1. CSCI 5857: Encoding and Encryption
Modern Block Ciphers
CSCI 5857: Encoding and Encryption

2. Outline Binary blocks and keys The XOR function
Structure of modern round cipher
Permutation and Substitution boxes

3. Block Ciphers Long plaintext messages broken up into blocks
Encryption substitutes n bit block of ciphertext for n bit block of plaintext
Example: 
Key question: Good block size
8 bits too small: just maps one ASCII character to another (monoalphabetic cipher)
Usually 64, 128, 256, or 512 bits

4. Binary Keys Key: Binary number 32 to 256 bits long
Minimum size now 128 bits to defeat exhaustive search attacks
Amount of information stored by key is limited (128 bit key equivalent to 16 ASCII characters)

5. Substitution and Block Ciphers
Standard binary key insufficient to represent even simple monoalphabetic substitution cipher
Example: Block size 64 bits
264 possible blocks, each of which needs a corresponding ciphertext block listed
Key: 264 x 64 bits long
>> 256 bits for normal binary key
Number of mappings with 256-bit key << all possible mappings of 64 bit blocks

6. Transposition and Binary Text
Transposition ciphers of binary text easy to break
Small alphabet reduces distinguishable permutations
encrypted with 
Example: 64-bit ciphertext block with 8 1’s and 56 0’s
Only (64 x 63 x 62 x 61 x 60 x 59 x 58 x 57)/ (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) = 4,426,165, combinations of 8 1’s and 56 0’s
Easily broken with exhaustive search (each successive block reduces number of possible combinations)

7. Binary Functions
Since both text and key binary, can use binary function to encrypt/decrypt
Example: AND function
Plaintext:
Key:
Ciphertext:

8. Invertible Binary Functions
Problem: Binary function must be invertible
Otherwise, cannot uniquely decrypt message
AND not invertible
Plaintext: ?  could be either 1 or 0
Key: 0
Ciphertext: 0
???

9. Exclusive Or Function (XOR)
Definition:
1 if operands not equal 0 if operands equal
Plaintext P K
C = P  K 1 
Key
Ciphertext

10. XOR is Invertible   XOR is its own inverse: C = P  K  P = C  K 1
encryption
C = P  K K
P must be: 1
Plaintext
Plaintext  
Key
Ciphertext
Ciphertext
decryption

11. XOR and Block Ciphers
Most modern block ciphers use XOR to produce ciphertext from plaintext and key
Simple Example (8 bit key and blocks):
Encryption: Plaintext: Key: Ciphertext:
Decryption: Ciphertext: Key: Plaintext:

12. XOR Alone is Breakable  K = P  C Plaintext Ciphertext Key
Key can be computed from single known plaintext
“This is too easy!”

13. Confusion and Diffusion
Hiding relationship between plaintext and ciphertext
Changing one plaintext bit should change many bits in ciphertext
Confusion:
Hiding relationship between ciphertext and key
Changing one key bit should change many characters in ciphertext

14. Product Cipher
Substitution and permutation can be used to add diffusion and confusion
adds diffusion
Substitution permutation 
Substitution permutation
Plaintext
Ciphertext
Substitution permutation
adds confusion
Key

15. Invertibility  Transformations on plaintext must be invertible
Transformations on key do not
Don’t care if can’t recover key from ciphertext
Must be invertible
Substitution permutation 
Substitution permutation
Plaintext
Ciphertext
Substitution permutation
Does not have to be invertible
Key

16. Rounds in Product Cipher
Most ciphers have many rounds of substitution, permutation, and XOR
Maximizes diffusion
round 1
round 2
round n
subst/perm 
subst/perm 
subst/perm  P … C
key 1
key 2
key n

17. Key Generation
Most ciphers generate separate round keys from main key using substitution/permutation
round 1
round 2
round n
subst/perm 
subst/perm 
subst/perm  P … C
round key 1
round key 2
round key n …
subst/perm
subst/perm
subst/perm
main key K

18. Keyless Ciphers  Substitution/permutation not based on key
“Hardwired” into cipher
Assume known by adversary
Simply used to add diffusion/confusion
round i
“I know this, but still can’t figure out what P and K are”
subst/perm  C P … …
subst/perm K

19. P-Boxes for Permutation
Number in box gives position of corresponding input bit in output
Example: 16-bit P-Box
Input
Output

20. Invertible P-Boxes
P-Box invertible if each input maps to one and only one output
Example: Same 16-bit P-Box
Swap numbers and indices
Resort by indices

21. Shift and Swap P-Boxes Shift Box moves inputs over by some n bits
May be circular, shifting bits at end to beginning
Example: 8-bit right circular shift box
Swap box swaps two or more blocks of bits
Example: swapping two adjacent 4-bit blocks

22. Compression/Expansion P-Boxes
Compression P-Box: Not all inputs map to an output
Example: 8 x 6 P-Box
8 inputs, only 6 outputs
Note that inputs 3 and 5 do not map to an output

23. Compression/Expansion P-Boxes
Expansion P-Box: Some inputs map to multiple outputs
Example: 8 x 12 P-Box
8 inputs, 12 outputs
Note that inputs 1, 4, 5, and 7 map to two different outputs

24. Compression/Expansion P-Boxes
Compression and Expansion P-Boxes not invertible
Compression boxes lose information
Can invert expansion box only if output has identical values corresponding to inputs that are duplicated
1010   11010
?   10010
Used primarily in key generation
Example: Creating bit round keys from single 128-bit key

25. S-Boxes for Substitution
Map blocks of plaintext to ciphertext
Example: 3 x 3 S-Box
Often simplify by making “2 dimensional” Example: First bit of input determines row of output
Input
000
001
010
011
100
101
110
111
Output 00 01 10 11
011
101
111
100 1
000
010
001
110

26. Invertible S-Boxes Must have same number of inputs and outputs
Example: 3 x 2 compression S-Box
Each output must be unique 00 01 10 11 1
Input
000
001
010
011
100
101
110
111
Output