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properties of congruences) endobj 49 0 obj << /S /GoTo /D (section.2.3) >> endobj 52 0 obj (2.3 Solving linear congruences) endobj 53 0 obj << /S /GoTo /D (section.2.4) >> endobj 56 0 obj (2.4 The Chinese remainder theorem) endobj 57 0 obj << /S /GoTo /D (section.2.5) >> endobj 60 0 obj (2.5 Residue classes) endobj 61 0 obj << /S /GoTo /D (section.2.6) >> endobj 64 0 obj (2.6 Euler's phi function) endobj 65 0 obj << /S /GoTo /D (section.2.7) >> endobj 68 0 obj (2.7 Euler's theorem and Fermat's little theorem) endobj 69 0 obj << /S /GoTo /D (section.2.8) >> endobj 72 0 obj (2.8 Quadratic residues) endobj 73 0 obj << /S /GoTo /D (section.2.9) >> endobj 76 0 obj (2.9 Summations over divisors) endobj 77 0 obj << /S /GoTo /D (chapter.3) >> endobj 80 0 obj (3 Computing with large integers) endobj 81 0 obj << /S /GoTo /D (section.3.1) >> endobj 84 0 obj (3.1 Asymptotic notation) endobj 85 0 obj << /S /GoTo /D (section.3.2) >> endobj 88 0 obj (3.2 Machine models and complexity theory) endobj 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squares theorem) endobj 129 0 obj << /S /GoTo /D (section.4.6) >> endobj 132 0 obj (4.6 Rational reconstruction and applications) endobj 133 0 obj << /S /GoTo /D (section.4.7) >> endobj 136 0 obj (4.7 The RSA cryptosystem) endobj 137 0 obj << /S /GoTo /D (section.4.8) >> endobj 140 0 obj (4.8 Notes) endobj 141 0 obj << /S /GoTo /D (chapter.5) >> endobj 144 0 obj (5 The distribution of primes) endobj 145 0 obj << /S /GoTo /D (section.5.1) >> endobj 148 0 obj (5.1 Chebyshev's theorem on the density of primes) endobj 149 0 obj << /S /GoTo /D (section.5.2) >> endobj 152 0 obj (5.2 Bertrand's postulate) endobj 153 0 obj << /S /GoTo /D (section.5.3) >> endobj 156 0 obj (5.3 Mertens' theorem) endobj 157 0 obj << /S /GoTo /D (section.5.4) >> endobj 160 0 obj (5.4 The sieve of Eratosthenes) endobj 161 0 obj << /S /GoTo /D (section.5.5) >> endobj 164 0 obj (5.5 The prime number theorem \203and beyond) endobj 165 0 obj << /S /GoTo /D (section.5.6) >> endobj 168 0 obj (5.6 Notes) endobj 169 0 obj 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endobj 332 0 obj (11 Finding generators and discrete logarithms in Zp*) endobj 333 0 obj << /S /GoTo /D (section.11.1) >> endobj 336 0 obj (11.1 Finding a generator for Zp*) endobj 337 0 obj << /S /GoTo /D (section.11.2) >> endobj 340 0 obj (11.2 Computing discrete logarithms in Zp*) endobj 341 0 obj << /S /GoTo /D (section.11.3) >> endobj 344 0 obj (11.3 The Diffie--Hellman key establishment protocol) endobj 345 0 obj << /S /GoTo /D (section.11.4) >> endobj 348 0 obj (11.4 Notes) endobj 349 0 obj << /S /GoTo /D (chapter.12) >> endobj 352 0 obj (12 Quadratic reciprocity and computing modular square roots) endobj 353 0 obj << /S /GoTo /D (section.12.1) >> endobj 356 0 obj (12.1 The Legendre symbol) endobj 357 0 obj << /S /GoTo /D (section.12.2) >> endobj 360 0 obj (12.2 The Jacobi symbol) endobj 361 0 obj << /S /GoTo /D (section.12.3) >> endobj 364 0 obj (12.3 Computing the Jacobi symbol) endobj 365 0 obj << /S /GoTo /D (section.12.4) >> endobj 368 0 obj (12.4 Testing quadratic 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