Cover -- Public-key CryptographyTheory and Practice -- Copyright -- Contents -- Preface -- Notations -- Overview -- Introduction -- Common Cryptographic Primitives -- The Classical Problem: Secure Transmission of Messages -- Key Exchange -- Digital Signatures -- Entity Authentication -- Secret Sharing -- Hashing -- Certification -- Public-key Cryptography -- The Mathematical Problems -- Realization of Key Pairs -- Public-key Cryptanalysis -- Some Cryptographic Terms -- Models of Attacks -- Models of Passive Attacks -- Public Versus Private Algorithms -- Mathematical Concepts -- Introduction -- Sets, Relations and Functions -- Set Operations -- Relations -- Functions -- The Axioms of Mathematics -- Groups -- Definition and Basic Properties -- Subgroups, Cosets and Quotient Groups -- Homomorphisms -- Generators and Orders -- Sylow's Theorem -- Rings -- Definition and Basic Properties -- Subrings, Ideals and Quotient Rings -- Homomorphisms -- Factorization in Rings -- Integers -- Divisibility -- Congruences -- Quadratic Residues -- Some Assorted Topics -- Polynomials -- Elementary Properties -- Roots of Polynomials -- Algebraic Elements and Extensions -- Vector Spaces and Modules -- Vector Spaces -- Modules -- Algebras -- Fields -- Splitting Fields and Algebraic Closure -- Elements of Galois Theory -- Finite Fields -- Existence and Uniqueness of Finite Fields -- Polynomials over Finite Fields -- Representation of Finite Fields -- Affine and Projective Curves -- Plane Curves -- Polynomial and Rational Functions on Plane Curves -- Maps Between Plane Curves -- Divisors on Plane Curves -- Elliptic Curves -- The Weierstrass Equation -- The Elliptic Curve Group -- Elliptic Curves over Finite Fields -- Hyperelliptic Curves -- The Defining Equations -- Polynomial and Rational Functions -- The Jacobian -- Number Fields -- Some Commutative Algebra.

Number Fields and Rings -- Unique Factorization of Ideals -- Norms of Ideals -- Rational Primes in Number Rings -- Units in a Number Ring -- p-adic Numbers -- The Arithmetic of p-adic Numbers -- The p-adic Valuation -- Hensel's Lemma -- Statistical Methods -- Random Variables and Their Probability Distributions -- Operations on Random Variables -- Expectation, Variance and Correlation -- Some Famous Probability Distributions -- Sample Mean, Variation and Correlation -- Algebraic and Number-theoretic Computations -- Introduction -- Complexity Issues -- Order Notations -- Randomized Algorithms -- Reduction Between Computational Problems -- Multiple-precision Integer Arithmetic -- Representation of Large Integers -- Basic Arithmetic Operations -- GCD -- Modular Arithmetic -- Elementary Number-theoretic Computations -- Primality Testing -- Generating Random Primes -- Modular Square Roots -- Arithmetic in Finite Fields -- Arithmetic in the Ring F2[X] -- Finite Fields of Characteristic 2 -- Selecting Suitable Finite Fields -- Factoring Polynomials over Finite Fields -- Arithmetic on Elliptic Curves -- Point Arithmetic -- Counting Points on Elliptic Curves -- Choosing Good Elliptic Curves -- Arithmetic on Hyperelliptic Curves -- Arithmetic in the Jacobian -- Counting Points in Jacobians of Hyperelliptic Curves -- Random Numbers -- Pseudorandom Bit Generators -- Cryptographically Strong Pseudorandom Bit Generators -- Seeding Pseudorandom Bit Generators -- The Intractable Mathematical Problems -- Introduction -- The Problems at a Glance -- The Integer Factorization Problem -- Older Algorithms -- The Quadratic Sieve Method -- Factorization Using Elliptic Curves -- The Number Field Sieve Method -- The Finite Field Discrete Logarithm Problem -- Square Root Methods -- The Index Calculus Method -- Algorithms for Prime Fields.

