In this activity, you will generate a pair of RSA keys in Part A and use them for encryption and decryption in Part B. RSA was the first asymmetric cryptographic algorithm, as mentioned earlier in the module notes. In real usage, RSA keys are very long but this example will use small numbers in order to keep the calculations simple.
Use the textbook, course material, and independent research to write a brief paper on the following:
In this part, you will show the calculations to generate an RSA public key and the corresponding private key. The notation is explained in the Powerpoint slides for this module.
Select the following link to review the Asymmetric Key Cryptography presentation.
Asymmetric Key Cryptography [PPTX file size 1.2MB]
(a) Suppose Alice chooses p=5, q=11, and e=3. Show calculations to verify that Alices public key e=3 is valid.
(b) Show the calculations to verify that d=27 is Alices private key.
(c) Browse to the online RSA calculator at:
Popyack, J. L. (1997, October). RSA calculator (https://www.cs.drexel.edu/~jpopyack/IntroCS/HW/RSAWorksheet.html). Drexel University. Retrieved from https://www.cs.drexel.edu/~jpopyack/IntroCS/HW/RSAWorksheet.html
Enter p=5 and q=11, and select “set p,q”.
Enter K=81, and select “factor K”.
Enter e=3 and d=27, and select “check e & d”. The Consistency Check window should display “e*d mod r = 1”, [Formula 5] “e and r are relatively prime”, and “d and r are relatively prime”. This verifies that e=3 and d=27 is a valid RSA key pair.
Take a screenshot and keep the browser window open because the next part will return to this calculator.
(d) Show the calculations for the ciphertext given the plaintext message is m=7.
(e) Show the calculations to verify the ciphertext in part B(d) by decrypting it to the original plaintext.
(f) Return to the online RSA calculator at:
Popyack, J. L. (1997, October). RSA calculator ( https://www.cs.drexel.edu/~jpopyack/IntroCS/HW/RSAWorksheet.html ). Drexel University. Retrieved from https://www.cs.drexel.edu/~jpopyack/IntroCS/HW/RSAWorksheet.html
This will continue the calculation from Part A. Near the bottom of the window, enter Msg=7 and select “encode/decode.” Does the displayed ciphertext agree with your calculation in B(d)?
Answer all questions completely and submit along with required screenshots. If sources are used, follow APA guidelines for writing and citations. Post your work to the dropbox.