lecture3

lecture3 - Lecture 3: Public Key Cryptography CS 392/6813:...

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Lecture 3: Public Key Cryptography CS 392/6813: Computer Security Fall 2009 Nitesh Saxena * Adopted from Previous Lectures by Nasir Memon 9/24/2009 Lecture 3: Pubic Key Cryptography 2 Course Administration ± Good/Bad News ± HW#1 will not be graded! ± Not a trick – just for the benefit of this course ± HW#2 due coming Monday (09/28) ± HW#3 will be posted soon after
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9/24/2009 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 9/24/2009 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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9/24/2009 Lecture 3: Pubic Key Cryptography 5 Private key cryptography revisited. ± Good : Quite efficient (as you’ll see from the HW#2 programming exercise on AES) ± Bad : Key distribution and management is a serious problem – for N users O(N 2) keys are needed Message Source Cryptanalyst Key Source Destination X X X ^ K ^ Y Secure Channel K Encryption Algorithm Decryption Algorithm 9/24/2009 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!) Plaintext input Public key directory Transmitted ciphertext Plaintext output Encryption algorithm Alice Decryption algorithm Bob Joy Mike Ted Bob Bob's public key Bob 's private key
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9/24/2009 Lecture 3: Pubic Key Cryptography 7 Public Key Encryption ± Two keys: ± public encryption key e ± private decryption key d ± Encryption easy when is known ± Decryption easy when is known ± Decryption hard when 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 ± What’s the difference? 9/24/2009 Lecture 3: Pubic Key Cryptography 8 Group: Definition (G,.) (where G is a set and . : GxG Æ 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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9/24/2009 Lecture 3: Pubic Key Cryptography 9 Divisors ± x divides y (written | ) if the remainder is 0 when is divided by ± 1|8, 2|8, 4|8, 8|8 ± The divisors of are the numbers that divide ± divisors of 8: {1,2,4,8} ± For every number ± 1| ± | 9/24/2009 Lecture 3: Pubic Key Cryptography 10
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This note was uploaded on 11/18/2009 for the course CS 6813 taught by Professor Saxena during the Fall '09 term at NYU Poly.

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lecture3 - Lecture 3: Public Key Cryptography CS 392/6813:...

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