lecture3

lecture3 - Lecture3:PublicKeyCryptography...

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Lecture 3: Public Key Cryptography CS 392/6813: Computer Security  Fall 2008 Nitesh Saxena     * Adopted from Previous Lectures by Nasir Memon   
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10/13/11 Lecture 3: Pubic Key Cryptography 2 Course Admin Good/Bad News HW#1 will not be graded! Not a trick – just for the benefit of this course HW#2 due coming Monday (09/22) HW#3 will be posted soon after
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10/13/11 Lecture 3: Pubic Key Cryptography 3 Outline of Today’s Lecture Public Key Crypto Overview Number Theory Background Public Key Encryption RSA ElGamal Public Key Signatures (digital signatures) RSA DSS
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10/13/11 Lecture 3: Pubic Key Cryptography 4 Recall: Private Key/Public Key  Cryptography Private Key : Sender and receiver share a  common (private) key Encryption and Decryption is done using the  private key Also called conventional/shared-key/single-key/  symmetric-key cryptography Public Key : Every user has a private key and  a public key Encryption is done using the public key and  Decryption using private key Also called two-key/asymmetric-key cryptography
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10/13/11 Lecture 3: Pubic Key Cryptography 5 Private key cryptography revisited. Good : Quite efficient (as you’ll see from the HW#2  exercise on AES) Bad : Key distribution and management is a serious  problem – for N users O(N 2)  keys are needed
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10/13/11 Lecture 3: Pubic Key Cryptography 6 Public key cryptography model Good : Key management problem potentially simpler Bad : Much slower than private key crypto (we’ll see  later!) 
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10/13/11 Lecture 3: Pubic Key Cryptography 7 Public Key Encryption Two keys: public encryption key  e private decryption key  d Encryption easy when  e  is known Decryption easy when  d  is known Decryption hard when  d  is not known We’ll study such public key encryption  schemes; first we need some number theory. Security notions/attacks very similar to what  we studied for private key encryption
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10/13/11 Lecture 3: Pubic Key Cryptography 8 Group: Definition (G,.) (where G is a set and . : GxG G) is said to be a  group if following properties are satisfied: 1. Closure  : for any a, b G, a.b   G 2. Associativity :  for any a, b, c     G, a.(b.c)=(a.b).c 3. Identity  : there is an identity element such that a.e  = e.a = a, for any a    G 4. Inverse  : there exists an element a -1  for every a in  G, such that a.a -1  = a -1 .a = e Abelian Group : Group which also satisfies  commutativity  , i.e., a.b=b.a Examples : (Z,+) ; (Z,*)?; (Z m , “modular addition”)
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10/13/11 Lecture 3: Pubic Key Cryptography 9 Definitions related to a group An element g in G is said to be a 
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lecture3 - Lecture3:PublicKeyCryptography...

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