Introduction to Cryptography [Paperback]

1 Integers.- 1.1 Basics.- 1.2 Divisibility.- 1.3 Representation of Integers.- 1.4 O- and ?-Notation.- 1.5 Cost of Addition, Multiplication, and Division with Remainder.- 1.6 Polynomial Time.- 1.7 Greatest Common Divisor.- 1.8 Euclidean Algorithm.- 1.9 Extended Euclidean Algorithm.- 1.10 Analysis of the Extended Euclidean Algorithm.- 1.11 Factoring into Primes.- 1.12 Exercises.- 2 Congruences and Residue Class Rings.- 2.1 Congruences.- 2.2 Semigroups.- 2.3 Groups.- 2.4 Residue Class Rings.- 2.5 Fields.- 2.6 Division in the Residue Class Ring.- 2.7 Analysis of Operations in the Residue Class Ring.- 2.8 Multiplicative Group of Residues.- 2.9 Order of Group Elements.- 2.10 Subgroups.- 2.11 Fermats Little Theorem.- 2.12 Fast Exponentiation.- 2.13 Fast Evaluation of Power Products.- 2.14 Computation of Element Orders.- 2.15 The Chinese Remainder Theorem.- 2.16 Decomposition of the Residue Class Ring.- 2.17 A Formula for the Euler ?-Function.- 2.18 Polynomials.- 2.19 Polynomials over Fields.- 2.20 Structure of the Unit Group of Finite Fields.- 2.21 Structure of the Multiplicative Group of Residues mod a Prime Number.- 2.22 Exercises.- 3 Encryption.- 3.1 Encryption Schemes.- 3.2 Symmetric and Asymmetric Cryptosystems.- 3.3 Cryptanalysis.- 3.4 Alphabets and Words.- 3.5 Permutations.- 3.6 Block Ciphers.- 3.7 Multiple Encryption.- 3.8 Use of Block Ciphers.- 3.9 Stream Ciphers.- 3.10 Affine Cipher.- 3.11 Matrices and Linear Maps.- 3.12 Affine Linear Block Ciphers.- 3.13 Vigen?re, Hill, and Permutation Ciphers.- 3.14 Cryptanalysis of Affine Linear Block Ciphers.- 3.15 Exercises.- 4 Probability and Perfect Secrecy.- 4.1 Probability.- 4.2 Conditional Probability.- 4.3 Birthday Paradox.- 4.4 Perfect Secrecy.- 4.5 Vernam One-Time Pad.- 4.6 Random Numbers.- 4.7 Pseudorandom Numbers.- 4.8 Exercises.- 5 DES.- 5.1 Feistel Ciphers.- 5.2 DES Algorithm.- 5.3 An Example.- 5.4 Security of DES.- 5.5 Exercises.- 6 Prime Number Generation.- 6.1 Trial Division.- 6.2 Fermat Test.- 6.3 Carmichaell_