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104 Number Theory Problems: From the Training of the USA IMO Team
104 Number Theory Problems: From the Training of the USA IMO Team
This challenging problem book by renowned US Olympiad coaches, mathematics teachers, and researchers develops a multitude of problem-solving skills needed to excel in mathematical contests and research in number theory. Offering inspiration and intellectual delight, the problems throughout the book encourage students to express their ideas,...
Public Key Cryptography: Applications and Attacks (IEEE Press Series on Information and Communication Networks Security)
Public Key Cryptography: Applications and Attacks (IEEE Press Series on Information and Communication Networks Security)

This book covers public-key cryptography, describing in depth all major public-key cryptosystems in current use, including ElGamal, RSA, Elliptic Curve, and digital signature schemes. It explains the underlying mathematics needed to build these schemes, and examines the most common techniques used in attacking them. Illustrated with many...

Fault Analysis in Cryptography (Information Security and Cryptography)
Fault Analysis in Cryptography (Information Security and Cryptography)

In the 1970s researchers noticed that radioactive particles produced by elements naturally present in packaging material could cause bits to flip in sensitive areas of electronic chips. Research into the effect of cosmic rays on semiconductors, an area of particular interest in the aerospace industry, led to methods of hardening electronic...

Quantum Attacks on Public-Key Cryptosystems
Quantum Attacks on Public-Key Cryptosystems

The cryptosystems based on the Integer Factorization Problem (IFP), the Discrete Logarithm Problem (DLP) and the Elliptic Curve Discrete Logarithm Problem (ECDLP) are essentially the only three types of practical public-key cryptosystems in use. The security of these cryptosystems relies heavily on these three infeasible problems, as no...

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...
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...
Applications of Algebra to Communications, Control, and Signal Processing (SpringerBriefs in Computer Science)
Applications of Algebra to Communications, Control, and Signal Processing (SpringerBriefs in Computer Science)

Over the last 50 years there have been an increasing number of applications of algebraic tools to solve problems in communications, in particular in the fields of error-control codes and cryptography. More recently, broader applications have emerged, requiring quite sophisticated algebra - for example, the Alamouti scheme in MIMO...

Cryptography and Public Key Infrastructure on the Internet
Cryptography and Public Key Infrastructure on the Internet
Cryptography and Public Key Infrastructure on the Internet provides a thorough overview of the subject. It explains how susceptible networks are to hacking and how cryptography can help. This comprehensive and practical guide covers:

* Public Key Infrastructures (PKIs); important when using cryptography in a large organisation,
...
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...
Operator Theory and Numerical Methods (Studies in Mathematics and its Applications)
Operator Theory and Numerical Methods (Studies in Mathematics and its Applications)
The authors provide a very sharp theoretical study of numerical methods used to solve partial diferential equations of elliptic and parabolic type. Every numerical scheme is thoroughly dissected. As a whole, everything fits together in a harmonious way.

The book is efficiently organized and each chapter concludes with a very informative
...
Advances in Elliptic Curve Cryptography (London Mathematical Society Lecture Note Series)
Advances in Elliptic Curve Cryptography (London Mathematical Society Lecture Note Series)
    Since the appearance of the authors' first volume on elliptic curve cryptography in 1999 there has been tremendous progress in the field. In some topics, particularly point counting, the progress has been spectacular. Other topics such as the Weil and Tate pairings have been applied in new and important ways to cryptographic...
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,...
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