Einar's lecture

# Einar's lecture - ICS 180 May 4th 2004 Guest Lecturer Einar...

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1 ICS 180 May 4th, 2004 Guest Lecturer: Einar Mykletun

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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, 3-DES, AES, Blowfish xrhombus Problem: Key Distribution

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4 Public Key Crypto Solves Key Distribution problem …but…
5 Public-Key Cryptography xrhombus Each user has a unique public-private 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 one-way function of the private- key (hard to compute private key from public one) xrhombus Used for key distribution/agreement, message encryption, and digital signatures

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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 “public-key” because Alice & Bob need only exchange public keys to set up a secret channel xrhombus Invented earlier by British at CESG
7 Public-Key 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

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8 Diffie-Hellman 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).

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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 Alice barb2right Bob: C K = E Bpub (K), C M = E K (M)
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