BIT112 - The RSA Public Key Cryptography System Works And Technical report Writing IT/Computer Science Assignment Help

Assignment Task -

Making your first RSA encryption system:

(i) Using Wolfram Alpha determine 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) Add 2020 to your student number. From your exploration in (ii), use the Wolfram Alpha  “nextprime” function to find the next two prime numbers after your changed student  number (student number plus 2020) which are of the form 4 +1, i.e. such that P1=4 1+1  and P2=4 2+1. 

(iv) Using Wolfram Alpha determine how many bits P1 and P2 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 P1 and P2 and next compute the totient of N which is φ(N). (vii) Decide upon and encryption key e which is a natural number between 1 and φ-1 and  which has to be relatively prime with φ. A simple way to decide on e is to choose a smal  prime number such as e = 17 but this doesn’t always work so you may have to select  another prime number for e. 

(viii) The final step to make your RSA encryprion 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 totient  value φ above. 

(ix) Now decrypt your student number using the decryption key d and give it (your  decrypted student number) and e and N to a fellow student to encrypt with e. Never  release your decryption key d. Did he get your student number?

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