Demonstrating Symmetric Encryption Using Photoshop^® 

Nov 23, 2009 by Bill Soley

Brief Introduction to Encryption Terminology

"In cryptography, encryption is the process of transforming information (referred to as plaintext) using an algorithm (called cipher) to make it unreadable to anyone except those possessing special knowledge, usually referred to as a key. The result of the process is encrypted information ([...] referred to as ciphertext)." (wikipedia)

We will use the symbol p for the plaintext, ⊕ for the cipher operation, k for the key, and c for the ciphertext. The ⊕ symbol is commonly used to denote boolean exclusive-or, which happens to be the cipher operation chosen for our demonstration. All together we can write the encryption operation as ...

p ⊕ k = c

... which we would read as "plaintext p is encrypted with key k producing ciphertext c."

The process of turning the ciphertext back into the plaintext is called decryption. A good cipher only allows decryption by those that know the key. In our demonstration, the operation to decrypt is the same as the operation to encrypt, so we will use the same symbol, ⊕ as we did for encryption. Also, since our example uses a symmetric cipher, the key used to decrypt is the same as the key used to encrypt, so will will use the same symbol, k, for that, too. Decryption can then be written as ...

c ⊕ k = p

... which we would read as "ciphertext c is decrypted with key k producing plaintext p."

Typical Use Case

If Alice wants to send a secret message, p, to Bob, then Alice and Bob must first agree on a key, k, which they must keep secret.

Once Alice knows the key, k, she can encrypt her message plaintext, p, to create the ciphertext, c.

p ⊕ k = c

Alice then sends the ciphertext, c, to Bob. It does not matter if anyone else sees the ciphertext on its way to Bob because only Alice and Bob know the key, so they are the only ones that can decrypt the ciphertext.

Once Bob receives the ciphertext, c, since Bob already knows the key, k, he may decrypt the message.

c ⊕ k = p

Alice has successfully used encryption to send a message, p, to Bob while keeping the contents of the message private even though there may be evesdroppers (in step 5) that can see the ciphertext, c, as it is being delivered to Bob.

Exclusive-or Cipher

The cipher we will be using in our demonstration is based on the exclusive-or operator, abbreviated as xor (pronounced like ecks-ore). The most common mathematical symbol for the exclusive-or operation is ⊕. This operator is boolean (or logical) operation, which means it operates in the domain of true and false (or 1 and 0). The result of ⊕ is 1 only if one of its inputs is 1, but not both. In other words, the output is 1 unless both inputs are the same. Here is a truth table for exclusive-or ...

0 ⊕ 0

 = 0

0 ⊕ 1

 = 1

1 ⊕ 0

 = 1

1 ⊕ 1

 = 0

Some facts about exclusive-or:

a ⊕ b

 = 

b ⊕ a

(a ⊕ b) ⊕ c

=

a ⊕ (b ⊕ c)

a ⊕ a
a

=
=

0
0 ⊕ a

a ⊕ ¬a
¬a

=
=

1
1 ⊕ a

The key will be a randomly chosen string the same length as the plaintext. This technique is called a one time pad. It is very simple, so it makes a good demonstration. In spite of its simplicity it can be perfectly secure under the proper conditions. As long as the key is kept secret and the same key is never used for more than one message, then the one time pad is the only known provably secure cipher.

Simulating Exclusive-or in Photoshop

This demonstration uses images manipulated in the Adobe Photoshop^® program. While Photoshop does not directly support blending images using exclusive-or, it does support a function, which it calls difference, that is close enough to use for this demonstration.

Warning: The difference operation behaves exactly like exclusive-or only as long as the images being blended contain only the basic eight colors: black, red, yellow, green, cyan, blue, magenta, and white. If the images contain any other hues or shades then the function does not behave like exclusive-or and the demonstration will fail. We must therefore carefully make sure that only the basic colors are present.

The chart at left shows a truth table for the Photoshop difference operation over the basic eight color domain. The rows and columns represent the inputs to the difference function, and the corresponding square in the grid shows the output for the given pair of inputs. For example, follow the yellow (Y) row, and the cyan (C) column, to see magenta for the result:

yellow ⊕ cyan = magenta

Notice that each row and column in the truth table contains each and every color exactly once. This is an important property if the function is to be used for encryption. Without this property, more than one plaintext message could encrypt to the same ciphertext thereby making decryption impossible because there would be no way to know which of the possible plaintexts was correct.

