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Elliptic Curves: Number Theory and Cryptography, Second Edition (Discrete Mathematics and Its Applications)
Elliptic Curves: Number Theory and Cryptography, Second Edition (Discrete Mathematics and Its Applications)
Over the last two or three decades, elliptic curves have been playing an increasingly important role both in number theory and in related fields such as cryptography. For example, in the 1980s, elliptic curves started being used in cryptography and elliptic curve techniques were developed for factorization and primality...
Topics in Mathematical Analysis (Series on Analysis, Applications and Computation)
Topics in Mathematical Analysis (Series on Analysis, Applications and Computation)
This volume consists of a series of lecture notes on mathematical analysis. The contributors have been selected on the basis of both their outstanding scientific level and their clarity of exposition. Thus, the present collection is particularly suited to young researchers and graduate students. Through this volume, the editors intend to provide...
Algorithmic Cryptanalysis (Cryptography and Network Security)
Algorithmic Cryptanalysis (Cryptography and Network Security)
Focusing on both private- and public-key cryptographic algorithms, this book describes algorithmic methods with cryptographically relevant examples. After introducing modern cryptography and elementary number theory and algebra, it covers linear algebra, sieving, brute force, algorithms based on the birthday paradox,...
An Introduction to Partial Differential Equations
An Introduction to Partial Differential Equations
"This is an introductory book on the subject of partial differential equations which is suitable for a large variety of basic courses on this topic. In particular, it can be used as a textbook or self-study book for large classes of readers with interests in mathematics, engineering, and related fields. Its usefulness stems from its clarity,...
Partial Differential Equations: Modelling and Numerical Simulation (Computational Methods in Applied Sciences)
Partial Differential Equations: Modelling and Numerical Simulation (Computational Methods in Applied Sciences)
This book is dedicated to Olivier Pironneau.

For more than 250 years partial differential equations have been clearly the most important tool available to mankind in order to understand a large variety of phenomena, natural at first and then those originating from human activity and technological development. Mechanics, physics and their...

The Arithmetic of Elliptic Curves (Graduate Texts in Mathematics)
The Arithmetic of Elliptic Curves (Graduate Texts in Mathematics)

The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic theory of elliptic curves in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. The book begins with a brief discussion of the...

An Introduction to Mathematical Cryptography (Undergraduate Texts in Mathematics)
An Introduction to Mathematical Cryptography (Undergraduate Texts in Mathematics)
This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required...
Real Analysis and Foundations, Second Edition (Textbooks in Mathematics)
Real Analysis and Foundations, Second Edition (Textbooks in Mathematics)

Students preparing for courses in real analysis often encounter either very exacting theoretical treatments or books without enough rigor to stimulate an in-depth understanding of the subject. Further complicating this, the field has not changed much over the past 150 years, prompting few authors to address the lackluster or overly complex...

DSP for MATLAB and LabVIEW III: Digital Filter Design (Synthesis Lectures on Signal Processing)
DSP for MATLAB and LabVIEW III: Digital Filter Design (Synthesis Lectures on Signal Processing)

This book is Volume III of the series DSP for MATLAB™ and LabVIEW™. Volume III covers digital filter design, including the specific topics of FIR design via windowed-ideal-lowpass filter, FIR highpass, bandpass, and bandstop filter design from windowed-ideal lowpass filters, FIR design using the transition-band-optimized Frequency...

Partial Differential Equations: Second Edition (Cornerstones)
Partial Differential Equations: Second Edition (Cornerstones)

This self-contained text offers an elementary introduction to partial differential equations (pdes), primarily focusing on linear equations, but also providing some perspective on nonlinear equations. The classical treatment is mathematically rigorous with a generally theoretical layout, though indications to some of the physical origins of pdes...

Guide to Elliptic Curve Cryptography (Springer Professional Computing)
Guide to Elliptic Curve Cryptography (Springer Professional Computing)
The study of elliptic curves by algebraists, algebraic geometers and number theorists
dates back to the middle of the nineteenth century. There now exists an extensive literature
that describes the beautiful and elegant properties of these marvelous objects. In
1984, Hendrik Lenstra described an ingenious algorithm for factoring
...
Algebraic Curves in Cryptography (Discrete Mathematics and Its Applications)
Algebraic Curves in Cryptography (Discrete Mathematics and Its Applications)

The reach of algebraic curves in cryptography goes far beyond elliptic curve or public key cryptography yet these other application areas have not been systematically covered in the literature. Addressing this gap, Algebraic Curves in Cryptography explores the rich uses of algebraic curves in a range of cryptographic...

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