Encryption and Security

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Encryption and Security
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Outline

• Overview of encryption
• Terminology
• History
• Common issues
• Secret-key encryption
• Block and stream ciphers
• DES
• RC5

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Overview

• Intro, history and terminology
• Symmetric-key encryption
• Techniques
• DES, RC5
• Public-key encryption
• RSA, hash functions, digital signatures
• Key exchange, certificates, PKI

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Overview
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Terminology

• Code
• Replacement based on words or semantic structures
• Cipher
• Replacement based on symbols

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Terminology

• Cryptography
• The science of encrypting or hiding secrets.
• Cryptanalysis
• The science of decrypting messages or breaking
  codes and ciphers.
• Cryptology
• The combination of the two.

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Terminology

• Plaintext an unencrypted message
• Cyphertext an encrypted message
• Security a combination of
• Authentication
• Access control

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Three eras of cryptology

• Pre-WWII
• Cryptography as a craft
• Widely used, but few provable techniques
• 1940s-1970
• Secret key encryption introduced
• Information theory used to characterize security
• 1970-present
• Public key systems introduced

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Early cryptography

• Caesar cipher
• Replace each letter l with l 3 mod 26
• Attack at dawn becomes
• Dwwdfn dw gdzq
• Two components
• Algorithm Shift characters by a fixed amount
• Key the fixed amount.
• Note Knowing the algorithm (but not the key)
  makes this cipher much easier to crack
• 26 possibilities vs 26!

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Weaknesses of the Caesar Cipher

• Word structure is preserved.
• Break message into equal-length blocks.
• dww dfn dwg dzq
• Letter frequency is a big clue
• e,t,a,o most common English letters.
• Using a single key preserves frequency.
• Solution use multiple keys
• E.g. shift by (3,5,7)
• Attack at dawn becomes dya dhr dyk dbu
• Better, but frequency information still present.
• An attacker that knows the block size can
  separate out characters encoded with different
  keys.

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Caesar Cipher

• The Caesar cipher is still useful as a way to
  prevent people from unintentionally reading
  something.
• ROT-13
• By decrypting, the user agrees that they want to
  view the content.
• Fundamental problem key length is shorter than
  the message.

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Vernam Cipher

• 1920s introduction of the one-time pad.
• Randomly generated key
• Same length as message
• XORed with message
• Theoretically unbreakable
• Attacker can do no better than guessing
• Ciphertext gives no information about plaintext.

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Vernam Cipher

• Example winning lottery number is 117
• 1110101 (7 bits)
• Randomly generated key 0110101
• XOR 1000000
• No two bits are encoded with the same mapping
  an attacker has no frequency information to help
  guess the key.
• Problem keys are very large.
• How to distribute this key?
• Shared source of randomness?

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Symmetric Key Encryption

• The Caesar Cipher and the one-time pad are
  examples of symmetric-key (secret-key)
  encryption.
• Single key shared by all users.
• Fast
• How to distribute keys?

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Keyspace

• The keyspace is the set of all possible keys.
• Caesar cipher keyspace 0,1,2,,25
• Vernam cipher keyspace 2n 1
• Size of the keyspace helps us estimate security.
• Assumption exhaustive search is the only way to
  find a key.

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Substitution Ciphers

• Symbols are replaced by other symbols according
  to a key.
• Caesar cipher is a substitution cipher.
• To escape frequency analysis, we can use a
  homophonic substitution cipher
• Map symbols to multiple symbols.
• e.g 0 -gt 01, 10, 1-gt00,11
• 011010010 becomes 011100101101011110
• Advantage frequencies hidden
• Disadvantage message and key are longer
• Substitution is said to add confusion
• Measure of the relationship between plaintext and
  ciphertext

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Transposition Ciphers

• A transposition cipher is one that permutes the
  symbols of the message according to a preset
  pattern.
• Attack at dawn becomes cda tka wan tat
• Helps avoid detection of symbols based on
  correspondence.
• q followed by u.
• Said to increase diffusion
• Reduce redundancies in plaintext.

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Product ciphers

• By themselves, substitution and transposition
  ciphers are relatively insecure.
• By combining these operations, we can produce a
  secure cipher.
• This is how DES works.
• M -gt Sub(M) -gt Trans(Sub(M)).
• Might go through multiple rounds.

