.

1. How to Encrypt a
Message with RSA

2. Generate a Key

3. Choose 2 Prime Numbers p and q
ex. p=5, q=11

4. Multiply p and q together to get n
ex. n= p*q = 5*11 = 55

5. Multiply (p-1) and (q-1) together to get φ
ex. φ = (5-1)*(11-1) = 40

6. Choose a non-prime number K so that
the remainder of K divided by φ is 1
ex. Choose K = 161

7. Factor K into two numbers e and d such
that no number divides both e and n and
d and n evenly
ex. Choose d=23 and e=7

8. Encrypt a Message

9. Change message into numerical values
ex. Let message be “ababa”
and a=1, b=2, c=3,..., z=26
so that “apple” corresponds to 1 2 1 2 1

10. Raise each number to the e power
ex. 1 2 1 2 1 becomes 1 128 1 128 1

11. Divide each number by n and find the
remainder
ex. 1 128 1 128 1 becomes 1 18 1 18 1

12. Decrypting the message

13. Raise each value of message to d power
ex. 1 128 1 128 1 becomes 1 128^23 1
128^23 1

14. Divide by n and find remainder
ex. 1 128^23 1 128^23 1 becomes 1 2 1 2 1

15. Convert back to Letters
ex. 1 2 1 2 1 becomes “ababa”