Computational number theory. (2016)

• Record Type: Book
• Further Information: Note: Abhijit Das.
• Other Names: Das, Abhijit, 1968-
• Contents: Arithmetic of Integers; Basic Arithmetic Operations; GCD; Congruences and Modular Arithmetic; Linear Congruences; Polynomial Congruences; Quadratic Congruences; Multiplicative Orders; Continued Fractions; Prime Number Theorem and Riemann Hypothesis; Running Times of Arithmetic Algorithms Arithmetic of Finite Fields; Existence and Uniqueness of Finite Fields; Representation of Finite Fields; Implementation of Finite Field Arithmetic; Some Properties of Finite Fields; Alternative Representations of Finite Fields; Computing Isomorphisms among Representations Arithmetic of Polynomials; Polynomials over Finite Fields; Finding Roots of Polynomials over Finite Fields; Factoring Polynomials over Finite Fields; Properties of Polynomials with Integer Coefficients; Factoring Polynomials with Integer Coefficients Arithmetic of Elliptic Curves ; What Is an Elliptic Curve?; Elliptic-Curve Group; Elliptic Curves over Finite Fields; Some Theory of Algebraic Curves; Pairing on Elliptic Curves; Elliptic-Curve Point Counting Primality Testing; Introduction to Primality Testing; Probabilistic Primality Testing; Deterministic Primality Testing; Primality Tests for Numbers of Special Forms Integer Factorization; Trial Division; Pollard’s Rho Method; Pollard’s p - 1 Method; Dixon’s Method; CFRAC Method; Quadratic Sieve Method; Cubic Sieve Method; Elliptic Curve Method; Number-Field Sieve Method Discrete Logarithms; Square-Root Methods; Algorithms for Prime Fields; Algorithms for Fields of Characteristic Two; Algorithms for General Extension Fields; Algorithms for Elliptic Curves (ECDLP) Large Sparse Linear Systems; Structured Gaussian Elimination; Lanczos Method; Wiedemann Method; Block Methods Public-Key Cryptography; Public-Key Encryption; Key Agreement; Digital Signatures; Entity Authentication; Pairing-Based Cryptography Appendix A: Background; Appendix B: Solutions to Selected Exercises Index
• Publisher Details: Place of publication not identified : Chapman and Hall/CRC
• Publication Date: 2016
• Extent: 1 online resource, illustrations
• Subjects: 512.70285; Number theory -- Data processing; Data encryption (Computer science); COMPUTERS / Security / Cryptography; MATHEMATICS / Applied; MATHEMATICS / Number Theory
• Languages: English
• ISBNs: 9781482205824; 1482205823
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.