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Unformatted text preview: 1 ICS 180 May 4th, 2004 Guest Lecturer: Einar Mykletun 2 Symmetric Key Crypto 3 Symmetric Key xrhombus Two users who wish to communicate share a secret key xrhombus Properties – High encryption speed – Limited applications: encryption – Based on permutations and substitutions – No mathematical assumptions xrhombus Candidates: DES, 3DES, AES, Blowfish xrhombus Problem: – Key Distribution 4 Public Key Crypto Solves Key Distribution problem …but… 5 PublicKey Cryptography xrhombus Each user has a unique publicprivate key pair Alice  K Apriv , K Apub Bob  K Bpriv , K Bpub xrhombus The public key can be given to anyone xrhombus The private key is not shared with anyone, including a trusted third party (authentication server) xrhombus The public key is a oneway function of the private key (hard to compute private key from public one) xrhombus Used for key distribution/agreement, message encryption, and digital signatures 6 Origins of Public Key xrhombus Concept credited to Diffie and Hellman, 1976 “New Directions in Cryptography” xrhombus Motivation  wanted a scheme whereby Alice could send a message to Bob without the need for Alice and Bob to share a secret or for a Trusted Third Party  called “publickey” because Alice & Bob need only exchange public keys to set up a secret channel xrhombus Invented earlier by British at CESG http://www.cesg.gov.uk/about/nsecret.htm 7 PublicKey Agreement xrhombus Method whereby Alice and Bob can agree on a secret key to use with DES, AES, or some other symmetric encryption algorithm – Need a shared secret xrhombus They do this after exchanging only public keys xrhombus They each compute a secret session key K derived from their own private key and the other’s public key. They both arrive at the same K independently 8 DiffieHellman Method 1) Shared prime p and generator g Alice: private x a and public y a = g Xa mod p Bob: private x b and public y b = g Xb mod p x a = log g y a mod p (hard to compute) 2) They swap public keys Alice computes: K = y b Xa mod p = g Xb Xa mod p Bob computes: K = y a Xb mod p = g Xa Xb mod p What can K be used for? 9 Math Strength Depends on difficulty of computing the discrete logarithm The best known methods are exponentially hard  same as factoring e.g., given n, find p, q where n = p * q Need to use numbers on the order of 768 bits (230 digits) or bigger Implementations typically use 512 (155), 1024 (310) or 2048 (621) bits (digits). 10 Sending Messages To send message M to Bob, only Bob’s key is used Alice barb2right Bob: C = E Bpub (M) Bob decrypts: M = D Bpriv (C) In practice, use to distribute symmetric key K...
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This note was uploaded on 01/30/2008 for the course ICS 180 taught by Professor Jarecki during the Spring '04 term at UC Irvine.
 Spring '04
 Jarecki

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