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Block Ciphers

• The ciphers we have seen so far are known as
  block ciphers.
• Plaintext is broken into blocks of size k.
• Each block is encrypted separately.
• Advantages random access, potentially high
  security
• Disadvantages larger block size needed, patterns
  retained throughout messages.

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Stream Ciphers

• A stream cipher encodes a symbol based on both
  the key and the encoding of previous symbols.
• Ci Mi XOR Ki XOR Mi-1
• Advantages
• can work on smaller block sizes little
  memory/processing/buffering needed.
• Disadvantages
• Random access difficult, hard to use large keys.
• Sender and receiver must be synchronized
• Inserted bits can lead to errors.

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Combinations

• Many ciphers combine stream and block properties.
• Work on multiple symbols, but contain a feedback
  loop.
• Electronic Code Book (ECB)
• Pure block cipher, no feedback

E-1
plaintext
E
ciphertext
plaintext
key
key
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Cipher-block Chaining

• XOR previous block
• Chaining dependency order matters.
• Some error propagation

XOR
plaintext
plaintext
key
E
key
E-1
XOR
ciphertext
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Cipher-Block Chaining

• Also incorporated into block ciphers.
• Makes tampering easier to detect.
• Helps prevent substitution and impersonation
  attacks.
• Secret key can also be used to construct a
  running-key generator.
• Longer sequence of pseudo-random numbers.
• Can be used to build a one-time pad.

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Modifications to CBC

• Cipher feedback
• Shift register is used to store data.
• r-bit are shifted into mask of size m.
• Allows a small number of bits to be immediately
  sent.
• Output feedback
• Like cipher feedback, but uses output of
  encryption function.
• Eliminates error propagation.

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DES

• Data Encryption Standard
• DEA is actually the algorithm.
• First commercial-grade algorithm with open
  implementation details.
• Uses a 64-bit key with 8 parity bits, for an
  effective key of 56 bits.
• Keyspace 256 1017

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DES

• Is a combination of a product cipher and a
  Feistel cipher.
• Product cipher transposition and substitution.
• Feistel cipher Iterates through a number of
  rounds of a product cipher mapping (L,R) to (R,
  L)
• 16 rounds
• Block size48
• In each round, a different 48-bit subkey is
  selected from the 56-bit key.

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Security of DES

• Keyspace is approximately 1017
• Thought to be secure in 70s.
• Recently, 56-bit DES broken in under 1 day.
• Combination of distributed.net EFFs DeepCrack.
• Able to search several billion keys per second.

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Extensions to DES

• 3DES
• Message is run through DES 3 times
• C k3 (k2 (k1(M)))
• Backwards-compatible with DES if all three keys
  are the same.
• Keyspace is 1042
• Drawback bit-oriented operations are slow to
  implement in software

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RC5

• Symmetric encryption algorithm
• Word-oriented block cipher.
• Can vary word length, number of rounds, and key
  length.
• Goals fast, easy to understand and implement,
  flexible, low memory requirements, secure.
• Uses stream techniques to modify data

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RC5

• Uses three mathematical operations
• Twos complement addition
• XOR
• Left cyclic rotation by variable amounts.
• These are all fast operations that are directly
  supported by most modern processors.

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RC5 Algorithm

• Parameters K (key), w (word length), r (number
  of rounds)
• Input a 2w length plaintext in registers A and
  B.
• Output a 2w length ciphertext.
• 1. Expand K into a table S2(r1) keys.
• To encrypt
• A A S0 B B S1
• For i 1 to r do
• A ((A xor B) ltlt B) S2 i
• B ((B xor A) ltlt A) S2i 1
• Decryption is the same thing in reverse.

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RC5

• Simple algorithm key is the data-dependent
  rotations.
• Keys are accessed sequentially, allowing for
  small caches.
• Security still unclear, but looks good.
• 56-bit key 250 days by distributed.net
• 64-bit key 1747 days by distributed.net
• 1.02x1011 keys/sec, 1.5 x1019 keyspace
• 72-bit key in progress.
• 4.8x1010 keys/sec, 4x1021 keyspace
• 100 in 788,747 days 2160 years

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Summary

• Secret-key algorithms (DES, RC5) have been widely
  studied.
• Fast
• Potentially highly secure
• Well-understood.
• Excellent for repeated communication.
• Hard to use in open environments, one-shot
  communications
• Works for hiding secrets what about signing
  things?
• Public-key encryption evolved as an answer to
  this problem.