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Unformatted text preview: Modern Cryptography Lecture 5 Yongdae Kim 2 Admin Stuff Email Subject should have [5471] in front, e.g. [5471] Project proposal CC TA and PostDoc: hkang@cs.umn.edu, aaram@cs.umn.edu Office hours Me: T 1:30 ~ 2:30, Th 10:00 ~ 11:00 (and by appointment) TA: M 1:15 PM ~ 2:15 PM Work on projects Full proposal due: Feb 23 (Firm Deadline: Read instruction) Meeting with groups: This week and next week 3rd assignment is due: 3/2 9:00 AM. Programming, Test vector, Your name Study Guide Come and talk to me and TA as much as possible. (Google chat is good!) Check Calendar 3 Recap Math Proof techniques Direct/Indirect proof, Proof by contradiction, Proof by cases, Existential/Universal Proof, Forward/backward reasoning Divisibility: a divides b (ab) if c such that b = ac GCD, LCM, relatively prime, existence of GCD Eucledean Algorithm d = gcd (a, b) x, y such that d = a x + b y. gcd(a, b) = gcd(a, b + ka) Modular Arithmetic a b (mod m ) iff m  ab iff a = b + mk for some k a b (mod m ), c d (mod m ) a+c ( b+d ) (mod m ), ac bd (mod m ) gcd(a, n) =1 a has an arithmetic inverse modulo n. 3 Recap Math Proof techniques Direct/Indirect proof, Proof by contradiction, Proof by cases, Existential/Universal Proof, Forward/backward reasoning Divisibility: a divides b (ab) if c such that b = ac GCD, LCM, relatively prime, existence of GCD Eucledean Algorithm d = gcd (a, b) x, y such that d = a x + b y. gcd(a, b) = gcd(a, b + ka) Modular Arithmetic a b (mod m ) iff m  ab iff a = b + mk for some k a b (mod m ), c d (mod m ) a+c ( b+d ) (mod m ), ac bd (mod m ) gcd(a, n) =1 a has an arithmetic inverse modulo n. Counting, probability, cardinality, 4 Recap (cnt) Security Symmetric Key vs. Public Key, Hash function, MAC, Digital signature, Key management through SKE and PKE, certificate Block Cipher Modes of operation and their properties: ECB, OFB, CFB, CBC, CTR Meetinthemiddle attack and the Double (triple) DES Feistal Cipher and DES 5 New Era! DES broken DES III Challenge by RSA Idle CPU time of around 100,000 computers In 22 hours Triple DES? Original DES was designed for H/W implementation 64 bit block size too small for security and efficiency Now what? 6 Advanced Encryption Standard In 1997, NIST issued a call for proposal Block length = 128 bit Key size = 128, 192, 256 bits In the first round, 15 algorithms were accepted Second round, 5 algorithms were selected In November 2001, final standard was published Rijndel, FIPS PUB 197 http://csrc.nist.gov/publications/fips/fips197/fips197.pdf Joan Daemen and Vincent Rijmen 7 AES Evaluation Criteria Security Actual security: compared with other submissions Randomness: output is indistinguishable from random...
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This note was uploaded on 10/21/2011 for the course CSCI 5471 taught by Professor Staff during the Spring '08 term at Minnesota.
 Spring '08
 Staff

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