2 RSA encryption For the following questions, we are using the RSA cryptosystem.

Question

2 RSA encryption For the following questions, we are using the RSA cryptosystem. For each of the questions below, write down the operation you need to perform in addition to the answer that you get. Wolfram Alpha is suitable for all the calculations you will need to do. a. Given the primes p 2027 and 2593, and using e-7 i. Generate the corresponding public RSA key. 1 mark. ii. Generate the corresponding private RSA key. 1 mark b. Using the public key above, encrypt the message 1024. 1 mark. c. Using the private key above, decrypt the message 3054908. 1 mark. d. You are given the public key (n -7354943,e7). Determine the private key by first factoring the public key. Wolfram Alpha is able to perform the necessary factorisation. 1 mark.

Explanation / Answer

Hi,
Given p=2027, q=2593 and e=7,
a. The public key in RSA cryptosystem is given by (n,e) where n=p*q=2027*2593=5256011
The private key in RSA cryptosystem is selected as

d*e % z = 1 and d<z, where z=(p-1)*(q-1)=2026*2592=5251392
i,e d*7%5251392 =1
therefore d= 7-1(5251392)=750199
hence the private key becomes (n,d)=(5256011,750199)

b.Now, to encrypt a message,

c.Now to decrypt a message,

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