1. History and Background Part 3: Polyalphabetic Ciphers
CSCI 5857: Encoding and Encryption

2. Outline
The Vigenére polyalpabetic cipher
Enigma
One-time pads

3. Polyalphabetic Substitution
Single plaintext character may map to multiple possible ciphertext characters
Character mapped to depends on position in plaintext
Ci = f(pi, i)
Frequency analysis attacks much harder

4. Vigenére cipher Key = some word or phrase of length n
ci = (pi + ki mod n) mod 26
Example:
Key: “python”
Plaintext: “rabbitwithbigpointyteeth”

5. Vigenére Cipher Example
Create table with plaintext in one row, key in next row
If size of key < plaintext, repeat as necessary
“Add” values in corresponding column to get ciphertext
r+p = = 6 = G
a+y = 0+24 = 24 = Y
b+t = 1+19 = 20 = U
b+h = 1+7 = 8 = I (note difference!)

6. Frequency Analysis
Vigenére cipher still vulnerable to frequency-based cryptanalysis
Guess key size n
Treat like n different monoalphabetic substitutions
General principle: Larger n  more secure
(that is, number of characters before repetition)

7. Enigma Developed by Germany in WW2
Arguably most complex pre-computer substitution cipher
Flash simulation at

8. Enigma Structure Consists of 3 to 5 rotors
Each rotor is a monoalphabetic mapping of a plaintext character to a ciphertext character
Output of one rotor fed into input of next rotor so final output the result of 3 to 5 monoalphabetic substitutions
Rotors turn after each character!
Fast rotor: every character
Middle rotor: every 26 characters
Slow rotor: every 26 x 26 = 676 characters

9. Enigma Diagram

10. Enigma Analysis
26 x 26 x 26 = 17,576 characters entered before repetition
Essentially invulnerable to frequency-based cryptanalysis (particularly if rotors changed at regular intervals)
Required Alan Turing’s Bletchley Group to crack
Captured machines to understand patterns
Large numbers of known plaintexts
Exhaustive searches using primitive computers

11. One-Time Pad
Idea: Make key as long as the message itself! (Joseph Mauborgne)
Unconditionally secure since inherently ambiguous for attacker
Only example of an unconditionally secure encryption algorithm

12. One-Time Pad Example
Example ciphertext: NZAKBMK
Ciphertext: NZAKBMK NZAKBMK
Possible keys: nlvwker wtnkxmm
Plaintext: goforit runaway
Which key is correct? We have no way of knowing since both are plausible plaintext!

13. One-Time Pad Weakness Only get to use a key for one message
Unlikely that different possible keys would still both result in plausible plaintext for more than one message
Adversary could find correct key by process of elimination
Ciphertext: WMGKZX WMGKZX
Possible keys: nlvwke wtnkxm
Plaintext: jblopt attack
Would need to securely distribute a new key for each message!
“This is the one!”

14. What’s Next Let me know if you have any questions
Continue on to the next lecture on transposition ciphers