### Cryptography for Kids

January 12, 2012

I'm amazed that I survived my mathematics education. My first memory of math is learning how to "properly" write the number two. The teacher wanted us to write it with a little loop at the bottom; I had learned to write it from my father in the way that it appears in print; that is, "2." Why there was a problem, I still don't know.

My next memory was our memorization of the multiplication table. Yes, that knowledge is very useful, but for a child, very boring. I had trouble with (8 x 9), until I realized that it's just (8 x 10) - 8. Much elementary mathematics is boring, so how you can make mathematics interesting to children?

Children love keeping secrets. As a child, one of my favorite chemistry experiments (if it can be called that) was writing with invisible ink. I wrote about this in a previous article (Watermark Ink, August 8, 2011). That article includes some recipes you can share with your children with suitable adult supervision (see figure). Nowadays, this exercise is called steganography, and it's applied to digital images, also.

Invisible ink

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)

Today, electronic circuitry is quite inexpensive, and digital secret-keeping technology has been applied to children's toys. One intereting example of this is the Radica Girl Tech Password Journal Electronic Diary that I've seen in television commercials. You can view a YouTube video of one of these commercials, here. This diary unlocks to a spoken password, and a patent application on the concept has been filed by Radica.[1]

Obviously, the algorithm used in a toy must be quite simple, which leads to an interesting science fair type of project. Using speech synthesizers available as free-open-source-software (FOSS), you can try to tailor the synthesized voice to break the password protection. This is somewhat like what Spock did in the Star Trek episode, The Menagerie, when he synthesized Kirk's voice to hijack the Enterprise.

One possible means of secret messaging is the codebook in which words are replaced by symbols. The Alchemists did this, using symbols for the elements. Chemists today do the same thing using the letter abbreviations for the elements. There's not much secrecy in that anymore, unless you try to explain why tungsten is "W" and antimony is "Sb."

Physicians have their own codes, using Greek and Latin nomenclature. They go a further step in obfuscation by using abbreviations. Thus, in prescriptions, p.o., per os, means by mouth, and q.h.s., quaque hora somni, means every night at bedtime.

In an effort to interest children in careers in cryptography, the US National Security Agency has a web site called CryptoKids®.[2] The web site has a variety of games and puzzles suitable for children through high school age, including the following "brainteaser" that requires high school level algebra:
The difference of two positive numbers is 1. The product of these same two numbers is also 1. What is the difference of the cubes of these two numbers?[3]
The Crypto Kids include the two interesting chatacters shown below.

T. Top® character from NSA CryptoKids web site.

T. Top is a computer scientist.

Image provided Courtesy of the National Security Agency)

Slate® character from NSA CryptoKids web site.

Slate is a mathematician. The allusion to Ronald Graham is apparent.

Image provided Courtesy of the National Security Agency)

I've written an online secret message program for children that can be found here.[4] A phrase of up to 25 characters can be entered, and the result is a PDF file that contains a page of random characters with the phrase embedded in it, and a second mask page. When the mask is laid over the first page, the phrase appears through the holes.

This implementation is definitely not what you would call cryptographically secure, but it's great fun for children; and it proves that I can still write code - The computer kind, that is.

### References:

1. Laureen A. Trotto, Maureen T. Trotto, Rober A. Ruginis and Robert W. Jeffway, "Interactive Multimedia Diary," US Patent Application 20070124673, May 31, 2007.
2. CryptoKids® Web Site, US National Security Agency.
3. Answer: Y is (-1 + √5 )/2; X=(1 + √5)/2; the difference of the cubes is four.
4. Secret Message Program from Tikalon. This program has been tested with FireFox 3.6.24, Google chrome 16.0.912.63 and Internet explorer 8, version 8.0.60001.18702. Thanks to Mike Gualtieri of Kiddix Computing and Steve Sund for checking the compatibility for PDF on their web browsers.

Linked Keywords: Mathematics education; memorization; multiplication table; secrecy; keeping secrets; chemistry; experiment; invisible ink; watermark; recipe; steganography; digital image; lemon juice; milk; electric stove; electronic circuitry; television commercial; YouTube; patent application; algorithm; science fair; speech synthesizer; free-open-source-software; FOSS; Spock; Star Trek; The Original Series; The Menagerie; Kirk; Enterprise; codebook; symbol; Alchemist; element; chemists; tungsten; antimony; physicians; Greek; Latin<; nomenclature; obfuscation; abbreviations used in medical prescriptions; prescription; cryptography; US National Security Agency; CryptoKids®; high school; algebra; NSA CryptoKids web site; Ronald Graham; random; source code; US Patent Application 20070124673; US National Security Agency; Kiddix Computing.

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