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PC Technician explains RSA encryption

Example of RSA encryption and decryption

1. choose two distinct prime numbers ( we will use
    small numbers - to keep it simple - the actual 
    RSA algorithm would use far bigger numbers)
    p = 13 and q = 19

2. Compute  n = pq
     so n = 13 * 19   = 247

3. compute  φ(n) = (p-1)(q-1)   which is
        φ(247) = (13-1)(19-1)  = 216

4. Now we have to pick a number  e   such that
           1 < e <  216 and is coprime to 216

    by choosing a prime number for e we only have to make 
    sure that it is not a divisor of 216

        let  e = 11

5. Compute d, the modular multiplicative  inverse of  1/e(mod (φ(n))
    which is:
        d = 59

Getting the modular inverse is not a trivial problem - so I used  a Math Cad 
program called "scientific notebook"  and here is the calculation:

          (1/11)mod216= 59

Thus, we have :

public key is (n=247, e=11)  and the private key is (n=247, d=59)

Let's look at our message   "ATTACK"
The letter "A" is represented by decimal 65 so let's encrypt "A"
 by using the public key. The private key is held by the recipient 
 let's call her Mary. So Bill  who wants to send Mary a message
 uses her public key and encrypts  the  message - then Mary 
 would use her private key to decrypt it. 

    ie,   c = me ( mod n)     : where m is the decimal value of  "A".
                                                   (the first letter of  Bill's message)
       c = 6511 ( mod 247)  =  221   so Bill's message would start off with
 221 ..............( +    other encrypted letters ) .....

Mary wants  to decrypt  the message:  ie,  calculate   
m = cd (mod 247)  : where c is the first letter
                                       of the message.
         m = 22159 ( mod 247)  =  65    which is the decimal equivalent of "A"

 Mary's decrypted message is : 

        "A"  ...... +   the other letters ......   OR  "ATTACK"

You can use the microsoft calculator ( in scientific  mode ) to 
do the other letters  and have your friends try to break the coded message.
Remember it is not a simple key as explained on the pc technician home
page where Encryption basics are explained.

Now that you have mastered the public key encryption algorithm, let's look at what has been described as the "the world's most mysterious manuscript". This early 15th century book is a cryptologist's nightmare, ie, it contains text written in some kind of ciphertext that todate has been unbreakable.
It is called the Voynich Manuscript and has defied all attempts to be deciphered. You can read all about it below:

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