Modern Block Ciphers

Modern Block Ciphers CSIS 5857: Encoding and Encryption

Block Ciphers • Encrypting one bit at a time ineffective(only one possible substitution: 1  0, 0  1) • Must map one block of plaintext bits to ciphertextExample: 11010010 01101011 • Key question: Good block size • 8 bits too small: just maps one ASCII character to another (monoalphabetic cipher) • Usually 32, 64, 128, 256, or 512 bits

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)

Substitution and Block Ciphers • Standard binary key insufficient to represent even a 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

Transposition and Binary Text Transposition ciphers of binary text easy to break • Small alphabet reduces distinguishable permutations • Allows possible permutations to be quickly narrowed down • Example: • 64-bit bock 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) = 4,426,165,368 combinations of 8 1’s and 56 0’s • Easily broken with exhaustive search (each successive block reduces number of possible combinations)

Binary Functions • Since both text and key binary, can use binary function to encrypt/decrypt • Example: AND function • Plaintext: 1001101110101100 • Key: 1101100011001010 • Ciphertext: 1001100010001000

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

Exclusive Or Function (XOR) • Definition: • 1 if operands not equal0 if operands equal Plaintext  Key Ciphertext

XOR is Invertible • XOR is its own inverse: C = P  K  P = C  K encryption Plaintext Plaintext   Key Ciphertext Ciphertext decryption

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:10010101 00100110 01110101Key: 10100110 10100110 10100110Ciphertext: 00110011 10000000 01010011 • Decryption:Ciphertext: 00110011 10000000 01010011Key: 10100110 10100110 10100110Plaintext:10010101 00100110 01110101

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

Confusion and Diffusion • 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

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

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

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

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

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

P-Boxes for Permutation • Number in box gives position of corresponding input bit in output • Example: 16-bit P-Box 12 7 1 8 15 11 2 5 16 4 13 10 9 3 14 6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Input1 1 0 1 0 1 0 1 0 0 0 1 0 1 1 0 1 0 1 1 1 0 1 0 0 1 0 0 0 0 1 1 Output

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 12 7 1 8 15 11 2 5 16 4 13 10 9 3 14 6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 12 7 1 8 15 11 2 5 16 4 13 10 9 3 14 6 3 7 14 10 8 16 2 4 13 12 6 1 11 15 14 9 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

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 8 1 2 3 4 5 6 7 5 6 7 8 1 2 3 4

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 7 4 1 8 6 2

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 6 5 1 8 7 2 7 4 5 3 1 4

Compression/Expansion P-Boxes • Compression and Expansion P-Boxes are not invertible • Compression boxes lose information • Cannot invert expansion box if two different outputs would map to the same input • Used primarily in key generation • Example: Creating 16 32-bit round keys from single 128-bit key

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

Invertible S-Boxes • Must have same number of inputs and outputs • Example: 3 x 2 compression S-Box • Each output must be unique

Modern Block Ciphers