'Let p and q be prime numbers and n be their product'
p=233
q=151
is_prime(p)
is_prime(q)
n=p*q
n
(p-1)*(q-1)
l=lcm(p-1,q-1)
l

'Chose a number e that is relativiely prime to (p-1)(q-2)'
e=17
e
gcd(e,l)
'Bob Will Publish (n,e)'
(n,e)

'Find the inverse of e modulo n'
h=xgcd(e,(p-1)*(q-1)) #Run the Extended Euclidean Algorithm to find s and t such that es + nt = 1. Then, the s becomes the inverse of e modulo n
d=h[1]
d #d is the inverse of e
mod(e*d,(p-1)*(q-1)) #Test to ensure e and d are inverses modulo n

'To send a message x to Bob we compute y = x^e mod n and send that to Bob.'
x = 24024;
y=mod(x^e,n)
y

'To decode the message Bob simply computes z = y^d mod n. (We have that (x^e)^d = x^(ed) = x mod n)'
mod(y^d,n)