The way the RSA scheme works using software such as Maple.

- Sassie
Sallyfinds 2 large prime numbers from a list of primes on the web:

p= 20940089q= 20940253- She gets
n:n= 20940089*20940253 = 438490761502517.

- She gets f(
n) = (20940089-1)*(20940253-1) = 438490719622176.

- She picks a random odd number beneath f(
n) and checks if it is coprime with f(n) ; if not she tries another one. Chances are she will get one within three tries. She checks the number 43849087.

gcd(43849087, 438490719622176) = 1. It works so she lets

e= 43849087.

- She solves for 43849087
d= 1 (mod 438490719622176) :

With Maple : msolve(43849087*d= 1, 438490719622176).Maple gives

d= 45051024550015.

- Sassie
Sallyposts the publlic key (e, n) = (43849087, 438490761502517)

- Sillie Sender
Suelooks up SassieSally's public key since she wants to send her the message BOOK = 2151511.

Encryption : Sillie SenderSuesolves forCin 2151511=^{e}C(modn)2151511

^{43849087}=C(mod 438490761502517 )With Maple : msolve(2151511&^43849087 =

C, 438490761502517);Maple gives

C= 371350643872343.Sillie Sender

Suesends the encrypted message 371350643872343.Saddam Hussein eavesdrops but is totally confused and mystified by this encrypted message since this number

n =438490761502517 is two big for him get the factorspandqby only using his little Zellers Casio calculator.

- Sassie
Sallyreceives 37135064387234. She says "Hmmmm, what's this?"

She decrypts with 371350643872343

=^{d}R(mod 438490761502517).With Maple : msolve(371350643872343&^45051024550015 =

R, 438490761502517);Maple gives

R= 2151511.Sassie Sally transfers from digits to letters and reads the message. She says : "Oh, it's the word BOOK!"

Note: The number n still too small for Silly Sender's message to be safe, since Maple easily finds its two prime factors.The number n has to be several thousand digits long for it to be safe.