Paul B. Garrett

Indeholder "Preface", "Introduction", "1. Simple Ciphers", " 1.1 The Shift Cipher", " 1.2 Reduction/Division Algorithm", " 1.3 The One-Time Pad", " 1.4 The Affine Cipher ", "2. Probability", " 2.1 Counting", " 2.2 Basic Ideas", " 2.3 Statistics of English", " 2.4 Attack on the Affine Cipher ", "3. Permutations", " 3.1 Substitutions", " 3.2 Transpositions", " 3.3 Permutations", " 3.4 Shuffles", " 3.5 Block Interleavers ", "4. A Serious Cipher", " 4.1 The Vigenere Cipher", " 4.2 LCMs and GCDs", " 4.3 Kasiski Attack", " 4.4 Expected Values", " 4.5 Friedman Attack ", "5. More Probability", " 5.1 Generating Functions", " 5.2 Variance, Standard Deviation", " 5.3 Chebycheff's Inequality", " 5.4 Law of Large Numbers ", "6. Modern Symmetric Ciphers", " 6.1 Design Goals", " 6.2 Data Encryption Standard", " 6.3 Advanced Encryption Standard ", "7. The Integers", " 7.1 Divisibility", " 7.2 Unique Factorization", " 7.3 Euclidean Algorithm", " 7.4 Multiplicative Inverses", " 7.5 Computing Inverses", " 7.6 Equivalence Relations", " 7.7 The Integers mod m", " 7.8 Primitive Roots, Discrete Logs ", "8. The Hill Cipher", " 8.1 Hill Cipher Operation", " 8.2 Hill Cipher Attacks ", "9. Complexity", " 9.1 Big-Oh/Little-Oh Notation", " 9.2 Bit-Operations", " 9.3 Probabilistic Algorithms", " 9.4 Complexity", " 9.5 Subexponential Algorithms", " 9.6 Kolmogorov Complexity", " 9.7 Linear Complexity", " 9.8 Worst-Case versus Expected ", "10. Public-Key Ciphers", " 10.1 Trapdoors", " 10.2 The RSA Cipher", " 10.3 Diffie-Hellman Key Exchange", " 10.4 ElGamal Cipher", " 10.5 Knapsack Ciphers", " 10.6 NTRU Cipher", " 10.7 Arithmetica Key Exchange", " 10.8 Quantum Cryptography", " 10.9 U.S. Export Regulations ", "11. Prime Numbers", " 11.1 Euclid's Theorem", " 11.2 Prime Number Theorem", " 11.3 Primes in Sequences", " 11.4 Chebycheff's Theorem", " 11.5 Sharpest Asymptotics", " 11.6 Riemann Hypothesis ", "12. Roots mod p", " 12.1 Fermat's Little Theorem", " 12.2 Factoring Special Expressions", " 12.3 Mersenne Numbers", " 12.4 More Examples", " 12.5 Exponentiation Algorithm", " 12.6 Square Roots mod p", " 12.7 Higher Roots mod p ", "13. Roots Mod Composites", " 13.1 Sun Ze's Theorem", " 13.2 Special Systems", " 13.3 Composite Moduli", " 13.4 Hensel's Lemma", " 13.5 Square-Root Oracles", " 13.6 Euler's Theorem", " 13.7 Facts about Primitive Roots", " 13.8 Euler's Criterion ", "14. Weak Multiplicativity", " 14.1 Weak Multiplicativity", " 14.2 Arithmetic Convolutions", " 14.3 Mobius Inversion ", "15. Quadratic Reciprocity", " 15.1 Square Roots", " 15.2 Quadratic Symbols", " 15.3 Multiplicative Property", " 15.4 Quadratic Reciprocity", " 15.5 Fast Computation ", "16. Pseudoprimes", " 16.1 Fermat Pseudoprimes", " 16.2 Non-Prime Pseudoprimes", " 16.3 Euler Pseudoprimes", " 16.4 Solovay-Strassen Test", " 16.5 Strong Pseudoprimes", " 16.6 Miller-Rabin Test ", "17. Groups", " 17.1 Groups", " 17.2 Subgroups", " 17.3 Lagrange's Theorem", " 17.4 Index of a Subgroup", " 17.5 Laws