Public Key Cryptography Works - IT Computer Science Assignment Help

Assignment Task :

Task: Explore how Public Key Cryptography works.
Using your Student ID, generate two primes and encrypt your student ID with your own Private Key. Send this to a recipient with a Public Key and recover your original Student ID.
Use the Wiener attack to break your private key and is this way steal your identity by using your private key to encode another number and masquerade as you.
(1) Making your own Keys:
(i) Explore how Public Key Cryptography works and summarise this in your own words with particular attention to how the method generates these keys.
(ii) From your exploration above, generate Private and Public Keys using an example.
(iii) Using your student ID, determine how bits the number part can be represented with.
(iv) For a particular number of binary bits determine the number of prime numbers available in that bit range.
(v) (a)  Using the Wolframalpha “nextprime” function and your student ID create two prime numbers which are of the form 4x+1.  Such that P1=4x 1+1 and P2=4x 2+1. 
(b)  Check that they have the same number of binary bits.
(vi) (a)  Using the Wolframalpha “nextprime” function and your student ID create two prime numbers which are of the form 4x+3.  Such that P3=4x 3+3 and P4=4x 4+3. 
(b)  Check that they have the same number of binary bits.
(vii) (a)  Use P1 and P2 to generate your public keys and encrypt your student ID.
(b) Use P3 and P4 to generate your public keys and encrypt your student ID. 
(viii)    Create a private key and use this to decrypt and recover your student ID.

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