Stimulating Understanding of Computational science through Collaboration, Exploration, Experiment, and Discovery for students with Hearing Impairments
a collaboration of the Shodor Education Foundation, Inc., Eastern North Carolina School for the Deaf, Barton College, the National Technical Institute for the Deaf, and Interpreters, Inc.

For Teachers!

RSA Cryptology 

Terminology: 

Acceptable terms for this module are encrypt, encipher, decrypt, decipher, and cipher. The terms encode, decode, and code are not correct terminology for this module. A code has an arbitrary assignment for each letter or word. A cipher uses a repeatable process, often mathematical, to change the letters. 

Note to the Signer: Just a quick note to those of you who are signing. Some of these words may not have signs assigned to them. However, please be careful about choosing signs to represent these words. For example, please refrain from signing the kind of key used to unlock a door for "key," as this is not the type of key we are referring to. Feel free to consult our technical sign dictionary online for possible signs. 

About N: 

N is the product of P and Q. Students are asked to calculate this value. In Encryption and Decryption they are asked to input N. For the activity, N must be used. However, the program will accept the input P * Q or an input of N. 

Limits on Primes:

Unfortunately, the computer can only do the calculations so fast. I have therefore included a limit on how large the two primes that the students choose can be. The limit has been set such that P * Q must be less than 200,000. The older the computers you are using, the longer it will take to calculate numbers. If you are using old models you may want to try some numbers out on your own and decrease the maximum number. Another limit on the primes is that P * Q must be greater than 925. 925 is the maximum number the computer will encounter when encrypting and therefore the mod must be greater than 925. 

Possible Errors:

In Choosing Variables: The two primes must be of equal length, positive, not equal to one, and meet the prime limit conditions above. Error Alerts will occur for breaking any of these conditions. 

In Encryption: There must be values for N, E, and Message or an error will prompt for this information to be input. The message may not contain numbers or letters. If it does the program will give an error. If a student wants to send a number, they must spell it out(1 becomes one), or their cipher will not properly decrypt. 

In Decryption: Many possible errors can occur in decryption. Values must be input for N, D, and Cipher or else an error will occur that prompts for this information. All other errors will be represented by the same alert: "There is a problem deciphering your cipher. Please check your cipher." This can be caused by a number of things. The D value used must be the one corresponding to the E value that was used to encrypt the message. The cipher can not have extra spaces. If there is more than one space between number blocks, an error will occur. If the cipher is typed incorrectly an error may occur as well. 

Other Notes: There are troubleshooting guides in the help section for each activity. The help section is available by clicking on the "Help" button. If any errors occur that you cannot resolve please contact the SUCCEED-HI team so that we may modify the program as needed. 

Help! Common problems using the calculators:

Selecting variables:

I cannot find a value for E that gives a GCD of 1
Try using a prime number. 

It is taking my computer too long to find D.
Your computer may be taking too long because the numbers are too large for it. Try smaller primes or a smaller E. 

Encrypting:

I get NaN for my cipher.
Make sure the values you put in for N and E are numbers. 

The computer will not encipher my message.
Make sure that there are no spaces in front of your message. This might be causing the problem. 

Decrypting:

My message does not make sense!
Make sure that the D value you are using is the one that matches the E value you used. 

An error keeps coming up that says, "There is a problem deciphering your cipher. Please check your cipher."
Make sure that you typed your cipher in correctly. Make sure that there is only one blank space between each number set. Make sure that there are spaces between number sets. Make sure there are no punctuation or letters in your cipher. 

Practice Answers:

1) Cryptography is safe because it uses very large prime numbers to encrypt information. 

2) N and E are made public. 

3) A key is a number that is used to encrypt or decrypt information. 

4) E and (P-1)(Q-1) have a GCD of 5 and not of 1. 

5) Answers will vary depending on the student's name. A is 01, B is 02, and so on until Z is 00. 

6) 6927 2204 5195 4019 421 6243 7852 618 3382 7238 7676 5880 6202 1138 7575 4006 3134 2998 

7) You made an A on the test. 

8) Answers will vary. They should match the page "What the Computer Does." 

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The Shodor Education Foundation, Inc.

Copyright © 1999-2001 by The Shodor Education Foundation, Inc.

This project is supported, in part, by the National Science Foundation Opinions expressed are those of the authors and not necessarily those of the National Science Foundation.