Spike Clancy (hclancy@dimacs.rutgers.edu)

**General Information**

This lesson uses a TI-83 calculator to help understand RSA. Although RSA starts with two large primes this lesson will start with two small primes p & q. The product (p-1)(q-1) will be labeled in and then two numbers congruent to 1 mod m will be used. One will be called s and the other t. The product of p & q will be called n and be made public along with s.

**Category**

The lesson can be used in any math class.

**Grade Levels**

Grades 7-12

**Materials**

TI-83 calculators

TI-83 view screen

**Procedures**

On the TI-83:
1. Use the <sto->> key and 1->A : 2 ->B : 3->C : ... : 26->Z

2. Choose

p=5

q=7

n=35

m=24

s=5

t=5

3. Use <and> {Type message using commas and close}

ex) {M, E, S, S, A, G, E}

4. <Enter> and on the screen appears:
{13, 5, 19, 19, 1, 7, 5}

5. Store to List 1; <sto->> <and> L1

6. To encode use <math> num round(

7. Hit (<math> num FPart(
8. You want the screen to read:

Round ((FPart (CL1^5/35))*35),2)

9. Hit enter and screen shows the encoded message:

{13, 10, 24, 24, 1, 7, 10}

10. Store the encoded message in List 2:

<sto->> L2

11. To send the message to another TI-83, use <and> Link List and send L2.

12. Link the second TI-83 to receive List 2.

To decode on second TI-83:

13. Enter

Round ((FPart ((l2^5/35)*35),2)

14. Hit Enter and read:

{13 5 19 19 1 7 5}

**References**

__Loads of Codes__, Comap