1. CSCI 5857: Encoding and Encryption
History and Background Part 2: Polyalphabetic Substitution and Transposition
CSCI 5857: Encoding and Encryption

2. Outline The Vigenére polyalpabetic cipher Enigma One-time pads
Transposition ciphers
Attacks on transposition ciphers
Effectiveness of using multiple keys
Avalanche effect as a goal of encryption
Kerckhoff’s Principle

3. Polyalphabetic Substitution
Single plaintext character may map to multiple possible ciphertext characters
Frequency analysis attacks much harder
Example: Vigenére cipher
Key = some word or phrase of length n
ci = (pi + ki mod n) mod 26

4. Vigenére cipher

5. Vigenére cipher Example: Key: “python”
Plaintext: “rabbitwithbigpointyteeth”
Ciphertext: r a b i t w h g p o n y e p y t h o n G Y U I V L M N H P B R

6. Polyalphabetic Substitution
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 Consists of 3 to 5 rotors Rotors turn after each character!
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

10. Enigma 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

12. One-Time Pad
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 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. Transposition Cipher Ciphertext = Permutation of plaintext
Simple example: runaway  r n w y u a a
 rnwyuaa
Key = permutation order
Above example:

15. Column Transposition Ciphers
Break plaintext into columns
Example plaintext: longlongagoinagalaxyfaraway Key: (size n of key = 7 columns)
longlon gagoina galaxyf arawayx
Break plaintext into rows of size n of key
Insert extra chars to fill columns (padding)

16. Column Transposition Ciphers
l o n g l o n g a g o i n a g a l a x y f a r a w a y x
For column with label i:
Append contents of column i to ciphertext
Resulting ciphertext: goaw oaar nafx ngla lgga onyy lixa
This column first
This column second, and so on

17. Column Transposition Ciphers
Decryption:
Divide ciphertext into n strings
Arrange strings into columns, with order of columns determined by key
goawoaarnafxnglalggaonyylixa
l o n g l o n g a g o i n a g a l a x y f a r a w a y x

18. Attacks on Transposition Ciphers
Brute force: Trying all possible permutations
Key of size n  n! possible keys
Solution: Choose key such that n! tests is computationally secure
Cryptographic attacks:
Eliminate column pairs with unlikely adjacent letters
l i x a
n a f x

19. Attacks on Transposition Ciphers
Can apply transposition multiple times with same key to defeat cryptographic attacks
Ciphertext after first permutation: goawoaarnafxngla lggaonyylixa
Ciphertext after second permutation: wfglonayagoaaaly grnlanaxoxgi
g o a w o a a
r n a f x n g
l a l g g a o
n y y l i x a

20. Using Multiple Keys Is this more secure than C = E(p, k1)?
Important question: Does using multiple keys always make encryption more secure?
Brute force attacks
Cryptographic attacks
Mathematically: C = E(E(p, k1), k2)
Is this more secure than C = E(p, k1)?

21. Using Multiple Keys Example: Caesar cipher with 2 keys K1 = 3 K2 = 8
Equivalent to single key K3 = 11
Still only 26 possible mappings from P to C
Example: Transposition cipher with 2 keys K1 = K2 =
Equivalent to single key K3 =
Still only 7! possible mappings from P to C
No more secure in either case!

22. Using Multiple Keys Only if:
Using multiple keys greatly increases the number of possible ciphertexts
Applying multiple keys is not equivalent to applying a single key No k3 such that E(E(p, k1), k2) = E(p, k3)
After applying K1 and K2
Possible ciphertexts
Possible ciphertexts
After applying K1

23. Avalanche Effect Small change in key  Large change in ciphertext
Desirable property of cipher Knowing some of key  rest of key still hard to find
Not a property of substitution ciphers
Property of transposition ciphers (particularly if applied multiple times)

24. Avalanche Effect
Example: two similar keys applied twice
plaintext = longlongagoinagalaxyfaraway
k1 = ciphertext = wfglonayagoaaalygrnlanaxoxgi
k2 = ciphertext = wfglaalylaoaonrygaangoaxnxgi
Already different in 14 of 28 characters

25. Substitution and Transposition
Most modern block ciphers combine substitution and transposition
Substitution gives large number of possible keys to defeat brute force attacks
Transposition gives avalanche effect to defeat cryptographic attacks

26. Kerckhoff’s Principle
c = E(p, k)
If can’t hide k, can we hide the encryption algorithm E?
Assumption: Adversary knows algorithm we use
All encryption algorithms currently in use are well known!
Much easier to conceal/change key than entire algorithm