Description
1 Overview
How are messages transferred in a secure way? How is your browser sure that it
is talking to the website it should be instead of an imposter? How can we carry
key-chains that tell us a password that changes every five seconds? The answer
to all of these questions is asymmetrical encryption. Asymmetric encryption allows us to take a message and turn it into gibberish using a digital key, and turn
it back into the original message using a different key.
We can give out a public
key to the world, and let them encrypt messages that can only be decrypted
using our private key. The public and private keys are mathematically related,
but it is computationally intractable to compute a private key from only the
public key.
Today we will be implementing one such asymmetrical encryption algorithm
known as RSA, named for its inventors Ron Rivest, Adi Shamir and Leonard
Adleman. RSA uses randomly generated prime numbers to generate a key pair,
and then uses exponentiation and modulation to encrypt and decrypt messages
using this key. RSA, while being surplanted by the more sophisticated SHA
family of algorithms, is still commonly used for digital security. The mathematics proving RSA to be secure are beyond the scope of this course. The
implementation of RSA, however, is of a reasonable level of complexity to be
implemented in the our lab, given the tools provided by Java’s class library.
2 Learning Outcomes
By the end of this project students should be able to:
• write algorithms based on a technical problem description;
• utilzie Java types.
• utlize Java’s BigInteger to perform high level computation;
• utilize asymmetric encryption to encrypt and decrypt messages;
• work effectively with a partner using pair-programming;
• write an effective report that describes the students’ problem solving process.
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3 Pre-Lab Instructions 2
3 Pre-Lab Instructions
Do this part and turn in your answer on BBLearn before you come
to lab:
This project will require you to use binary input and output streams, and
understand how to perform RSA encryption
• Read the Wikipedia article on the RSA algorithm: https://en.wikipedia.org/wiki/RSA_(cryptosystem)
• Walk through the process of applying key generation, encryption, and
decryption, where p = 20 and q = 17. Let 60 be the value you encrypt
and decrypt. List all of the intermediate variables you get along the way.
Include this process in your prelab BBLearn submission
– The following address can be used for computing the modular multiplicative inverse: http://planetcalc.com/3311/
– The following address can be used for computing the modular exponentiation: https://www.mtholyoke.edu/courses/quenell/s2003/ma139/js/powermod.html
• Read the documentation for Java’s BigInteger class. List the methods
that would be necessary to perform the calculations you did while walking
through the RSA algorithm.
– Also, how might your randomly generate prime numbers?
4 Lab Instructions
Do this part in lab:
Create a class with a main method for our RSA implemenation. Our program
will have three parts
1. Generating the public and private keys
2. Encrypting a number using the public key
3. Decrypting the number using the private key
Step 1
Use Java’s BigInteger data type to perform the same process shown in the
RSA example in steps 1 to 5. For each of the values computed, print those
labeled values to the screen. First uses the example values for p and q to ensure
your compuation is running correctly.
Once you are sure your code is working
properly, comment out the section where you set p and q and add lines to use
randomly generated prime numbers instead.You should be able to easily switch
back and forth between using the test numbers and randomly generated the
numbers by switching which line is commented. Each of these random prime
numbres should have a bitlength of 256.
5 Lab Report 3
Step 2
Print a labeled starting value to the screen. Now, go through the encryption
process. Remember that in order to do this, we will need the public key (the n
and e values.) When using the example values, the number 65 should encrypt
to 2790 durring this step. Once you have completed the encryption, print the
labeled value to the screen.
Step 3
Now perform the decryption process on your encrypted value. Remember that
in order to do this, we will need the private key (the n and d values.) In the
example values, this would decrypt 2790 back to 65. When using the randomly
generated keys, this should give you back the original value from step 2.
When this is complete you will have a simple but legitimate RSA implementation. Congratulations!
(n: 258242885512679503443813423030978068947, d: 227861369570011326539689092927973443353)
https://sites.google.com/a/nau.edu/249751615939781461903757255894139183723/
5 Lab Report
Each pair of students will write a single lab report together and each
student will turn in that same lab report on BBLearn. Submissions
from each student on a pair should be identical. In order to recieve
points, you MUST make a BBLearn submission.
Your lab report should begin with a preamble that contains:
• The lab assignment number and all partner names
• Your name(s)
• The date
• The lab section
It should then be followed by four numbered sections:
1. Problem Statement
In this section you should describe the problem in your own words. The problem
statement should answer questions like:
• What are the important features of the problem?
• What are the problem requirements?
5 Lab Report 4
This section should also include a reasonably complete list of requirements in
the assignment. Following your description of the problem, include a bulleted
list of specific features to implement.
If there are any specific funtions, classes or
numeric requirements given to you, they should be represented in this bulleted
list. It is recomended that you complete this section before you begin coding the
problem, as gathering these requirements may help you organize your thoughts
before you begin your soulation.
2. Planning
In the second section you should describe what planning you did in order to solve
the problem. You should include planning artifacts like sketches, diagrams, or
pseudocode you may have used. You should also describe your planning process.
List the specific data structures or techniques you plan on using, and why. How
do you plan on breaking up the problems into functions, classes and methods?
3. Implementation and Testing
In the third section you should demonstrate your implementation. As directed
by the lab instructor you should (as appropriate) include:
• a copy of your source code (Submitted in BBLearn as .java files, should
not be in your report document)
• a screen shot of your running application / solution. This should include
a screenshot of the output, be it a terminal window or graphical interface
• results from testing. This is specific to the lab, and not every lab will
include this element.
4. Reflection
In the last section you should reflect on the project. What part of the projec
was the most difficult? Where there other solutions to this problem that you
considered? Where there any new solutions you can think of now that you
couldn’t then? Do you think the way you chose was the best option, or would
you go about the problem differently if you had to start over? How might the
problem had been broken up into easier problems? If you had one more day
to work this problem, what improvements might you make? Every problem
has alternative solutions and solution has tradeoffs or improvements, you are
required to identify some of these elements.
5. Partner Rating
Every assignment you are required to rate your partner with a rating between 1
and 10. For each patener a name and rating should be submitted in the comment
section of the BBLearn submission, and not in the report document. You do
not have to tell your partner the rating you assign them. A rating 8 or more
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indicates that your partner was particularly helpful or contributed exceptional
effort. A rating of 5 indcates that your partner met the class expectations of
them. Rating your partner 3 or less means that they refused contribute to
the project, failed to put in a resonable effort or actively blocked you from
participating.
In the case where you give a very low rating, please explain why
in the comment section of the submission. Those who recieve low scores may
be asked to explain their actions to the lab staff, and additional low ratings
after a warning could lead to losing a letter grade, or even failing the course.
Consistant high ratings from partners are noted durring the grading process,
and may be taken into account when rounding your final grade.
Colophon
This project was developed by Richard Lester and Dr. James Dean Palmer of
Northern Arizona University. Except as otherwise noted, the content of this
document is licensed under the Creative Commons Attribution-ShareAlike 4.0
International License.
