Mollin R.A. RSA and public-key cryptography
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Mollin R.A. RSA and public-key cryptography / Mollin R.A. - Boca Raton: Chapman & Hall/CRC, 2003. - 291 p. - (Discrete mathematics and its applications; vol.21). - ISBN 1-58488-338-3.
 
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1 History and Basic Cryptographic Concepts ................ 1 1.1 Terminology ......................................... 1 1.2 Classical Ciphers .................................. 13 1.3 Classification of Attacks .......................... 25 2 Protocols, Discrete Log, and Diffie-Hellman ............ 33 2.1 Cryptographic Protocols ............................ 33 2.2 The Discrete Log Problem ........................... 39 2.3 Exponentiation Ciphers and Diffie-Hellman .......... 47 3 Public-Key Cryptography ................................ 53 3.1 One-Way Functions .................................. 53 3.2 Public-Key Cryptosystems and RSA ................... 60 3.3 ElGamal Cryptosystems .............................. 67 3.4 Symmetric vs. Asymmetric Cryptosystems ............. 73 3.5 Secret History of Public-Key Cryptography .......... 77 4 Probabilistic Primality Tests .......................... 79 4.1 Introduction ....................................... 79 4.2 Pseudoprimes and Carmichael Numbers ................ 81 4.3 Solovay-Strassen Test .............................. 84 4.4 Miller-Selfridge-Rabin Test ........................ 87 5 Factoring .............................................. 93 5.1 Universal Exponent Method .......................... 93 5.2 Pollard's p - 1 Method ............................. 96 5.3 Lenstra's Elliptic Curve Method .................... 99 5.4 Multipolynomial Quadratic Sieve ................... 104 5.5 The Number Field Sieve ............................ 108 6 Security of RSA ....................................... 111 6.1 Implementation Attacks ............................ 111 6.2 Exponent Attacks .................................. 115 6.3 Strong Moduli ..................................... 120 6.4 Generation of Random Primes ....................... 124 7 Authentication ........................................ 127 7.1 Identification, Impersonation, and Signatures ..... 127 7.2 Digital Signature Schemes ......................... 135 7.3 Digital Cash and Electronic Commerce .............. 143 8 Key Management ........................................ 153 8.1 Secret Sharing .................................... 153 8.2 Key Establishment ................................. 160 8.3 Public-Key Infrastructure (PKI) ................... 173 9 Applications and the Future ........................... 179 9.1 Secrecy and Authentication ........................ 179 9.2 Other Threats to System Security .................. 185 9.3 Wireless Security ................................. 190 9.4 Smart Cards and Biometrics ........................ 198 Appendix A: Letter Frequency Analysis ................. 203 Appendix B: Elementary Complexity Theory .............. 205 Appendix C: Fundamental Facts ......................... 212 Solutions to Odd-Numbered Exercises ................... 224 Bibliography .......................................... 249 List of Symbols ....................................... 267 Index ................................................. 268


Вверх Mollin R.A. RSA and public-key cryptography / Mollin R.A. - Boca Raton: Chapman & Hall/CRC, 2003. - 291 p. - (Discrete mathematics and its applications; vol.21). - ISBN 1-58488-338-3.

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