9' Cryptology

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9. Cryptology
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???(Cryptology)

• cryptography design of secret communications
  systems
• cryptanalysis study of ways to compromise
  secret communications systems
• ????
• military, diplomatic
• computer file systems
• electronic funds transfer systems
• ??
• protect our computer files and our bank accounts
  from criminals

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Rules of the Game (1)

• cryptosystem
• sender encrypt a message (plaintext to
  ciphertext)
• receiver decrypt a message (ciphertext to
  plaintext)
• encryption method
• decryption method
• some key parameters
• cryptanalyst
• knows about encryption and decryption method
• recover the plaintext from ciphertext without
  knowing the key parameters

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Rules of the Game (2)

• rule
• the more key parameters, the more secure the
  cryptosystem
• the more inconvenient it is to use
• economic motivation
• build simple encryption and decryption devices
• reduce the amount of key information to be
  distributed
• cryptographers aim
• develop a low-cost system with the property that
  it would cost the cryptanalyst much more to read
  messages than he would be willing to pay

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Simple Methods (1)

• Caesar cipher
• if a letter in the plaintext is the Nth letter in
  the alphabet, replace it by the (NK)th letter
• Caesar used K 3
• using general table
• much powerful than the simple Caesar cipher
• easy to break because of letter frequencies
• Vigenere cipher
• use more than one table
• the longer the key, the better
• make more complicated by using different general
  tables for each letter of the plaintext

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Simple Methods (2)

• Vernam cipher
• one-time pad
• the key is as long as the plaintext
• the only provably secure cryptosystem known
• repeatedly used for the Washington-Moscow hotline
  and other vital applications
• if the message is binary
• use the exclusive-or function
• to encrypt the plaintext, exclusive-or it with
  the key
• to decrypt the ciphertext, exclusive-or it with
  the key

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Encryption/Decryption Machine

• using pseudo-key
• encryption machine generates a long stream of key
  bits (pseudo-key) by using some cryptovariables
  (true key)
• exclusive-or of these bits and the plaintext
  forms the ciphertext
• decryption machine generates same key stream to
  exclusive-or against the ciphertext and to
  retrieve the plaintext
• key generation is very much like hashing and
  random-number generation

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Public-Key Cryptosystem

• to transmit a message
• the sender looks up the receivers public key
• uses it to encrypt a message
• transmit the message
• to read a message
• the receiver uses his private decryption key to
  decrypt
• read the message
• conditions
• S(P(M)) M
• All (S, P) pairs are distinct
• Deriving S from P is as hard as reading M
• Both S and P are easy to compute

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RSA Public-Key Cryptosystem (1)

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RSA Public-Key Cryptosystem (2)

• In the RSA cryptosystem, a message can be
  encrypted in linear time
• The keys for the RSA cryptosystem can be created
  without excessive computation
• to encrypt a message M
• compute C P(M) MP mod N
• to dncrypt a message C
• compute P S(C) CS mod N
• the best factoring algorithms known would take
  millions of years to factor a 200-digit number,
  using current technology

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???

• attractive feature
• complicated computation involving N, p, and s are
  performed only once for each user
• much more frequent operations of encryption and
  decryption involve only breaking up the message
  and applying the simple exponentiation procedure
• drawback
• the exponentiation procedure is actually
  expensive by cryptographic standards