Codes and Inverse Operations

Valetta Eshbach (eshbach@dimacs.rutgers.edu)

Category
Inverse Operations

The Problem
A coded message is given to students. In order for the message to be determined they must know how it was coded. With that information and their understanding of inverse operations they can decode and respond.

Grades 8 - 12 whenever inverse operations are taught.

Suggested Materials
Prior to the class, the teacher must prepare a coded message and a description of the coding procedure. Included is a sample of one possibility. For this example, graph paper is needed for each student and some sample grilles to be used as keys.

A list of resource books is helpful to get students started in their search for more types of codes.

Prerequisites
An understanding of inverse operations is needed.

Activity Description
PART 1

1. A coded message is given to the class.
ex: RRVIE OMTEA SSRLL LYE AT GIEN SCHLIE DGSGE!

2. Students are challenged to decode the message. The discussion usually leads them to ask you to tell them how to decode. A perfect lead-in to your response, "I won't tell you how to decode but I will tell you what I did to create this message."
ex: a. I wrote each letter of my message to you in the holes of this grille I am giving you. I started in the upper left corner and proceeded horizontally row-by-row.
b. After I exhausted the holes I turned the grille 90 degrees counter-clockwise and began again. I continued in this fashion until my message was complete.
c. I then lifted the grille and wrote the coded message by reading horizontally.

We summarized these instructions as WRITE in holes in grille, READ by rows.

3. Ask students to consider the inverse of your actions to decode the message.
ex: WRITE by rows, READ from holes in grille.

4. Now is a nice time to talk a little about codes: how long they have been around, how important it is to keep things secret, when they are used, who uses them today.

PART 2

1. Armed with their newfound interest in codes students are grouped in pairs and given the following assignment:
a. Research codes, ciphers, cryptography.
b. Choose a code to use or devise one of your own and code a message.
c. Present the coded message to the class along with a description of how you encoded.
d. Submit a typed report explaining the history of the code you chose, a description of the coding and decoding procedure, and your sources of information.

2. Students are given a list of resource books to stimulate their search for codes in the library or on the internet.

PART 3

After all messages are presented and decoded and the typed reports have been submitted a follow-up quiz can be given. One question is asked of each student. Each question is different and pertains to their written report. The question is written in the code presented by the student. Their answer can be written in plaintext.

Analysis
The activity will require at least two class periods depending on the number of groups presenting coded messages. They seemed pleased with the quiz which gave them a chance to demonstrate their understanding of the code.

Samples of Student Efforts
1. UREHUW MRUGDQ LV DQ HAFHOOHQW ZULWHU
encryption: add three to position in alphabet
decoding: subtract three from position in alphabet

2. VPA ESP ICQ DEP FOE WSH LDZ FGX NNU VIX MBF
encryption: add alphabet positions of the letters in HANDY sequentially to the letters in the coded message (HANDY is a shared key)
decoding: subtract...

3. TEOH SNII FESC MSTE EE
encryption: write vertically in 3 X 6 matrix (3 X 6 is a shared key) read horizontally
decoding: write horizontally in a 3 X 6 matrix, read vertically

Attachment

References
Gaines, Helen Fouche, Cryptoanalysis, Dover Publications, New York, c1956.
Garfunkel, Solomon, et. al., For All Practical Purposes, 4th ed., W. H. Freeman for COMAP, c1997.
Gleason, Norma, Fun With Codes and Ciphers Workbook, Dover Publications, New York, c1987.
Johnson, Bud, Break the Code: Cryptography for Beginners, Dover Publications, New York, c1997.
Malkevitch, Joseph, Froelich, Gary, Loads of Codes, COMAP, MA, c1993.
Pallas, Norman, Games with Codes and Ciphers, Dover Publications, New York, c1971.
Smith, Laurence Dwight, Cryptography, The Science of Secret Writing, Dover Publications, New York, c1943.