# Using the TI-83 to Understand RSA

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.

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 [itex] num round(
7. Hit ([itex] 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.
To decode on second TI-83:
13. Enter
Round ((FPart ((l2^5/35)*35),2)
{13 5 19 19 1 7 5}

References