of Exponents", " 17.6 Cyclic Subgroups", " 17.7 Euler's Theorem", " 17.8 Exponents of Groups ", "18. Sketches of Protocols", " 18.1 Basic Public-Key Protocol", " 18.2 Diffie-Hellman Key Exchange", " 18.3 Secret Sharing", " 18.4 Oblivious Transfer", " 18.5 Zero-Knowledge Proofs", " 18.6 Authentication", " 18.7 e-Money, e-Commerce ", "19. Rings, Fields, Polynomials", " 19.1 Rings, Fields", " 19.2 Divisibility", " 19.3 Polynomial Rings", " 19.4 Euclidean Algorithm", " 19.5 Euclidean Rings ", "20. Cyclotomic Polynomials", " 20.1 Characteristics", " 20.2 Multiple Factors", " 20.3 Cyclotomic Polynomials", " 20.4 Primitive Roots", " 20.5 Primitive Roots mod p", " 20.6 Prime Powers", " 20.7 Counting Primitive Roots", " 20.8 Non-Existence", " 20.9 Search Algorithm ", "21. Random Number Generators", " 21.1 Fake One-Time Pads", " 21.2 Period of a pRNG", " 21.3 Congruential Generators", " 21.4 Feedback Shift Generators", " 21.5 Blum-Blum-Shub Generator", " 21.6 Naor-Reingold Generator", " 21.7 Periods of LCGs", " 21.8 Primitive Polynomials", " 21.9 Periods of LFSRs", " 21.10 Examples of Primitives", " 21.11 Testing for Primitivity", "22. More on Groups", " 22.1 Group Homomorphisms", " 22.2 Finite Cyclic Groups", " 22.3 Infinite Cyclic Groups", " 22.4 Roots and Powers in Groups", " 22.5 Square Root Algorithm ", "23. Pseudoprimality Proofs", " 23.1 Lambda Function", " 23.2 Carmichael Numbers", " 23.3 Euler Witnesses", " 23.4 Strong Witnesses ", "24. Factorization Attacks", " 24.1 Pollard's Rho Method", " 24.2 Pollard's p-1 method", " 24.3 Pocklington-Lehmer Criterion", " 24.4 Strong Primes", " 24.5 Primality Certificates ", "25. Modern Factorization Attacks", " 25.1 Gaussian Elimination", " 25.2 Random Squares Factoring", " 25.3 Dixon's Algorithm", " 25.4 Non-Sieving Quadratic Sieve", " 25.5 The Quadratic Sieve", " 25.6 Other Improvements ", "26. Finite Fields", " 26.1 Making Finite Fields", " 26.2 Examples of Field Extensions", " 26.3 Addition mod P", " 26.4 Multiplication mod P", " 26.5 Multiplicative Inverses mod P ", "27 Discrete Logs", " 27.1 Baby-step Giant-step", " 27.2 Pollard's Rho Method", " 27.3 The Index Calculus ", "28. Elliptic Curves", " 28.1 Abstract Discrete Logarithms", " 28.2 Discrete Log Ciphers", " 28.3 Elliptic Curves", " 28.4 Points at Infinity", " 28.5 Projective Elliptic Curves ", "29. More on Finite Fields", " 29.1 Ideals in Commutative Rings", " 29.2 Ring Homomorphisms", " 29.3 Quotient Rings", " 29.4 Maximal Ideals and Fields", " 29.5 Prime Ideals and Integral Domains", " 29.6 More on Field Extensions", " 29.7 Frobenius Automorphism", " 29.8 Counting Irreducibles", " 29.9 Counting Primitives ", "Appendices", " A1. Sets and Functions", " A2. Searching, Sorting", " A3. Vectors", " A4. Matrices", " A5. Stirling's Formula ", "Tables", " T1. Factorizations under 600", " T2. Primes Below 10,000", " T3. Primitive Roots under 100 ", "Bibliography", "Answers to Selected Exercises", "Index".

Lærebog og introduktion til kryptologi.… (mehr)