public key cryptography (RSA)

Public key - available to everyone.  K+
Private key - secret  K-

Message: a
Encrypt: K+(a)
Decrypt: K-(K+(a)) = a

Can't use K+ to decrypt the message.

Public Key: n=11 and r=15
Private Key: m=3

Encode: a = 7

Calculate: a^n mod r
           7^11 mod 15 = 13
           
Decode: c = 13

Calculate: c^m mod r
          13^3 mod 15 = 7
          
          
Find the private key!

 r = p * q  (where p and q are prime)
  for r = 15 so p=5, q=3 

    (for big numbers, this takes a long time!)
    
 m*n = k*(p-1)*(q-1) + 1
 m*n = k*4*2 + 1 = 8k + 1
 
 m = (8k + 1)/11 (m must be an integer)
 
 k    (8k+1)/11
 1    9/11
 2    17/11
 3    25/11
 4    33/11 = 3 (private key)
 
 
Session keys
Use RSA to exchange a secret key 
Use the secret key to send messages.
Rebuild secret key

Signatures
  sign a document with my private key
  you decode with my public key


RSA Homework (Due Friday 5/3)

public key n=47, r=989

- decode one group of 3 digits at a time.
- Use the RSA calculator
- Show steps for underlined number
- Don't put leading zero in RSA calculator
- If you get a 2 digit number out, put a zero
  on the left to make it three digits
- Take numbers in pairs and turn them to characters.

e.g. 727 172
-> 72 71 72
-> H  G  H