# Cryptography Implementation

Robert M. Scher (rscher@dimacs.rutgers.edu)

New York City School Chancellor's theme of "literacy" was implement in math class with a term project in cryptography. Each student was asked to either:
1. do a research paper on cryptography, or
2. invent a code. write a secret message in code. provide a decryption of the message.

Two math fun days were introduced. Cryptologoy puzzles were both handed out and described on the chalk board (hand out attached). Codes covered were:
1. Caesar cipher
2. Rotating grill
3. Rail fence
4. Matrix crypt
5. Pig-pen
6. Columnar transposition

Cryptography supplemental lessons to graphing linear equations

Pre-requisite lessons
1. Basic graphing
2. Graphing equations
3. Graphing by slope-intercept method
4. Inverse equations

Aim: How do we use coding with linear equations?

Do Now
Decode this "secret" message:

```x= 23, 8, 1, 20, 19  13, 25  12, 9, 14, 5 ?
y= ?```

Use the "decoding" equation y= x
x= # on circle
y= # secret letter

Handout: "coding circle" ditto

Example for discussion
Try this secret message:

`PDWK LV IXQ`

Discuss the "secret coding" equation

`y= x+3`

Find the decoding equation by solving for x
Decoding equation

`x= y-3`

Practice
1. If y= 2x+3 is encoding, what is the decoding equation?

Class Activity
1. Each student writes a 25 letter coded message using a simple
y= x+a equation where
-6 < a < 6
Give each student a different number. Work in pairs coding and decoding.

Topics Covered
Equations
Graphing
Evaluating

Aim: How to use graphing to find a secret in a linear equation.

Do Now
1. Write the equation of the line through points (-3, 3) and (3, 21)
2. Graph the equation.

Handout: Graph paper
Have students number the y axis from 0 to 26. Place the letters A through Z along the y axis beginning with A=1 through Z=26.

There are 2 sets of secret equations:
 A B 1. y= x+2 1. 15x+18 2. y= 19x+3 2. 4x+9 3. y= 9x+1 3. 14x+1 4. y= 19x+1 4. 20x+5 5. y= 9x+19 5. 9x+19 6. y= 24x 6. 25x

Students work in pairs. Each pair of students is given 6 papers numbered A1-A6 or B1-B6. Each paper has a pair of points. Students are told to: 1. Write the equation in y =mx+b form
2. Graph the equation
3. Decode the message as follows: "M" number of A1 is first letter of message. "B" number is second letter of message, etc. Use the y axis to convert #'s to letters.

Use these pairs of points as possible values:
 A1 (0, 2)(3. 5) B1 (-1, 3)(0, 18) A2 (-1, -16)(0, 3) B2 (1, 13)(-1, 5) A3 (-2, 1)(-3, -8) B3 (0, 1)(1, 15) A4 (0, 1)(1, 20) B4 (-1, -15)(0, 5) A5 (-1, 10)(0, 19) B5 (-1, 10)(-2, 1) A6 (1, 24)(0, 0) B6 (1, 25)(0, 0)

Secret messages decode as follows:
A: "Abscissa is x"
B: "Ordinate is y"