Prof. Jk LEE/security1 Secure Encryption Systems Prof. Jk LEE/security2 3.Secure Encryption Systems Symmetric encryption Asymmetric encryption Encryption algorithms DES,RSA and El Gamal Hash algorithms Clipper Prof. Jk LEE/security3 Hard Problems:complexity NP-complete problems: easy to state,no hard understand, straight forward to solve satisfiability: true or false Knapsack: target Clique: a graph in which each vertex is connected to every other vertex Prof. Jk LEE/security4 Characteristics of NP-complete problems The class P and NP NP-completeness and Cryptography Prof. Jk LEE/security5 Properties of Arithmetic Primes Greatest common divisor Modular arithmetic Properties of Modular Arithmetic Fermats theorem Algorithm for computing Inverses Prof. Jk LEE/security6 Public key encryption Systems Proposed by Diffie and Hellman 1976 Merkle-Hellman knapsacks Rivest-Shamir-Adelman(RSA) Encryption El Gamal and Digital Signature Algorithms Hash Algorithms Prof. Jk LEE/security7 Symmetric systems(SS) Symmetric systems(SS) Single key system-->symmetric system problem of ss: if the key revealed? Distribution of key? The number of keys increase? Weak about the attack? Prof. Jk LEE/security8 DES( data Encryption Standard ) Developed by US gov. for use by the general public Plain text:64bit key: 56bit Prof. Jk LEE/security9 Using Encryption:protocols and Practices Prof. Jk LEE/security10 Distributed center for EI Prof. Jk LEE/security11 Cycles of Substituition and Permutation Prof. Jk LEE/security12 A Cycle in the DES Prof. Jk LEE/security13 Prof. Jk LEE/security14 Prof. Jk LEE/security15 Prof. Jk LEE/security16 Key transformation Prof. Jk LEE/security17 Prof. Jk LEE/security18 P-Boxs Prof. Jk LEE/security19 Prof. Jk LEE/security20 Prof. Jk LEE/security21 Decryption Decryption Prof. Jk LEE/security22 DES 56 DES