#sage users do not need this line
import sage.all as sg

#sage users do not need the sg prefix
p = sg.random_prime(100,lbound=15)
q = sg.random_prime(100,lbound=15)
[p,q]                 #secret...sh!

n = p*q               #making the modulus n
n                     #public -- anyone can know this!

phi_n = sg.euler_phi(n)
phi_n                 #secret!

my_public_exponent = sg.randint(10,phi_n) 
while sg.gcd(my_public_exponent,phi_n) != 1:
    my_public_exponent = sg.randint(10,phi_n-1)
my_public_exponent         #public (duh)

my_private_exponent = sg.inverse_mod(my_public_exponent,phi_n)
my_private_exponent        #secret!

message = sg.randint(0,n-1)  #the message can be anything
message     #secret

ciphertext = sg.power_mod(message,my_public_exponent,n)    
ciphertext            #public

decoded_ciphertext = sg.power_mod(ciphertext,my_private_exponent,n)
decoded_ciphertext