Cryptography

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Cryptography

• Funny and serious stuff

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The language of cryptography
Alices encryption key
Bobs decryption key
encryption algorithm
decryption algorithm
ciphertext
plaintext
plaintext

• symmetric key crypto sender, receiver keys
  identical
• public-key crypto encryption key public,
  decryption key secret (private)

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Symmetric key cryptography

• Substitution cipher substituting one thing for
  another- e.g. Caesar cipher substituting every
  letter of a plaintext by a letter that is K
  letters later (allowing wrap around).
• For example if K 3 than the letter a in
  plaintext becomes d in ciphertext.
• Value of K serves as the key. This cipher is
  pretty easy to break as there are only 25
  possible key values.

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Symmetric key cryptography

• Improvement over the Caesar cipher is
  monoalphabetic cipher substitute one letter for
  another but without a specific pattern

plaintext abcdefghijklmnopqrstuvwxyz
ciphertext mnbvcxzasdfghjklpoiuytrewq
E.g.
Plaintext bob. i love you. alice
ciphertext nkn. s gktc wky. mgsbc

• Q How hard to break this simple cipher?
• brute force (how hard?)
• other?

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Symmetric key cryptography

• Polyalphabetic encryption
• Using multiple monoalphabetic ciphers, with a
  specific monoalphabetic cipher to encode a letter
  in a specific position in the plaintext message.
  For example we may use two Caesar ciphers with k1
  5 and k219 in repeating pattern C1, C2, C2,
  C1, C2
• To break such a cipher it is necessary to know
  the keys and the pattern.

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Symmetric key cryptography
encryption algorithm
decryption algorithm
ciphertext
plaintext
plaintext message, m
K (m)
A-B

• symmetric key crypto Bob and Alice share (know)
  same (symmetric) key K
• e.g., key is knowing substitution pattern in mono
  alphabetic substitution cipher
• Q how do Bob and Alice agree on key value?

A-B
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Symmetric key crypto DES

• DES Data Encryption Standard
• US encryption standard NIST 1993
• 56-bit symmetric key, 64-bit plaintext input
• How secure is DES?
• DES Challenge 56-bit-key-encrypted phrase
  (Strong cryptography makes the world a safer
  place) decrypted (brute force) in 4 months
• no known backdoor decryption approach
• making DES more secure
• use three keys sequentially (3-DES) on each datum
• use cipher-block chaining

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Symmetric key crypto DES

• initial permutation
• 16 identical rounds of function application,
  each using different 48 bits of key
• final permutation

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Chapter 2

• Symmetric Encryption Message Confidentiality

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Outline

• Symmetric Encryption Principles
• Symmetric Encryption Algorithms
• Cipher Block Modes of Operation
• Location of Encryption Devices
• Key Distribution

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Symmetric Encryption Principles

• An encryption scheme has five ingredients
• Plaintext
• Encryption algorithm
• Secret Key
• Ciphertext
• Decryption algorithm
• Security depends on the secrecy of the key, not
  the secrecy of the algorithm

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Symmetric Encryption Principles
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Cryptography

• Classified along three independent dimensions
• The type of operations used for transforming
  plaintext to ciphertext
• The number of keys used
• symmetric (single key)
• asymmetric (two-keys, or public-key encryption)
• The way in which the plaintext is processed

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Cryptanalysis

• Ciphertext only
• most difficult,
• brute force approach of trying all possible keys,
• the easiest to defend,

• Ciphertext and plaintext pair
• known pattern in a file as well,
• probable-word attack (e.g. placement of certain
  key words in the header of a file)
• key can be deduced,

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Cryptanalysis

• Chosen plaintext
• analyst get the source system to insert into the
  system a message chosen by the analyst,
• plaintext message chosen by cryptanalyst,
  together with its corresponding decrypted
  plaintext generated with the secret key,

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Cryptanalysis

• Chosen ciphertext
• purported ciphertext chosen by the analyst,
  together with its corresponding decrypted
  plaintext generated with the secret key

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Computational security of an encryption

• The cost of breaking the cipher exceeds the value
  of the encrypted information,
• the time required to break the cipher exceeds the
  useful lifetime of the information

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Average time required for exhaustive key search
Key Size (bits) Number of Alternative Keys Time required at 106 Decryption/µs
32 232 4.3 x 109 2.15 milliseconds
56 256 7.2 x 1016 10 hours
128 2128 3.4 x 1038 5.4 x 1018 years
168 2168 3.7 x 1050 5.9 x 1030 years
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Feistel Cipher Structure

• Virtually all conventional block encryption
  algorithms, including DES have a structure first
  described by Horst Feistel of IBM in 1973
• The realization of a Feistel Network depends on
  the choice of the following parameters and design
  features (see next slide)

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Feistel Cipher Structure

• Block size larger block sizes mean greater
  security
• Key Size larger key size means greater security
• Number of rounds multiple rounds offer
  increasing security
• Subkey generation algorithm greater complexity
  will lead to greater difficulty of cryptanalysis.
• Fast software encryption/decryption the speed of
  execution of the algorithm becomes a concern

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Symmetric Encryption Algorithms

• Data Encryption Standard (DES)
• The most widely used encryption scheme
• The algorithm is referred to as the Data
  Encryption Algorithm (DEA)
• DES is a block cipher
• The plaintext is processed in 64-bit blocks
• The key is 56-bits in length

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DES

• The overall processing at each iteration
• Li Ri-1
• Ri Li-1 F(Ri-1, Ki)
• Concerns about
• The algorithm and the key length (56-bits)

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Time to break a code (106 decryptions/µs)
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Triple DEA

• Uses three keys and three executions of the DES
  algorithm (encrypt-decrypt-encrypt)
• C ciphertext
• P Plaintext
• EKX encryption of X using key K
• DKY decryption of Y using key K
• Effective key length of 168 bits

