Select two distinct primes

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Select two distinct primes. Call them p q.   

Let n = p*q

print n, p and q

Select an integer e in the range 1 < e < n such that gcd (e, (p-1)(q-1) ) = 1.

This means that e and (p-1)*(q-1) do not share a common factor. Recall that 35(==7*5) and 6(==2*3) are relatively prime even though neither is prime

 

The public key is the pair (e,n)   Compute d in the range 1 < d < n  such that d*e = 1 mod ( ( p-1)*(q-1) )

This statement can be computed as follows:

Find a d such that

e*d -1 == k(p-1)*(q-1) è d = [k(p-1)*(q-1) +1] /e for k = 1, 2 3 4 5 etc. 

(use a while loop for k = 1, 2, 3,  4 until [k(p-1)*(q-1) +1] /e does NOT result in a decimal value for d this is your d )

The private key is the pair (d,n) This should be kept secret!

print d

  Ask the user for an integer in the dictionary below

See the message values below but the user input should be an integer in the range 70 - 82

print m

 Encode the message m by using the public key as follows:

c = m^e mod n  See Khan video for assistance

             print c  as follows: print("the encoded text is ",c) 

 Decode: We decrypt message c to obtain the orginal message m using the private key d

 m = c^d mod n  

print (key, m) (should be the key and the original message )

for example if the user enters the integer 77 in step 5 then you should print out 77 and the text 'Enjoy your morning beverage' 

Use the messages dictionary available

# dictionary

d = {  70:'What is up?',

       71:'You are fast!',

       72:'All your trinkets belong to us.',

       73:'Someone on our team thinks someone on your team are in the same class.',

       74:'You are the weakest link.',

       75:'Encryption is fun;',

       76:'Spring is my favorite season',

       77:'Enjoy your morning beverage',

       78:'I am an early riser',

       79:'I am not an early riser',

       80:'Wake Tech is my school',

       81:'CSC 120 Computing Fundamentals',

       82:'Best wishes to you'

    }  # end of dictionary

print('Here is your original dictionary', d)