Block%20Ciphers

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Block Ciphers

• Breno de Medeiros

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Block Ciphers

• Block ciphers operate by splitting the (binary
  string representation of the) plaintext into
  fixed-size blocks, and encrypting one block at a
  time.
• For a fixed key, the block cipher encryption is a
  simple substitution cipher over a VERY large
  alphabet.
• Typical block sizes 64 or 128 bits.

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Block cipher operation
Block Cipher
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Block cipher terminology

• Blocksize The length of a block in bits.
• Both size of plaintext and ciphertext blocks.
• Key length Length of the key in bits.
• Keyspace K The set of valid key values.
• Effective key length
• Let K the number of valid keys.
• Then t log2K is the effective key length.

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Example DES

• DES operates on 8-byte data chunks. Therefore
  the blocksize is 64 bits.
• DES Keyspace K
• 64-bit binary strings such that each 8-th bit
  chunk has even parity
• Effective key length is 56 256 possible keys,
  determined by eight 7-bit chunks.

0 1 0 0 0 1 0 0 0 0 1 0 1 1 0 1
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Block cipher properties

• The encryption operation is invertible
• Each key K determines a PERMUTATION on the block
  space.
• For a block of n bits, there are
• 2n blocks, (2n)! possible permutations
• at most (2n)! possible keys, or effective key
  length at most log2 (2n)! n2n (!!!!)
• In practice, MUCH smaller keyspace and shorter
  keys.

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Designing a practical cipher

• A fully general substitution cipher either
• Has small block size and is efficient lookup
  tables, but is easy to break
• Has large block sizes and too large lookup
  tables.
• Restrict the class of substitution ciphers so
  that may simultaneously have
• large block sizes (for security)
• smaller keys (for efficiency)
• Idea Combined substitution and permutation

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Confusion and Diffusion

• Shannon suggested use of confusion and diffusion
  as two techniques that ciphers should implement
  to deter cryptanalysts.
• Diffusion Dissipate the statistical properties
  of the plaintext over the whole ciphertext.
• Concretely For a block cipher, if each bit of
  the output block changes with 50 probability for
  any flipped bit in the input block, the cipher
  has good diffusion properties.

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Substitution and Permutation

• For good diffusion properties to exist, the
  cipher has to employ shuffling or re-ordering of
  bits (permutation operations).
• Confusion refers to the property that the
  ciphertext (and its statistical properties) is
  not easily relatable to the key.
• Key must involve non-linear substitution
  algorithms.

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Feistel Cipher

• The Feistel network design combines permutations
  and substitutions effectively.
• The parameters of a Feistel cipher are
• The block size.
• The round function F, and corresponding key size.
• The key schedule, or subkey generation algorithm.
• The number of rounds.
• Usually, there is an initial permutation (not
  shown).

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Decryption

• The decryption algorithm of a Feistel cipher
  equals its encryp-tion algorithm with a reversed
  key schedule.

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Example DES

• DES defines 3 fixed (key independent)
  permutations
• Initial permutation IP, applied to plaintext
  before and after the Feistel network
• Permuted choices 1, 2 (and per-round shift
  amounts) for the key schedule.
• Each DES round is a pure Feistel cipher round.

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Initial permutation
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A DES ROUND
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Expansion/Permutation functions
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The Round Function F()
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