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Unformatted text preview: An introduction to cryptography and cryptanalysis Edward Schaefer Santa Clara University eschaefer@scu.edu I have given history shortshrift in my attempt to get to modern cryptography as quickly as possible. As sources for these lectures I used conversations with K. Dyer, B. Kaliski, H.W. Lenstra, P. Makowski, Jr., K. McCurley, A. Odlyzko, C. Pomerance, M. Robshaw, and Y.L. Yin as well as the publications listed in the bibliography. I am very grateful to each person listed above. Any mistakes in this document are mine. Please notify me of any that you find at the above email address. Table of contents Part I: Introduction 1 Vocabulary 2 Concepts 3 History 4 Crash Course in Number Theory 4.1 Calculator Algorithms  Reducing a(mod m) and Repeated Squares 5 Running Time of Algorithms Part II: Cryptography 6 Simple Cryptosystems 7 Symmetric key cryptography 8 Finite Fields 9 Finite Fields, Part II 10 Modern Stream Ciphers 10.1 RC4 10.2 SelfSynchronizing Stream Ciphers 10.3 OneTime Pads 11 Modern Block Ciphers 11.1 Modes of Operation of a Block Cipher 11.2 The Block Cipher DES 11.3 The Block Cipher AES 12 Public Key Cryptography 12.1 RSA 12.2 Finite Field Discrete Logarithm Problem 12.3 Diffie Hellman Key Agreement 12.4 Lesser Used Public Key Cryptosystems 1 12.4.1 RSA for Message Exchange 12.4.2 ElGamal Message Exchange 12.4.3 Massey Omura Message Exchange 12.5 Elliptic Curve Cryptography 12.5.1 Elliptic Curves 12.5.2 Elliptic Curve Discrete Logarithm Problem 12.5.3 Elliptic Curve Cryptosystems 12.5.4 Elliptic Curve Diffie Hellman 12.5.5 Elliptic Curve ElGamal Message Exchange 13 Hash functions and Message Authentication Codes 13.1 The MD5 hash function 14 Signatures and Authentication 14.1 Signatures with RSA 14.2 ElGamal Signature System and Digital Signature Standard 14.3 Schnorr Authentication and Signature Scheme 14.4 Pairing based cryptography for digital signatures Part III: Applications of Cryptography 15 Public Key Infrastructure 15.1 Certificates 15.2 PGP and WebofTrust 16 Internet Security 16.1 Transport Layer Security 16.2 IPSec 17 Timestamping 18 KERBEROS 19 Key Management and Salting 20 Quantum Cryptography 21 Blind Signatures 22 Digital Cash 23 Secret Sharing 24 Committing to a Secret 25 Digital Elections Part IV: Cryptanalysis 26 Basic Concepts of Cryptanalysis 27 Historical Cryptanalysis 27.1 The Vigen` ere cipher 28 Cryptanalysis of modern stream ciphers 2 28.1 Continued Fractions 28.2 b/p Random Bit Generator 28.3 Linear Shift Register Random Bit Generator 29 Cryptanalysis of Block Ciphers 29.1 Brute Force Attack 29.2 Standard ASCII Attack 29.3 MeetintheMiddle Attack 29.4 Oneround Simplified AES 29.5 Linear Cryptanalysis 29.6 Differential Cryptanalysis 30 Attacks on Public Key Cryptography 30.1 Pollards algorithm 30.2 Factoring 30.2.1 Fermat Factorization 30.2.2 Factor Bases 30.2.3 Continued Fraction Factoring 30.2.4 H.W. Lenstra Jr.s Elliptic Curve Method of Factoring 30.2.5 Number Fields 30.2.6 The Number Field Sieve30....
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 Spring '12
 YoungheLiu

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