Lecture7 - IS 2150 / TEL 2810 Introduction to Security...

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2150 / TEL 2810 IS 2150 / TEL 2810 Introduction to Security James Joshi Associate Professor, SIS , Lecture 7 ct 2 0 1 1 Oct 4, 2011 Basic Cryptography etwork Security 1 Network Security
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Objectives Understand/explain/employ the basic yptographic techniques cryptographic techniques Review the basic number theory used in cryptosystems yp y Classical system ublic- ey system Public key system Some crypto analysis essage digest 2 Message digest
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Secure Information Transmission (network security model) Trusted Third Party arbiter, distributer of secret information Sender Receiver ssage Secret Information Security related Secret Information ge Me s formation channel transformation ure Messa g Information channel 3 Opponent Sec
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Security of Information Systems (Network access model) Gate Keeper Opponent - hackers ccess Channel ternal Data Software -software Access Channel Internal Security Control Gatekeeper – firewall or equivalent, password-based login ternal Security Control ccess control Logs audits virus scans etc 4 Internal Security Control – Access control, Logs, audits, virus scans etc.
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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 yp yy ,p the security services Physical and logical placement of security mechanisms Countermeasures need to be considered 5
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Cryptology CRYPTOLOGY CRYPTOGRAPHY CRYPTANALYSIS Private Key (Secret Key) Public Key Block Cipher Stream Cipher Integer Factorization Encipher, encrypt 6 Discrete Logarithm c p e , e c ypt Decipher, decrypt
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Elementary Number Theory Natural numbers N = {1,2,3,…} hole numbers W = {0,1,2,3, …} Whole numbers W {0,1,2,3, …} Integers Z = {…,-2,-1,0,1,2,3, …} ivisors Divisors A number b is said to divide a if a = mb for some m where a, b, m Z , , We write this as b | a 7
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Divisors Some common properties If a | 1, a = +1 or –1 nd en + r If a|b and b|a then a = +b or –b Any b Z divides 0 if b 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 8
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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 569 = 3 x 3 x 29 x 29 = 3 2 29 2 7569 = 3 x 3 x 29 x 29 = 3 x 29 5886 = 2 x 27 x 109 = 2 x 3 3 x 109 4900 = 7 2 x 5 2 x2 2 100 = ? 250 = ? This process is called Prime Factorization 9
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Greatest common divisor (GCD) Definition: Greatest Common Divisor This is the largest divisor of both a and b Given two integers a and b, the positive integer c is called their GCD or greatest common divisor if and nly if only if c| aand c| b Any divisor of both a and b also divides c Notation: gcd(a, b) = c Example: gcd(49,63) = ?
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Lecture7 - IS 2150 / TEL 2810 Introduction to Security...

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