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CONTENTS:

Video Game University
It's All Up in the Air
Flying Carpets on Wheels
What's the Password?
Saw Me a Tune
Guess What?

Classroom Activities:
Juggling 101
Roller Coaster Physics
Enciphering for Fun
The Math of Music
Delicious Estimating

Go Figure Home

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Go Figure was produced in partnership with MATHCOUNTS, the national math coaching and competition program that promotes seventh-and eighth-grade mathematics achievement. The video, which demonstrates how math is at work everywhere outside the classroom, was distributed to an estimated 6,900 schools participating in the MATHCOUNTS program.

 

Encryption has been used since ancient times for recording sacred writings.

Encryption has been used since ancient times for recording sacred writings.



 

Thomas Jefferson communicated with James Madison at least twice by a special code.

Thomas Jefferson communicated with James Madison at least twice by a special code.



















Encryption machines were developed in the early 1900s.

Encryption machines were developed in the early 1900s.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Go Figure

Teaching Guide

This teaching guide is designed to complement the 20-minute video, Go FigureClick here to request the video.  Please note that video supplies are limited and may no longer be available.

What's the Password?
Cracking the Code

Paranoid Man in the Go Figure video believes there's "something weird going on" what with all the numbers in our lives -- Social Security, driver's license, passport, credit cards, zip code, area code, etc. Maybe. But the use of codes isn't weird at all.

Early Jewish writers of sacred texts did it. Ancient Spartan soldiers did it. Cardinal Richlieu did it, as did Thomas Jefferson and James Madison. And the U.S. government, while very secretive about it, does it as well.

What all these disparate folks have in common is using codes and ciphers to conceal and send messages. It's an old art and right in keeping with human nature. As soon as there was some sort of written communication, no doubt, some people wanted to keep a secret just between themselves.

Code or Cipher?
By definition, code refers to using predetermined words, numbers, or symbols to represent other words and phrases. A code is usually impossible to read without the key code book.

A cipher is a method of transposing or substituting the letters of a plain text, or unencrypted, message with other letters or symbols. Ciphers of various types have been devised, but all of them fall into one or both of the two categories, substitution and transposition.

Authors of ancient Jewish sacred writings practiced one of the first known ciphers. They reversed the alphabet, using the last letter of the alphabet in place of the first, the next last for the second, and so on. This system of letter substitution, called ATBaSH, has an example in the Bible. In Jeremiah 25:26, the word "Sheshech" is written for "Babel" (Babylon) using the second and 12th letters from the end of the Hebrew alphabet instead of from the beginning. [In Hebrew there are no vowels between letters, so Babel is "B b l." Since B is the second letter of the alphabet, the second letter from the end (which has the sound "sh") was substituted for "B and b" in Babel. L, the 12th letter of the alphabet, was replaced with the 12th letter from the end of the alphabet (the sound "ch").]

Letter substitution is one of the oldest and most practiced ciphers, with the Roman emperor Julius Caesar inventing his own. He used a system of advancing each letter four places; for example, in English, "a" would become "d," "b" would be "e," and so on. Today the process is called the Caesar Shift.

Church Secrets
In Renaissance Italy, a small group of devotees to the art of cryptography pioneered the kind of cipher that is now called polyalphabetic substitution.

A country away and a few years later, France's Cardinal Richlieu continued the intrigue. He invented a grille, a card with holes in it, and placed it over a sheet of paper. He'd write a secret message in the holes, then fill in the rest of the paper to look like an innocent letter. Only a person with an identical grille could read the words of the secret message.

A couple of our Founding Fathers got in on the act. A letter written in May 1789 from James Madison to Thomas Jefferson was partially in code. Jefferson had sent the code to Madison four years earlier, and Madison used it to report on the opening of the new federal government. The original letter, in Madison's papers, shows Jefferson's decoded translation written between the lines.

Native American Code Talkers
War and conflict are always an impetus for secrecy, so World Wars I and II were major developments in codes and ciphers. Cipher machines were stock in trade on every side, and code and code breakers were essential. One of the most unusual methods was the use of Native American language by the United States. Choctaw Indian "code talkers" posted in strategic areas simply used their native tongue to send messages during both World Wars I and II. Navajo and Comanche code talkers also were instrumental during World War II. Throughout the two wars, enemy forces were never able to interpret the messages, providing the United States with one of the most secure "codes" of the conflict.

