What were the circumstances that led to the development of our cognitive abilities from a primitive hominid to an essentially modern human? The answer to this question is of profound importance to understanding our present nature. Since the steep path of our cognitive development is the attribute that most distinguishes humans from other mammals, this is also a quest to determine human origins. This collection of outstanding scientific problems and the revelation of the many ways they can be addressed indicates the scope of the field to be explored and reveals some avenues along which...
What were the circumstances that led to the development of our cognitive abilities from a primitive hominid to an essentially modern human? The answer...
The central theme of this book is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three of its most basic aspects. The book contains more than 350 exercises and the text is largely self-contained. Much more sophisticated techniques have been brought to bear on the subject of Diophantine equations, and for this...
The central theme of this book is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in...
The computation of invariants of algebraic number fields such as integral bases, discriminants, prime decompositions, ideal class groups, and unit groups is important both for its own sake and for its numerous applications, for example, to the solution of Diophantine equations. The practical com- pletion of this task (sometimes known as the Dedekind program) has been one of the major achievements of computational number theory in the past ten years, thanks to the efforts of many people. Even though some practical problems still exist, one can consider the subject as solved in a satisfactory...
The computation of invariants of algebraic number fields such as integral bases, discriminants, prime decompositions, ideal class groups, and unit gro...
The Handbook of Elliptic and Hyperelliptic Curve Cryptography is the first exhaustive study of virtually all of the mathematical aspects of curve-based public key cryptography. This carefully constructed volume is a state-of-the-art study that explores both theory and applications. It provides a wealth of ready-to-use algorithms enabling fast implementation along with recommendations for selecting appropriate algorithms. The book also considers side-channel attacks and implementation aspects of smart cards. Broad, comprehensive coverage makes this a complete resource for elliptic and...
The Handbook of Elliptic and Hyperelliptic Curve Cryptography is the first exhaustive study of virtually all of the mathematical aspects of curve-base...
With the advent of powerful computing tools and numerous advances in math- ematics, computer science and cryptography, algorithmic number theory has become an important subject in its own right. Both external and internal pressures gave a powerful impetus to the development of more powerful al- gorithms. These in turn led to a large number of spectacular breakthroughs. To mention but a few, the LLL algorithm which has a wide range of appli- cations, including real world applications to integer programming, primality testing and factoring algorithms, sub-exponential class group and regulator...
With the advent of powerful computing tools and numerous advances in math- ematics, computer science and cryptography, algorithmic number theory has b...
This book constitutes the refereed post-conference proceedings of the Second International Algorithmic Number Theory Symposium, ANTS-II, held in Talence, France in May 1996. The 35 revised full papers included in the book were selected from a variety of submissions. They cover a broad spectrum of topics and report state-of-the-art research results in computational number theory and complexity theory. Among the issues addressed are number fields computation, Abelian varieties, factoring algorithms, finite fields, elliptic curves, algorithm complexity, lattice theory, and coding.
This book constitutes the refereed post-conference proceedings of the Second International Algorithmic Number Theory Symposium, ANTS-II, held in Talen...
With the advent of powerful computing tools and numerous advances in math- ematics, computer science and cryptography, algorithmic number theory has become an important subject in its own right. Both external and internal pressures gave a powerful impetus to the development of more powerful al- gorithms. These in turn led to a large number of spectacular breakthroughs. To mention but a few, the LLL algorithm which has a wide range of appli- cations, including real world applications to integer programming, primality testing and factoring algorithms, sub-exponential class group and regulator...
With the advent of powerful computing tools and numerous advances in math- ematics, computer science and cryptography, algorithmic number theory has b...
This book deals with several aspects of what is now called "explicit number theory." The central theme is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three of its most basic aspects. The local aspect, global aspect, and the third aspect is the theory of zeta and L-functions. This last aspect can be...
This book deals with several aspects of what is now called "explicit number theory." The central theme is the solution of Diophantine equations, i....
The central theme of this book is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three of its most basic aspects. The book contains more than 350 exercises and the text is largely self-contained. Much more sophisticated techniques have been brought to bear on the subject of Diophantine equations, and for this...
The central theme of this book is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in...
Written by an authority with great practical and teaching experience in the field, this book addresses a number of topics in computational number theory. Chapters one through five form a homogenous subject matter suitable for a six-month or year-long course in computational number theory. The subsequent chapters deal with more miscellaneous subjects.
Written by an authority with great practical and teaching experience in the field, this book addresses a number of topics in computational number t...
