1. History and Background Part 4: Transposition Ciphers
CSCI 5857: Encoding and Encryption

2. Outline Transposition ciphers Attacks on transposition ciphers
Effectiveness of using multiple keys
Avalanche effect as a goal of encryption

3. Transposition Cipher Ciphertext = Permutation of plaintext
Permutation = integers from 1 to n rearranged
n = number of characters in block of text
Example: A permutation of size 7 might be
That permutation is the transposition key K

4. Transposition Algorithm
Assign each plaintext character a number based on position
Move each plaintext character into ciphertext position given by permutation
Mathematically ci = pK[i]
Simple example: Plaintext: runaway Permutation: Ciphertext: rnwyuaa

5. 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)

6. Column Transposition Example
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 second, and so on
This column first

7. Column Transposition 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

8. 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

9. Multiple 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

10. 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)?

11. Multiple Keys Examples
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!

12. Multiple Key Effectiveness
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)
Possible ciphertexts
After applying K1 and K2
After applying K1

13. 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)

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

15. 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

16. What’s Next Let me know if you have any questions
Begin work on Assignment 1: History and Background