Cryptology

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Cryptology

• Making Breaking Codes Ciphers

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Cryptology

• Cryptography
• Science of creating codes or ciphers
• Cryptanalysis
• Science of breaking codes and ciphers

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Codes vs. Ciphers

• Code
• Substitution of words or phrases by others
• Example Navajo code talkers of WW II
• turtle means tank
• sea turtle means landing craft
• Cipher
• Algorithmic scrambling/unscrambling
• Example Caesar cipher
• Replace each letter with the letter 3 positions
  after it in the alphabet (a ? d, b ? e, etc.)

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Terminology

• Plaintext
• The unencrypted (readable) message
• Ciphertext
• The encrypted version of the message
• Secure channel
• A communications path safe from eavesdropping
• Insecure channel
• A communications path that may be tapped

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Stream Block Ciphers

• Stream cipher acts on one character at a time
• Replaces each character with a different symbol
• Fixed Each plaintext a is always replace by
  the same ciphertext symbol
• Example Caesar cipher (a always replaced by
  d)
• Example rot13 (used to encode obscene text)
• Variable Different occurrences of a in the
  plaintext are replaced with different symbols in
  the ciphertext
• Example German Enigma cipher machine of WWII

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Jeffersons Cipher Machine

• A stack of code wheels threaded on a central axis
• Could be any length, but typically 30
• Each had all letters of the alphabet, but no two
  were identical
• To encrypt a message
• Divide message into blocks stack size
• Turn wheels so plaintext shows on one row
• Lock the wheels
• Transmit any other row

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Jeffersons Cipher Machine

• To decrypt a message
• Set wheels to match the ciphertext for each block
• Lock the wheels
• Look for the one row that contains readable
  plaintext
• Jeffersons machine was used, successfully, for
  almost a century

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Zimmermann Telegram
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Enigma Ultra

• Used by Germany during WW II
• Considered it unbreakable
• Broken in 1940 by Britain (Ultra)
• Team at Bletchley Park, headed by Alan M. Turing

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How Enigma Worked

• Operator typed plaintext message
• 3 rotors scrambled each letter
• Ciphertext character lit up on upper panel
• Rotors turned after every letter

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How Enigma was Solved

• Lots of similar messages
• Germans sent weather information to U-boats every
  day, all in same format
• Human error
• Lazy or tired operators re-used rotor settings
  instead of changing them
• Repeated first 3 characters of message
• Weakness of algorithm
• Would never translate a letter to itself

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How Enigma was Solved

• The Bombe
• Computer at Bletchley Park
• Searched thousands of possible Enigma settings,
  looking for one that yielded readable plaintext
• Captured code books
• Naval vessels carried books of Enigma settings
• British captured U-559 in Sept. 1942
• By 1943, Britain could read intercepted Enigma
  messages before the Germans could!

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Exchanging Keys

• Prior to 1976, all ciphers were symmetric
• Used the same key to encrypt and decrypt
• Problem with all old encryption schemes is the
  key exchange
• Recipient must have the same key as the sender
• How do you transmit a secret key over an insecure
  channel?

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Public-Key Cryptography

• New Directions in Cryptography
• Whitfield Diffie Martin Hellman, 1976
• Proposed using two keys
• One to encrypt messages (the public key)
• A different key to decrypt (the private key)
• Also known as asymmetric cryptography
• Two keys are related, but one cannot be derived
  from the other
• Public key can be published

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The RSA System

• Select two prime numbers, p and q
• Ex choose p 11, q 3
• Compute n pq, f (p-1)(q-1)
• Ex n 11 ? 3 33, f 10 ? 2 20
• Choose e, the encryption key, less than n, so
  that e and f have no common factors
• Ex choose e 3

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The RSA System

• Find d (the decryption key)
• Need ( e ? d / f ) to leave a remainder of 1
• Ex 3 ? d / 20 leaves remainder 1 if d 7
• Key pair is (n,e) and (n,d)
• Encryption (public) key is (33, 3)
• Decryption (private) key is (33, 7)

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The RSA System

• Encrypting a message
• ciphertext (plaintext)e mod n
• Ex plaintext 13
• ciphertext 133 mod 33 2197 mod 33 19
• Decrypting the message
• plaintext (ciphertext)d mod n
• plaintext 197 mod 33 893871739 mod 33 13

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Why is RSA Secure?

