Cryptography

1
Cryptography

• CS-103
• Chapter 8

2
History

• Humans have been devising systems to encode
  information for at least 4000 years.
• The original message is in plaintext while the
  encoded message is in ciphertext.

3
History Some Encoding Schemes

• Caesar Shift
• Substitution Cipher
• Vigenere Cipher
• One-Time Pad Cipher
• Enigma
• Public Key Cryptography

4
History Caesar Shift

• First used by Julius Caesar
• Uses a simple alphabetic shift
• Plaintext is shifted a certain number of letters
  forward or backward

• Example
• Plaintext - AUTO
• Ciphertext BVUP
• Alphabet is shifted on letter forward AB, BC,
  etc.

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Caesar Shift (Contd)

• This type of cipher is relatively easy to break
  by trial-and-error.
• Recipient must only know the number of places the
  alphabet has been shifted.
• Still used during the Civil War to send messages
  on the battlefield.

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History Substitution Cipher

• Encoded letters are randomly scrambled.
• Recipient must know the scrambled alphabet.
• May use a key word to begin scrambling.

• Alphabet
• A B C D E F G H
• Scrambled
• C O D E A B F G
• Plaintext
• FACE
• Ciphertext
• BCDA

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Substitution Cipher (Contd)

• Because letter frequencies in various languages
  are well established, this type of cipher is
  relatively easy to break.
• Newspapers often contain an encoded puzzle that
  uses this method of encryption.

8
Substitution Cipher (Contd)

• If the alphabet is randomly scrambled, the
  recipient must know the entire substitution
  scheme.
• If a keyword is used, the recipient must only
  know the keyword to complete the substitution
  scheme.

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History Vigenere Cipher

• Modification of the Substitution Cipher
• The alphabet is re-scrambled for each letter of
  the plaintext message
• Requires a keyword or phrase to start the
  substitution sequence
• Requires use of a Vigenere Table

10
Vigenere Cipher (Contd)

• Considered unbreakable for several centuries.
• Eventually Babbage, Kasiski, and Kerchoff devised
  a method to break the Vigenere cipher.
• Be sure you understand how this cipher works.
  Use the website provided in the on-line text.

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History One-Time Pad Cipher

• Modification of the Vigenere Cipher
• Message length is limited to some prescribed
  number of characters
• Key is longer than any message
• Each key is used only once and then destroyed.

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One-Time Pad Cipher (Contd)

• Recipient must know which pad and key were used
  to encode the message
• Once the message is decoded, the key and the
  pad on which it was recorded are destroyed
• The pad and key are never used again

13
One-Time Pad Cipher (Contd)

• This cipher method was used by many governments
  for diplomatic communications
• Since each pad was used only once, the
  Babbage-Kasiski-Kerchoff method could not be used
  to decipher messages
• Drawback both sender and recipient had to know
  the number of the pad being used to encode the
  message

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History The Engima Machine

• Germany developed this encoding device during
  WWII
• England enlisted some of the greatest
  mathematicians of the time to attempt to break
  the code
• Alan Turing, the father of modern computer
  science was part of this team
• Enigma code was not broken until a German
  submarine was captured and a machine and code
  book were found

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History Public-Key Cryptography

• Computers ushered in a new age of cryptography
• Increased electronic transmission of sensitive
  data required new levels of security
• Requires the use of two keys a public key and a
  private key

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Public-Key Cryptography (Contd)

• Public Key
• Known to everyone who wishes to send an encoded
  message to a recipient
• Cant be used to decode message

• Private Key
• Known only to the recipient
• Can only be used to decode a message

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Public-Key Cryptography (Contd)

• Diffie, Hellman, and Merkle discovered and
  published the key concepts for this method
• Rivest, Shamir, and Adleman devised an algorithm
  that could be used to implement the idea
• The RSA algorithm has become the foundation for
  modern electronic security methods

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Public-Key Cryptography (Contd)

• RSA method is based upon the idea that some
  mathematical processes are easy to implement but
  almost impossible to reverse.
• Multiplying two large prime numbers is easy
• Factoring this product to find the original prime
  numbers is very difficult
• Current methods use products of more than 300
  digits.

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Public-Key Cryptography (Contd)

• As computer speeds increase and new methods of
  factoring large numbers are discovered, perhaps
  the RSA method will someday be broken.

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TheEnd