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February 22, 2021

Throughout history, men have always sought to gain some advantage over other men. In the Stone Age, a large rock was better than a small stone in battle. Later, a crossbow had the advantage over a traditional bow and arrow. Advantage was also gained in efficient transmission of commands, and keeping those commands secret from the enemy.

Julius Caesar (100 BC-15 BC) used a simple code, now called the Caesar cipher, to maintain the secrecy of his messages. In this code, alphabet letters were shifted three places, with 'a' becoming 'd', a method called substitution. At the end of the alphabet, you needed to move to the start, with 'x' becoming 'a', etc. Cryptography in the digital age has advanced far beyond this, since computers are very good at breaking simple ciphers.

Steganography is another method of secret communication. The word, “steganography,” is derived from the Greek words στεγανός (steganos, "covered or concealed"), and γραφή (graphia, "writing"). As I wrote in my children's book about secret codes, there's an interesting example of steganography in ancient times.[1] A man's head was shaved, and a message was written on his bare head. When his hair grew back, the message was hidden, and it was revealed when his head was again shaved.

As I wrote in an earlier article (Watermark Ink, August 8, 2011), I wrote messages using "invisible ink" as a child. You can write a message on paper with lemon juice, and the message is invisible when the liquid dries. Subsequent heating of the paper by holding it over a candle, or placing it in a hot pan on a cook stove, will cause the invisible message to appear. Although I did this myself as a child, this is one experiment in which adult supervision is required. I didn't let my children do 90% of the things I did when I was a child!

The lemon juice invisible ink works because the ascorbic acid in lemon juice decomposes at about 375°F, a little below the memorable combustion point of paper, 451°F. The presence of other organic chemicals in the juice helps. Milk works a little better than lemon juice. Its various proteins and fats decompose when heated to good effect (see figure).

Figure caption

Invisible ink experiment.

The top line was written with lemon juice, the bottom with milk.

The writing was exposed by holding the paper a few inches above an electric stove heating element, but a safer option would be the use of a pan.

In our modern age, it's more common for our documents to be digital, rather than paper. There is also a plethora of digital images; so, many techniques have been developed for hiding messages in digital images through slight variation of the color codes. Images we see on most computers contain an amazing 16,777,216 different colors.

As a crude example of image steganography, I wrote a computer program in the C programming language that converts a short text file into 24-bit color color codes in which the message is encoded in the red color channel (See figure. source code here). These colors can be embedded as nearly invisible single pixels in an image. This particular encoding is easily cracked by a skilled cryptographer. However, variations of this, such as embedding the message with prior encryption as changes in the least-significant bits of the color encoding, are not.

message encoded in red color channel Image of Jupiter's red spot with message embedded as single pixels

Crude image steganography example. The image on the left shows the first paragraph of this article encoded as data in the red color channel. The image on the left shows single pixels of these colors overlaid on a NASA image of Jupiter. The encoding was done using a simple C language program (source code here). Note that this quickly coded program may contain some undetected errors. (Click for a larger version of the left image.. Magnifying this image on your web browser (multiple key presses of ctrl and + on my Firefox web browser) will reveal the pixels.)

The right image was created by using a rectangle size of 1x1 in the program, importing the resultant SVG image into the GNU Image Manipulation Program (GIMP), setting the background as transparent, and then overlaying the image with the Jupiter image. Note that saving images using lossy compression (as in JPEG), or shrinking images in size, will corrupt the message data.

Joab Kose, Oscar Bautista, and Vashish Baboolal of Florida International University (Miami, Florida) have recently posted a short review article about steganography techniques on arXiv.[2] This article summarizes the methods for image steganography, and the similar idea of steganography in audio files using essentially the same techniques.

Just as cryptography has its complementary discipline of cryptanalysis, steganography has its steganalysis. The easiest method is when a copy of the unmodified source file is available. The first check is a file hash to determine whether or not the source file has been modified. Using the Linux command line for my Jupiter example, above, we get the following:
md5sum -b Jupiter_raw.png

md5sum -b Jupiter_with_data.png
Now that we know that the source file has been modified, we can do an XOR operation between bytes of the files to see which bytes were modified. After that, standard cryptanalysis methods can be used on the digital data. I'm not a cryptographer, and this is an extremely simple example of something that can be quite difficult. As I once remarked to a fellow scientist, "If it was easy, they wouldn't be paying us so much money to do it."[3]

The arXiv authors summarize the principal uses of steganography. These include digital watermarking of image, audio, and video files, moderately secure transmission of information that's not visible to unintended recipients, and a means by which corporations can hide portions of trade secret information. arXiv presently has more than 200 papers that have the word, "steganography," in their titles.

Printer identification dots

Printer Steganography - Yellow printer identification dots, barely visible, encoding the printing date, type of printer and printer identification. These are on every page printed by some printers. (Left image, a Wikimedia Commons image by Parhamr. The right image has been color processed by the GNU Image Manipulation Program (GIMP) to accentuate the dots. See ref. 4 for further information.[4]


  1. Dev Gualtieri, "Secret Codes & Number Games: Cryptographic Projects & Number Games for Children Ages 5-16, Tikalon Press, December 20, 2014, 90 pp., ISBN:978-1942459019 (via Amazon).
  2. Joab Kose, Oscar Bautista, Vashish Baboolal, "Review and Test of Steganography Techniques," arXiv, December 15, 2020.
  3. Physicist PhD Salary, Economic Research Institute.
  4. The Electronic Frontier Foundation, Is Your Printer Spying On You?.

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