C EK3DK2EK1P
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Triple DEA
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AES Advanced Encryption Standard

• new (Nov. 2001) symmetric-key NIST standard,
  replacing DES
• processes data in 128 bit blocks
• 128, 192, or 256 bit keys
• brute force decryption (try each key) taking 1
  sec on DES, takes 149 trillion years for AES

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Origins

• clear a replacement for DES was needed
• have theoretical attacks that can break it
• have demonstrated exhaustive key search attacks
• can use Triple-DES but slow with small blocks
• US NIST issued call for ciphers in 1997
• 15 candidates accepted in Jun 98
• 5 were short-listed in Aug-99
• Rijndael was selected as the AES in Oct-2000
• issued as FIPS PUB 197 standard in Nov-2001

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AES Requirements

• private key symmetric block cipher
• 128-bit data, 128/192/256-bit keys
• stronger faster than Triple-DES
• active life of 20-30 years ( archival use)
• provide full specification design details
• both C Java implementations
• NIST have released all submissions unclassified
  analyses

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AES Evaluation Criteria

• initial criteria
• security effort to practically cryptanalyse
• cost computational
• algorithm implementation characteristics
• final criteria
• general security
• software hardware implementation ease
• implementation attacks
• flexibility (in en/decrypt, keying, other factors)

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AES Shortlist

• after testing and evaluation, shortlist in
  Aug-99
• MARS (IBM) - complex, fast, high security margin
• RC6 (USA) - v. simple, v. fast, low security
  margin
• Rijndael (Belgium) - clean, fast, good security
  margin
• Serpent (Euro) - slow, clean, v. high security
  margin
• Twofish (USA) - complex, v. fast, high security
  margin
• then subject to further analysis comment
• saw contrast between algorithms with
• few complex rounds verses many simple rounds
• which refined existing ciphers verses new
  proposals

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The AES Cipher - Rijndael

• designed by Rijmen-Daemen in Belgium
• has 128/192/256 bit keys, 128 bit data
• an iterative rather than feistel cipher
• treats data in 4 groups of 4 bytes
• operates an entire block in every round
• designed to be
• resistant against known attacks
• speed and code compactness on many CPUs
• design simplicity

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Rijndael

• processes data as 4 groups of 4 bytes (state)
• has 9/11/13 rounds in which state undergoes
• byte substitution (1 S-box used on every byte)
• shift rows (permute bytes between groups/columns)
  
• mix columns (subs using matrix multiply of
  groups)
• add round key (XOR state with key material)
• initial XOR key material incomplete last round
• all operations can be combined into XOR and table
  lookups - hence very fast efficient

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Rijndael
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Byte Substitution

• a simple substitution of each byte
• uses one table of 16x16 bytes containing a
  permutation of all 256 8-bit values
• each byte of state is replaced by byte in row
  (left 4-bits) column (right 4-bits)
• eg. byte 95 is replaced by row 9 col 5 byte
• which is the value 2A
• S-box is constructed using a defined
  transformation of the values in GF(28)
• designed to be resistant to all known attacks

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Shift Rows

• a circular byte shift in each row
• 1st row is unchanged
• 2nd row does 1 byte circular shift to left
• 3rd row does 2 byte circular shift to left
• 4th row does 3 byte circular shift to left
• decrypt does shifts to right
• since state is processed by columns, this step
  permutes bytes between the columns

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Mix Columns

• each column is processed separately
• each byte is replaced by a value dependent on all
  4 bytes in the column
• effectively a matrix multiplication in GF(28)
  using prime poly m(x) x8x4x3x1

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Add Round Key

• XOR state with 128-bits of the round key
• again processed by column (though effectively a
  series of byte operations)
• inverse for decryption is identical since XOR is
  own inverse, just with correct round key
• designed to be as simple as possible

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AES Round
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AES Key Expansion

• takes 128-bit (16-byte) key and expands into
  array of 44/52/60 32-bit words
• start by copying key into first 4 words
• then loop creating words that depend on values in
  previous 4 places back
• in 3 of 4 cases just XOR these together
• every 4th has S-box rotate XOR constant of
  previous before XOR together
• designed to resist known attacks

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AES Decryption

• AES decryption is not identical to encryption
  since steps done in reverse
• but can define an equivalent inverse cipher with
  steps as for encryption
• but using inverses of each step
• with a different key schedule
• works since result is unchanged when
• swap byte substitution shift rows
• swap mix columns add (tweaked) round key

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Implementation Aspects

• can efficiently implement on 8-bit CPU
• byte substitution works on bytes using a table of
  256 entries
• shift rows is simple byte shifting
• add round key works on byte XORs
• mix columns requires matrix multiply in GF(28)
  which works on byte values, can be simplified to
  use a table lookup

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Implementation Aspects

• can efficiently implement on 32-bit CPU
• redefine steps to use 32-bit words
• can pre-compute 4 tables of 256-words
• then each column in each round can be computed
  using 4 table lookups 4 XORs
• at a cost of 16Kb to store tables
• designers believe this very efficient
  implementation was a key factor in its selection
  as the AES cipher

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Other Symmetric Block Ciphers

• International Data Encryption Algorithm (IDEA)
• 128-bit key
• Used in PGP
• Blowfish
• Easy to implement
• High execution speed
• Runs in less than 5K of memory

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Other Symmetric Block Ciphers

• RC5
• Suitable for hardware and software
• Fast, simple
• Adaptable to processors of different word lengths
• Variable number of rounds
• Variable-length key
• Low memory requirement
• High security
• Data-dependent rotations
• Cast-128
• Key size from 40 to 128 bits
• The round function differs from round to round