Secure Communication

Definition:A cryptosystem is a five-tuple (P,C,K,D,E) where the following conditions are satisfied:

  1. P is a finite set of possible plaintexts:
     
  2. C is a finite set of possible ciphertexts:
     
  3. K the keyspace, is the a finite set of possible keys:
     
  4. For each k∈K there is and encryption rule ek and a corresponding decryption rule dk.
    Where ek:P → E and dk:E → P.
    And dk•ek and ek•dk are the identity maps P → P and E → E.

Caesar cipher- Shift k letters.
P and C are both the english alphabet. ek is shift k letters and dk is shift back k.
The problem: There are really only 25 possible Caesar cyphers.
 
Alternative: Use permutations rather than shifts.There are
26! = 403291461126605635584000000 permutations.
 

A Useful calculator.

The Tests

  1. If I know P and C and the algorithms e and d but not k, and I also have captured encrypted messages, can I compute k and hence ek and dk?
     
  2. If I know P and C and e and d but not k, and I also somehow have access to ek so I can encrypt test messages. But, I do not have access to k itself. Can I compute k and hence dk?

Secret Key Exchange

To maintain two-way private communication between individuals, assuming both individuals know the plaintext and cybertext, they just have to share a secret key. For the Caesar cipher, simply know the shift number.
An assumption is that observers can see the encrypted conversation, maybe even understand the encryption algorithm, but cannot somehow create "experiments" with the secret key.

The Advanced Encryption Standard (AES)

AES is a symmetric 128-bit block data encryption technology adopted by the U.S government as a standard in 2000.