Another noteworthy property is that you can undo an exclusive-or operation by repeating it. For example, yellow (Y) ⊕ red (R) = green (G) and green (G) ⊕ red (R) = yellow (Y). You can see why from (8c) above. This property allows us to use the same operation to encrypt and decrypt.

To invoke the difference function in Photoshop, place each image in a separate layer with layer blending mode to difference. The blending mode appears in a pull-down control that Photoshop initializes to normal when a new layer is created. (See the screen shot on right.) The blending mode must be set separately for each layer by selecting the layer and then selecting difference in the pull-down control. 

Once the blending mode has been set to difference, you may enable and disable individual layers by clicking on the eye icon next to each layer. Photoshop will display the exclusive-or of all enabled layers.

Details of Layer Blending

You may skip this section unless you are particularly curious about how colors are represented and blended in Photoshop.

Each image of the type we are using for this demo is represented by three channels: red, green, and blue. This is commonly called an RGB image. The three channels represent the primary colors of light for humans and by adding them together in various proportions we can make any color. (Many people were taught the RYB color model based on red, yellow, and blue "primary" colors, however, RYB, as well as the more accurate CMY, are actually subtractive colors used for blending pigments or dyes and are do not apply when blending light.)

An image in Photoshop is made up of rows and columns of dots called pixels. Ideally these pixels are spaced so close together that they are not individually visible. Each pixel in the image has a numeric value for each channel. In our case that value is in the range 0 to 255, where 0 means no light for that color channel, and 255 means full brightness. For xample, if a particular pixel is yellow (red + green = yellow), it would have a red value of 255, a green value of 255, and a blue value of 0.

For this demonstration, we are interested in the difference blending function. Although we are using it to approximate exclusive-or, the actual function used by Photoshop is the absolute value of the difference of the two channel values.

Difference(a,b) := |a-b|

The eight basic colors: black, red, yellow, green, cyan, blue, magenta, and white, have RGB channel values consisting of 0 and 255 only.  Notice that if the domain of the channel values is limited to 0 and 255, then the result of the Photoshop difference operation is identical to exclusive-or.

If Photoshop had an exclusive-or blending function, then we could use ordinary digital photo images in the demo. However, due to only having the difference operation, we are forced to use line art with a pallete limited to the eight basic colors. The image in the examples, below, is an artistic sketch of me using only the eight basic colors.

Simulating the Encryption and Decryption

For this demonstration, I have chosen an artistic sketch of myself, which you can see, below, labeled plaintext. Once we have chosen the plaintext image, we create a key image that has the same dimensions as the plaintext image. The key image gets filled with random noise using the eight basic color pallete. You can see the one I created, below, labeled key. The next step is to import both images into Photoshop as layers and set the layer blending mode to difference. With both layers enabled, Photoshop will compute the blended image using our exclusive-or cipher and display the ciphertext on the screen. You can save the ciphertext to a file with layers merged.

	original plaintext		key			ciphertext
Alice:		⊕			=
			↓	key shared via secure channel		↓	message sent via insecure channel		reconstructed plaintext
Bob:					⊕			=

You can right-click on each image, above, and save them to a file, then import the files into Photoshop as separate layers. To save you some work, you may download a Photoshop file with the layers already imported. Either way, to view the encryption and decryption, make sure all the layers have their blending mode set to difference, then enable one or two layers at a time. The following table describes what you should see with various combinations of layers enabled:

Creating Your Own Plaintext

1. File→Open... (select file), [OK]
2. crop photograph if desired
3. Filter→Stylize→Glowing Edges..., adjust sliders to taste, [OK]
4. Image→Adjustments→Posterize..., levels=2, [OK]
5. Image→Adjustments→Invert   (optional)
6. File→Save As..., save as=plaintext.png, format=PNG, [Save]
7. File→Close All, [Don't Save]

You may have to play with the choice of filters and parameters in step 3 and repeat steps 3-5 to find results you like.

Creating Your Own Key

For a one time pad using exclusive-or, we simply need a random key the same length as the plaintext. Before creating the key, check the size of the image you wish to use as plaintext. The image I used in this example is 296 pixels wide, by 365 pixels high. Create a new image having the same dimensions as the plaintext image and fill it with random noise from our eight basic color pallete. We will use this image as our key.

