Lecture7 - IS2150/TEL2810 IntroductiontoSecurity JamesJoshi

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1 IS 2150 / TEL 2810 Introduction to Security James Joshi Associate Professor, SIS Lecture 7 Oct 20, 2009 Basic Cryptography Network Security
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2 Objectives Understand/explain/employ the basic  cryptographic techniques Review the basic number theory used in  cryptosystems Classical system Public-key system Some crypto analysis Message digest
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3 Secure Information Transmission (network security model) Trusted Third Party arbiter, distributer of secret information Opponent Secure Message Message Information channel Sender Receiver Secret Information Security related transformation Secret Information
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4 Security of Information Systems (Network access model) Gate Keeper Opponent - hackers - software Access Channel Internal Security Control Data Software Gatekeeper – firewall or equivalent, password-based login Internal Security Control – Access control, Logs, audits, virus scans etc.
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5 Issues in Network security Distribution of secret information to enable secure exchange of  information Effect of communication protocols needs to be considered Encryption  if used cleverly and correctly , can provide several of  the security services  Physical and logical placement of security mechanisms Countermeasures need to be considered 
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6 Cryptology CRYPTOLOGY CRYPTOGRAPHY CRYPTANALYSIS Private Key (Secret Key) Public Key Block Cipher Stream Cipher Integer Factorization Discrete Logarithm Encipher, encrypt Decipher, decrypt
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7 Elementary Number Theory Natural numbers N = {1,2,3,…} Whole numbers W = {0,1,2,3, …} Integers Z = {…,-2,-1,0,1,2,3, …} Divisors A number  b  is said to divide  a  if  a  =  mb  for  some   where  a b m    Z We write this as  b  |  a
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8 Divisors Some common properties If  a  | 1   a  = +1 or –1 If  a | b  and  b | a  then  a  = + or – b Any  b     Z    divides 0 if   0 If  b | g  and  b | h  then  b |( mg + nh ) where  b , m,n,g,h    Z Examples:  The positive divisors of 42 are ? 3|6 and 3|21 => 3|21m+6n for  m,n   Z
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Prime Numbers An integer  p  is said to be a prime number if its only positive  divisors are 1 and itself 2, 3, 7, 11, . . Any integer can be expressed as a  unique  product of prime  numbers raised to positive integral powers Examples 7569 = 3 x 3 x 29 x 29 = 3 2  x 29 2 5886 = 2 x 27 x 109 = 2 x 3 3  x 109 4900 = 7 2  x 5 x   2 2 100 = ? 250 = ?
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Lecture7 - IS2150/TEL2810 IntroductiontoSecurity JamesJoshi

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