crypto3-4 - 1 15-853 Page 1 15-853:Algorithms in the Real...

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Unformatted text preview: 1 15-853 Page 1 15-853:Algorithms in the Real World Cryptography 3 and 4 15-853 Page 2 Cryptography Outline Introduction: terminology, cryptanalysis, security Primitives: one-way functions, trapdoors, … Protocols: digital signatures, key exchange, .. Number Theory: groups, fields, … Private-Key Algorithms: Rijndael, DES Public-Key Algorithms: – Diffie-Hellman Key Exchange – RSA, El-Gamal, Blum-Goldwasser – Quantum Cryptography Case Studies: Kerberos, Digital Cash 15-853 Page 3 Public Key Cryptosystems Introduced by Diffie and Hellman in 1976. Encryption Decryption K 1 K 2 Cyphertext E k (M) = C D k (C) = M Original Plaintext Plaintext Public Key systems K 1 = public key K 2 = private key Digital signatures K 1 = private key K 2 = public key Typically used as part of a more complicated protocol. 15-853 Page 4 One-way trapdoor functions Both Public-Key and Digital signatures make use of one-way trapdoor functions. Public Key: – Encode: c = f(m) – Decode: m = f-1 (c) using trapdoor Digital Signatures: – Sign: c = f-1 (m) using trapdoor – Verify: m = f(c) 2 15-853 Page 5 Example of SSL (3.0) SSL ( Secure Socket Layer ) is the standard for the web ( https ). Protocol (somewhat simplified ): Bob -> amazon.com B->A: client hello : protocol version, acceptable ciphers A->B: server hello : cipher, session ID, |amazon.com| verisign B->A: key exchange , {masterkey} amazon’s public key A->B: server finish : ( [amazon,prev-messages,masterkey] ) key1 B->A: client finish : ( [bob,prev-messages,masterkey] ) key2 A->B: server message : (message1, [message1] ) key1 B->A: client message : (message2, [message2] ) key2 |h| issuer = Certificate = Issuer, <h,h’s public key, time stamp> issuer’s private key <…> private key = Digital signature {…} public key = Public-key encryption [..] = Secure Hash (…) key = Private-key encryption key1 and key2 are derived from masterkey and session ID hand- shake data 15-853 Page 6 Public Key History Some algorithms – Diffie-Hellman, 1976, key-exchange based on discrete logs – Merkle-Hellman , 1978, based on “knapsack problem” – McEliece , 1978, based on algebraic coding theory – RSA , 1978, based on factoring – Rabin , 1979, security can be reduced to factoring – ElGamal , 1985, based on discrete logs – Blum-Goldwasser, 1985, based on quadratic residues – Elliptic curves , 1985, discrete logs over Elliptic curves – Chor-Rivest, 1988, based on knapsack problem – NTRU , 1996, based on Lattices – XTR, 2000, based on discrete logs of a particular field 15-853 Page 7 Diffie-Hellman Key Exchange A group (G,*) and a primitive element (generator) g is made public. – Alice picks a, and sends g a to Bob – Bob picks b and sends g b to Alice – The shared key is g ab Note this is easy for Alice or Bob to compute, but assuming discrete logs are hard is hard for anyone else to compute....
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crypto3-4 - 1 15-853 Page 1 15-853:Algorithms in the Real...

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