A tour of main features

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• A tour of main features

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Contents
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Basic Problem of Cryptography

• Secure communication over an insecure channel
• Solution

Private key Encryption
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History
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Basic Terms

• Message m
• Plaintext p
• Key k
• Encryption algorithm E(k,m)
• Cipher text c E(k,m)
• Decryption algorithm
• D(k,c) m

• Cryptography
• Cryptanalysis
• Cryptology

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The substitution cipher

• Replace a letter by another letter.
• Example
• Key A D (3)
• Encryption 3
• Decryption -3
• Then
• TODAY WRGDB

• Permutation

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One time pad

• The common secret key is a pad.
• pad b1b2bn
• bi is 0 or 1.
• XOR operator.
• The problem is n and the length of the messages
  sending.

ABCDEF 010101011101010
XOR
pad 101010101010100
HAJSDE 111110101110110
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• A Computational Complexity based Theory

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Secure encryption scheme

• Prevent computational strength of the adversary
• Secure exchange
• Infeasibility of breaking the encryption
  scheme
  
• Primitives
• One-way functions
• Pseudo-random number generators
• Pseudorandom function families

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Public-key cryptography

• Public key is public and published.
• Suitcase exchange scheme
• Trapdoor function is a one-way fucntion with a
  trapdoor information.
  
• Diffie and Hellman 1976

• Public key
• Private key
• Public key encryption

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One-way function

• Easy to compute
• Hard to invert

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Factoring

• F (x, y) ? xy is conjectured to be a one way
  function.
  
• RSA n pq
• Current fastest algorithm
• Randomized algorithm
• Number field sieve

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The Discrete logarithm problem

• p prime
• Multiplicative group Zp \ 0 is cyclic
• So it generated by a generator g.
• F (p, g, x) ? gx mod p is conjectured a one-way
  function.
  
• Fast algorithm now
• Index-calculus

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Subset sum

• Given a set A of numbers a1, a2, , an and a
  number M. Find a subset of A has the sum equals
  to M.
  

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Minimal requirements

• Adversary see the ciphertext and know
  encryption/decryption algorithms can not recover
  the entire clear text.
  
• Hard to compute partial information
• Hard to detect message traffic, such the same
  message sent twice.

• Messages are drawn from arbitrary probability
  distributions defined on the set of all strings,
  or message spaces, which is known for to
  adversary.
• English language
• The set 0, 1

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The Model of the Adversary

• Passive adversary
• Can listen to the ciphertext
• Can read public file
• Can generate encryptions of any message of his
  own
  
• Can perform probabilistic polynomial time
  computation

• More powerful adversary
• Can intercept messages
• Can stop the delivery
• Can alter messages

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Road map to Encryption

• Our challenge
• Design secure private-key, public-key encryption
  systems
  
• Meet security
• Fast for senders and recievers

• Discuss
• How to define security in presence of a bounded
  adversary
  
• Current proposals of encryption systems and
  evaluate them
  
• How to design new systems