Secrets in the Computer Age
Even with the decline of Communism and the Cold War and the end of the Gulf War, secret messages are still an important issue to governments. In the United States, the field was dominated by the National Security Agency, a federal agency so clandestine that for many years the U.S. government denied the group existed.

The NSA, which gathers intelligence for national security purposes by eavesdropping on overseas telephone calls and cables, did everything in its power to make sure nobody had a code that it couldn't break. However, as computers–the engines of modern cryptography–have increased, so have ever more powerful encryption algorithms (algorithm: set of rules for solving a problem in a finite number of steps, as for finding the greatest common divisor). And recently, U.S. computer makers announced they are adopting a new encryption standard so strong that even the NSA couldn't crack it.

All of which has led to a conflict between personal privacy, the rights of business, and the government's need for maintaining security. The Constitution's framers could have had little idea that encryption would one day be the subject of discussions of personal rights and freedoms.

The NSA has formulated what is known as the Clipper Chip, a semiconductor device the agency developed and wants installed in every telephone, computer modem and fax machine. The chip combines a powerful encryption algorithm with a "back door"–the cryptographic equivalent of a master key.

Law enforcement agencies argue that they need the master-key capability in order to monitor drug runners, terrorists, and spies. Critics denounce the Clipper as "Big Brother" technology that will strip citizens of what privacy they have left in this age of computers and easy access to once-personal information.

Minding Your Ps and Qs:
Creating a Code or Cipher

Substitution, transposition, mono- and polyalphabetic and digraphic systems, Vigenere tables–these are just a few of the choices a budding cryptographer can make in sending a secret message. Most all use math and/or geometry in setting up the cipher, and numbers can be used in some substitution schemes.

Transposition ciphers involve the use of a geometric design, such as a square or rectangle. The cryptographer inscribes the plain text letters by one route in the design, then transcribes them by another route to form the cipher text. In columnar transposition, the cryptographer chooses a numerical key and writes the plain text letters under it, then takes the columns of letters in key-number order to form the cipher text.

Substitution
Substitution systems can also vary. In simple substitution ciphers, a particular letter or symbol is substituted for each letter in the plain text message. The letters are left in their normal order, usually with normal word divisions. These ciphers can be "decoded" by recognizing the occurrence of a set of normal letter frequencies attached to the wrong letters, for example the TH in the, there, they, these, etc.

In multiple substitution (polyalphabetic) ciphers, a keyword or number is used. The first message letter might be enciphered by adding the numerical value of the first letter of the keyword; the second message letter is enciphered in the same way, and so on, repeating the keyword as often as needed to encipher the whole message. Thus, to encipher the word TODAY by the code word DIG, T becomes W (since D is the fourth letter of the alphabet, we move over four letters from T, counting T as the first letter), O becomes W (since I is the ninth letter of the alphabet, we move over nine letters from O, and so on through the message).

Computer Ciphers
Then there are computer ciphers. Continual advancement in computer technology has allowed some very strong (that is, tough to translate) ciphers to be created. One method is to treat the characters in the message as digits in a very large number, raise that number to a power, divide it by another very large number and output the remainder. It would be nearly impossible to break the cipher randomly.

Besides the applications in math and geometry, cryptography could have some very practical applications for teachers. How many students could decipher a test-key written code?

Sources
American Memory Search. Online. America Online. 13 July 1998.

"Cryptography." Funk and Wagnalls New Encyclopedia. 1996. Online. America Online. 14 July 1998.

Elmer-Dewitt, Philip. Reported by David S. Jackson and Suneel Ratan. "Technology: Who Should Keep the Keys?" Time, Inc. Magazine Company and Compact Publishing, Inc. 1992-95. Online. America Online. 14 July 1998.

Wallich, Paul. "Cyber View: Cracking the U.S. Code." Scientific American. April 1997. Online. America Online. 13 July 1998.

Zorpette, Glenn. "Bright History of a Dark Science." Scientific American. April 1997. Online. America Online. 13 July 1998.

Video Game U. | Up in the Air | Flying Carpets | What's the Password?
Saw Me a Tune | Guess What? | Classroom Activities

 

Last Updated: 02/16/03
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