• Real versions use very large numbers
• Modulus, n, is at least 1024 bits long
• About 340 decimal digits
• So p and q are each about 200 digits long
• Numbers are easy to multiply, but hard to factor
• Its easy to compute n if you know both p and q
• Its almost impossible to factor n into p q

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Just How Secure Is It?

• No cipher is 100 unbreakable
• Except one-time pads, but they have other
  problems
• By making the modulus larger, RSA can be made
  arbitrarily hard to break
• With a 2048-bit modulus, all the computing power
  in the world would take over 70 years to break
  one cipher

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What are the Problems?

• Asymmetric encryption is S-L-O-W
• Can take even powerful computers 1-2 seconds to
  encrypt or decrypt a message
• Can be fooled by someone posing as someone else
• If Eve claims to be Bob and publishes Bobs
  public key, any messages encrypted with it will
  be readable by Eve, not Bob

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Speeding Things Up

• DES (Data Encryption Standard)
• Proposed in 1974 by NSA, IBM
• Symmetric cipher
• Algorithm can be implemented in hardware
• Key very short
• 56 bits long (40-bit key and 16-bit header)
• Could be broken by force with enough computing
  power (which NSA has)

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DES and 3DES

• Shortness of key used by DES considered a
  weakness
• Newer version is triple-DES or 3DES
• 136 bits long (120-bit key 16-bit header)
• AES (Advanced Encryption Standard)
• Uses 128-bit key
• DES, 3DES, and AES are all symmetric

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SSL

• Secure Sockets Layer (SSL)
• Invented by Netscape in 1995
• Uses RSA to exchange a session key
• DES, 3DES, or AES key used for that browser
  session only
• Gets both speed and security
• RSA only used to exchange session key
• Session key expires when user logs out

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Digital Certificates

• Overcome spoofing attack
• Perform same function as notary public
• Purchase from Certificate Authorities (CAs)
• VeriSign, Thawte, Comodo, GeoTrust,
• Contain my public key
• Signed by the root certificate
• Located in your browser

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Digital Signatures

• Asymmetric cryptography can be used to digitally
  sign documents
• Achieves all purposes of conventional signature
  (but better)
• Cannot be forged
• Cannot be stolen and re-used
• Cannot be repudiated
• Assume Alice wants to sign a document and send it
  to Bob. Here goes

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Digital Signatures

1. Alice computes the MD5 (or SHA-1) digest value
   for the document
2. She encrypts the (documentdigest) combination
   using her own private key
3. She then encrypts the previous message using
   Bobs public key and sends Bob the result.

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Digital Signatures

1. Bob decrypts the message from Alice using his own
   private key.
2. He then decrypts the resulting message using
   Alices public key.
3. He isolates the digest value and compares it with
   the value he computes for the rest of the
   message.
4. If everything matches, he knows that Alice signed
   this document.

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Digital Signatures

• Can Alice later repudiate her signature?
• No, because only she has her private key
• Can Bob or Eve forge Alices signature?
• No, for the same reason
• Can Eve steal Alices signature and use it to
  sign a different document?
• No, because then the digest values wouldnt match

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State of the Art

• Public-key cryptography allows people to
  communicate securely even if they have never met
• Necessary for electronic commerce
• Ciphers cannot be made 100 secure, but they can
  be made arbitrarily secure
• Use longer keys
• Both good guys and bad guys can use this
  technology
• Cryptanalysis is essentially obsolete