BIT112 - RSA Public Key Cryptography System Works, Technical Report Writing, Wolfram Alpha & RSA Encryption System - IT Assignment Help

Assignment Task

Assignment Part 
This assignment concerns exploring how the RSA Public Key Cryptography system works. For Part 3 you must write up a Technical Report on all your work.

(1)Making your second RSA encryption system:
(i)Using Wolfram Alpha determines how many bits your student number can be represented with.
(ii)Study how the RSA Public Key Cryptography works. You may need to look up what prime numbers, relatively prime numbers, and totient functions mean.
(iii)From your exploration in (ii), use the Wolfram Alpha “next prime” function to find the next two prime numbers after your student number which are of the form 4x+3.  Such that P3=4x 3+3 and P4=4x 4+3.
(iv)Using Wolfram Alpha determines how many bits P3 and P4 can each be represented with. Check that they have the same number of binary bits.
(v)How many prime numbers are there with this many bits?
(vi)Compute the product N’ of P3 and P4 and next compute the totient of N’ which is φ(N’).
(vii)Decide upon an encryption key a' which is a natural number between 1 and φ-1 and which has to be relatively prime with φ. A simple way to decide one is to choose a small prime number such as e = 17.
(viii)The final step to make your RSA encryption system is to find d’, the private or decryption key. To obtain d’, type this into Wolfram Alpha ‘Solve (17*d) mod φ = 1 using the appropriate totient value φ.
(ix)Now encrypt your student number using the decryption key d’ and give it and e’ and N’ to a fellow student to decrypt with e’. Never release your decryption key d’. Did he get your student number?

(2)Exchange your second RSA encryption system with another student. Try to break your friend’s second encryption system by both methods of Euler Factorization and Weiner attack.

(3)Final Technical Report: 

Your final report is a professional representation of Assignment parts 1 and 2, drawing on the online literature (including journals) where relevant and properly referencing all of them. You should also look at the links between parts 1 and 2 and explore the structures of primes with particular attention to why primes of the type 4x+1 are weaker than primes of type 4x+3. You must write this part in the proper Technical Report (TR) format which is explained in another document available to you on Moodle. Your TR will be marked on how well you have kept to the TR format and how much understanding of the issues involved in RSA encryption you show in the TR.In particular, your report should answer these questions:
•Why is the bit-size of N important?
•Why should the prime factors of N be of equal bit-size?
•Why should d be kept secret?
•If your Weiner attack failed try it again on the encryption system where e and d are swapped. Why does it work better after swapping?
•Why is it harder to crack when the factors of N are of type 4x+3 rather than 4x+1?

Note that the following points are frequent reasons for students.
•Not following the professional TR report format given to students.
•Uses Wolfram screenshots in the TR when told not to.
•Screen shots do not replace verbal explanations.
•Does not have parts 1 & 2 as appendices.
•Does not evaluate the strength of the encryption system.
•Your report is unstructured.
•Your report has lines of calculations instead of written explanations.
•Needs your verbal descriptions, explanations, and analysis to show us that you understand what you were doing.
•Your writing is too small for reading.
•Blank page found in TR.
•No Discussion section to discuss vulnerabilities, analyze and report on how strong your encryption system is.
•Needs to discuss vulnerabilities, analyze and report on how strong your encryption system is.
•Conclusion expressions hard to make sense of.
•Conclusion section is too short or is absent.
•No Conclusions section.
•Inadequate Conclusions section.
•Possible plagiarism because of the lack of a References section.
•Plagiarism may result from a lack of a References section.
•No citations of your references in the text of the TR.
•Reference section not in a standard format.
•You are repeating Parts 1 & 2 rather than giving a professional report on it.
•Double-dipping repeat of parts 1 & 2.
•Photos appended with wrong orientation and shrunk.
•TR is too short – not enough proper written explanations.
 

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