RSA Asymmetric Encryption

Question 1

What is the formula and steps for calculating an encryption key in RSA?

Answer 1

1) Choose two prime numbers (p) (q)
2) Calculate n —— n = pq [n = p multiplied by q]
3) Calculate 5n —— 5n = (p-1) (q-1)
4) Choose e (encryption key) (has to be a co-prime to 5n
5) Publish e and n

Question 2

What is the formula and steps for calculating the decryption key in RSA once the encryption key has been established?

Answer 2

1) Calculate d

d = (?x5n+1)/e

Try different numbers starting from 1 for ? until the answer from the equation gives a whole number

2) Keep d secret

Question 3

What is the formula and steps taken for a message to be encrypted with the encryption key before being transmitted?

Answer 3

1) The message (m) if in text needs to be converted to a number e.g. m = 8
2) Convert the message into cipher text with the following formula

c = m (to the power of) e mod n

3) Transmit c to recipient

Question 4

What is the formula and steps taken to decrypt the cipher text (c) that has been received?

Answer 4

1) Decrypt the message c with the following formula

m = c (to the power of) d mod n

If its too big for calculator then work out the answer for
c to the power of 1
c to the power of 2
c to the power of 4
c to the power of 8
c to the power of 16 ….. etc then multiply each of the answers you have used together mod n.

You find out which answers you need by adding up the powers used until it reaches d

Question 5

Briefly explain the process of sending a message using RSA between two people (not including the formulas)

Answer 5

1) Person A wants to send a message to Person B
2) B calculates encryption key (e) and n and publishes them
3) B also calculates the decryption key (d) and keeps this secret so it is only known by them
4) A changes their message (if text) into a number and then turns it into cipher text using e and n that was published by B
5) A transmits c to B
6) B uses his decryption key (d) to turn the cipher text (c) back to the original message (m)