1. File→New..., name: key, width=296, height=365, resolution=100 pixels/inch, color mode=RGB 8-bit, [OK]
2. double-click on foreground color to open color chooser, set R=128, G=128, B=128, [OK]
3. select paint bucket tool
4. click within the canvas to fill with 50% grey
5. Filter→Noise→Add Noise..., amount=50%, distribution=Unifrm,  Monochromatic, [OK]
6. Image→Adjustments→Posterize..., levels=2, [OK]
7. File→Save As..., save as=key.png, format=PNG, [Save]
8. File→Close All, [Don't Save]

Step 5 uses the internal Photoshop random number generator to generate random pixel values. Note that the random number source in Photoshop is not truely random and contains patterns and artifacts that might make the ciphertext easier to cryptanalyze. That's fine for a demo, but any serious use should utilize a cryptographic grade random number source.

Creating Your Own Ciphertext

In order to create your own ciphertext file by encrypting your plaintext file with your key, you must import the plaintext image and the key image into Photoshop as separate layers. Then set the layer blending mode to Difference. You can then save the result as a ciphertext file.

1. File→Open..., plaintext.png, [OK]
2. File→Open..., key.png, [OK]
3. Select→All
4. Edit→Copy
5. Window→plaintext.png
6. Edit→Paste
7. Layer→Layer Style→Blending Options..., Blend Mode=Difference, [OK]
8. File→Save As..., save as=ciphertext.png, format=PNG, [OK]
9. File→Close All, [Don't Save]

Decrypting Your Own Ciphertext

In order to decrypt your own ciphertext file using your key, you must import the ciphertext image and the key image into Photoshop as separate layers. Then set the layer blending mode to Difference.

1. File→Open..., ciphertext.png, [OK]
2. File→Open..., key.png, [OK]
3. Select→All
4. Edit→Copy
5. Window→ciphertext.png
6. Edit→Paste
7. Layer→Layer Style→Blending Options..., Blend Mode=Difference, [OK]
8. the image on the display should match the original plaintext
9. File→Close All, [Don't Save]

Creating a Duress Key

The cipher used in this demo has the property that there exists a key that will decrypt any ciphertext into any plaintext of the same size. This is not a common property of modern ciphers, but it is a feature of the one time pad. In fact this property is the basis of a proof that the one time pad provides  perfect privacy. The proof basically reasons that if there is a key that can transform a given ciphertext into any plaintext of the same size, then without knowing the original key, it is impossible to know which of the possible plaintexts of the same size is the true original plaintext.

We can take advantage of this property to create a duress key. This key would be created and kept by Alice or Bob in case some malevolent party attempts to coerce Alice or Bob to decrypt the plaintext by threating, for example, bodily harm. This technique is commonly called rubber-hose cryptanalysis. To create the duress key, we first need a decoy plaintext image, and the actual ciphertext. Follow the same steps described in Creating Your Own Plaintext to create a decoy plaintext, but save the file as decoy.png. The decoy plaintext must be the same size as the real plaintext.

1. File→Open..., ciphertext.png, [OK]
2. File→Open..., decoy.png, [OK]
3. Select→All
4. Edit→Copy
5. Window→ciphertext.png
6. Edit→Paste
7. Layer→Layer Style→Blending Options..., Blend Mode=Difference, [OK]
8. File→Save As..., save as=duress_key.png, format=PNG, [OK]
9. File→Close All, [Don't Save]

Now if you become the subject of coercion, from Mallory, you can give her your duress key. When Mallory decrypts the captured ciphertext using the key you supplied, she will see only the decoy image. You may feel a momentary smugness for having defeated your adversary, however, a serious problem with this situation is that if Mallory is not impressed with the decoy image and suspects it might be a decoy then she may increase the level of coercion in an attempt to get the real key. You might counter this by having multiple decoy images with multiple duress keys. Even when you reach your limit and decide to give Mallory the real key, she may still continue to apply increasing levels of coercion unless it is certain and obvious that you are not still holding out. Indeed you may put yourself in this position by using a cipher that supports duress keys even if you choose not to create one.

original plaintext

key

ciphertext

Alice:

⊕

=

decoy plaintext

↓

copy of ciphertext

duress key

Alice:

⊕

=

↓

captured ciphertext

↓

key obtained by coercion

reconstructed decoy

Mallory:

⊕

=

You can right-click on each image, above, and save them to a file, then import the files into Photoshop as separate layers. To save you some work, you may download a Photoshop file with the layers already imported.