of the image which can have adverse effects on the mean value of the image while the newly generated watermark does bear a

Slight resemblance to the original watermark the smiley face is barely visible for these last two tests I’ll consider some scenarios that can be physically modeled first I’ll project the photo onto the wall and take a photograph of this projection after manually registering this captured image to the original the watermark could

Still be regenerated despite the washed out and slightly noisy values introduced by the projector and camera finally I’ll print my photograph using a laser printer on generic printer paper and scan it back into the computer despite the resolution of the printer and noise introduced by the scanner the watermark could still be regenerated

Since I was able to generate my watermark from most of the modified versions of my image I can feel comfortable knowing that I have some more evidence to claim this image as my own in the event of a dispute next time I go hiking I’ll be sure to share all

The cool plants that I find thanks CC anytime you