Algorithms for Fields of Characteristic 2 -- The Elliptic Curve Discrete Logarithm Problem (ECDLP) -- The MOV Reduction -- The SmartASS Method -- The Xedni Calculus Method -- The Hyperelliptic Curve Discrete Logarithm Problem -- Choosing the Factor Base -- Checking the Smoothness of a Divisor -- The Algorithm -- Solving Large Sparse Linear Systems over Finite Rings -- Structured Gaussian Elimination -- The Conjugate Gradient Method -- The Lanczos Method -- The Wiedemann Method -- The Subset Sum Problem -- The Low-Density Subset Sum Problem -- The Lattice-Basis Reduction Algorithm -- Cryptographic Algorithms -- Introduction -- Secure Transmission of Messages -- The RSA Public-key Encryption Algorithm -- The Rabin Public-key Encryption Algorithm -- The Goldwasser-Micali Encryption Algorithm -- The Blum-Goldwasser Encryption Algorithm -- The ElGamal Public-key Encryption Algorithm -- The Chor-Rivest Public-key Encryption Algorithm -- The XTR Public-key Encryption Algorithm -- The NTRU Public-key Encryption Algorithm -- Key Exchange -- Basic Key-Exchange Protocols -- Authenticated Key-Exchange Protocols -- Digital Signatures -- The RSA Digital Signature Algorithm -- The Rabin Digital Signature Algorithm -- The ElGamal Digital Signature Algorithm -- The Schnorr Digital Signature Algorithm -- The Nyberg-Rueppel Digital Signature Algorithm -- The Digital Signature Algorithm -- The Elliptic Curve Digital Signature Algorithm -- The XTR Signature Algorithm -- The NTRUSign Algorithm -- Blind Signature Schemes -- Undeniable Signature Schemes -- Signcryption -- Entity Authentication -- Passwords -- Challenge-Response Algorithms -- Zero-Knowledge Protocols -- Standards -- Introduction -- IEEE Standards -- The Data Types -- Conversion Among Data Types -- RSA Standards -- PKCS #1 -- PKCS #3 -- Cryptanalysis in Practice -- Introduction -- Side-Channel Attacks.

Timing Attack -- Power Analysis -- Fault Analysis -- Backdoor Attacks -- Attacks on RSA -- An Attack on ElGamal Signatures -- An Attack on ElGamal Encryption -- Countermeasures -- Quantum Computation and Cryptography -- Introduction -- Quantum Computation -- System -- Entanglement -- Evolution -- Measurement -- The Deutsch Algorithm -- Quantum Cryptography -- Quantum Cryptanalysis -- Shor's Algorithm for Computing Period -- Breaking RSA -- Factoring Integers -- Computing Discrete Logarithms -- Symmetric Techniques -- Introduction -- Block Ciphers -- A Case Study: DES -- The Advanced Standard: AES -- Multiple Encryption -- Modes of Operation -- Stream Ciphers -- Linear Feedback Shift Registers -- Stream Ciphers Based on LFSRs -- Hash Functions -- Merkle's Meta Method -- The Secure Hash Algorithm -- Key Exchange in Sensor Networks -- Complexity Theory and Cryptography -- Introduction -- Provably Difficult Computational Problems Are not Suitable -- One-way Functions and the Complexity Class UP -- Introduction -- Security Issues in a Sensor Network -- The Basic Bootstrapping Framework -- The Basic Random Key Predistribution Scheme -- The q-composite Scheme -- Multi-path Key Reinforcement -- Random Pairwise Scheme -- Multi-hop Range Extension -- Polynomial-pool-based Key Predistribution -- Pairwise Key Predistribution -- Grid-based Key Predistribution -- Matrix-based Key Predistribution -- Location-aware Key Predistribution -- Closest Pairwise Keys Scheme -- Location-aware Polynomial-pool-based Scheme -- Complexity Theoryand Cryptography -- Hints to Selected Exercises -- References -- Index.

Public-key Cryptography provides a comprehensive coverage of the mathematical tools required for understanding the techniques of public-key cryptography and cryptanalysis. Key topics covered in the book include common cryptographic primitives and symmetric techniques, quantum cryptography, complexity theory, and practical cryptanalytic techniques such as side-channel attacks and backdoor attacks.Organized into eight chapters and supplemented with four appendices, this book is designed to be a self-sufficient resource for all students, teachers and researchers interested in the field of cryptography.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2018. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.