Advertisement
| elliptic curve discrete logarithm problem: Advances in Cryptology — ASIACRYPT’98 Kazuo Ohta, Dingyi Pei, 2003-06-29 ASIACRYPT’98, the international conference covering all aspects of theory and application of cryptology and information security, is being held at Beijing Friendship Hotel from October 18 to 22. This is the fourth of the Asiacrypt conferences. ASIACRYPT’98 is sponsored by the State Key Laboratory of Information Security (SKLOIS), University of Science and Technology of China (USTC), and the Asiacrypt Steering Committee (ASC), in cooperation with the International Association for Cryptology Research (IACR). The 16-member Program Committee organized the scientific program and considered 118 submissions. Of these, 32 were accepted for presentation. The authors’ affiliations of the 118 submissions and the 32 accepted papers range over 18 and 13 countries or regions, respectively. The submitted version of each paper was sent to all members of the Program Committee and was extensively examined by at least three committee members and/or outside experts. The review process was rigorously blinded and the anonymity of each submission are maintained until the selection was completed. We followed the traditional policy that each member of the Program Committee could be an author of at most one accepted paper. These proceedings contain the revised versions of the 32 contributed talks as well as a short note written by one invited speaker. Comments from the Program Committee were taken into account in the revisions. However, the authors (not the committee) bear full responsibility for the contents of their papers. |
| elliptic curve discrete logarithm problem: Public-key Cryptography Abhijit Das, C. E. Veni Madhavan, 2009 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. |
| elliptic curve discrete logarithm problem: Elliptic Curve Public Key Cryptosystems Alfred J. Menezes, 2012-12-06 Elliptic curves have been intensively studied in algebraic geometry and number theory. In recent years they have been used in devising efficient algorithms for factoring integers and primality proving, and in the construction of public key cryptosystems. Elliptic Curve Public Key Cryptosystems provides an up-to-date and self-contained treatment of elliptic curve-based public key cryptology. Elliptic curve cryptosystems potentially provide equivalent security to the existing public key schemes, but with shorter key lengths. Having short key lengths means smaller bandwidth and memory requirements and can be a crucial factor in some applications, for example the design of smart card systems. The book examines various issues which arise in the secure and efficient implementation of elliptic curve systems. Elliptic Curve Public Key Cryptosystems is a valuable reference resource for researchers in academia, government and industry who are concerned with issues of data security. Because of the comprehensive treatment, the book is also suitable for use as a text for advanced courses on the subject. |
| elliptic curve discrete logarithm problem: Elliptic Curves Lawrence C. Washington, 2008-04-03 Like its bestselling predecessor, Elliptic Curves: Number Theory and Cryptography, Second Edition develops the theory of elliptic curves to provide a basis for both number theoretic and cryptographic applications. With additional exercises, this edition offers more comprehensive coverage of the fundamental theory, techniques, and application |
| elliptic curve discrete logarithm problem: Innovative Mobile and Internet Services in Ubiquitous Computing Leonard Barolli, Fatos Xhafa, Nadeem Javaid, Tomoya Enokido, 2018-06-07 This book presents the latest research findings, methods and development techniques related to Ubiquitous and Pervasive Computing (UPC) as well as challenges and solutions from both theoretical and practical perspectives with an emphasis on innovative, mobile and internet services. With the proliferation of wireless technologies and electronic devices, there is a rapidly growing interest in Ubiquitous and Pervasive Computing (UPC). UPC makes it possible to create a human-oriented computing environment where computer chips are embedded in everyday objects and interact with physical world. It also allows users to be online even while moving around, providing them with almost permanent access to their preferred services. Along with a great potential to revolutionize our lives, UPC also poses new research challenges. |
| elliptic curve discrete logarithm problem: Elliptic Curves in Cryptography Ian F. Blake, G. Seroussi, N. Smart, 1999-07-08 This book summarizes knowledge built up within Hewlett-Packard over a number of years, and explains the mathematics behind practical implementations of elliptic curve systems. Due to the advanced nature of the mathematics there is a high barrier to entry for individuals and companies to this technology. Hence this book will be invaluable not only to mathematicians wanting to see how pure mathematics can be applied but also to engineers and computer scientists wishing (or needing) to actually implement such systems. |
| elliptic curve discrete logarithm problem: Finite Fields and Applications Dieter Jungnickel, H. Niederreiter, 2012-12-06 This volume represents the refereed proceedings of the Fifth International Conference on Finite Fields and Applications (F q5) held at the University of Augsburg (Germany) from August 2-6, 1999, and hosted by the Department of Mathematics. The conference continued a series of biennial international conferences on finite fields, following earlier conferences at the University of Nevada at Las Vegas (USA) in August 1991 and August 1993, the University ofGlasgow (Scotland) in July 1995, and the University ofWaterloo (Canada) in August 1997. The Organizing Committee of F q5 comprised Thomas Beth ( |
| elliptic curve discrete logarithm problem: Computational Cryptography Joppe Bos, Martijn Stam, 2021-12-09 The area of computational cryptography is dedicated to the development of effective methods in algorithmic number theory that improve implementation of cryptosystems or further their cryptanalysis. This book is a tribute to Arjen K. Lenstra, one of the key contributors to the field, on the occasion of his 65th birthday, covering his best-known scientific achievements in the field. Students and security engineers will appreciate this no-nonsense introduction to the hard mathematical problems used in cryptography and on which cybersecurity is built, as well as the overview of recent advances on how to solve these problems from both theoretical and practical applied perspectives. Beginning with polynomials, the book moves on to the celebrated Lenstra-Lenstra-Lovász lattice reduction algorithm, and then progresses to integer factorization and the impact of these methods to the selection of strong cryptographic keys for usage in widely used standards. |
| elliptic curve discrete logarithm problem: Handbook of Elliptic and Hyperelliptic Curve Cryptography Henri Cohen, Gerhard Frey, Roberto Avanzi, Christophe Doche, Tanja Lange, Kim Nguyen, Frederik Vercauteren, 2005-07-19 The discrete logarithm problem based on elliptic and hyperelliptic curves has gained a lot of popularity as a cryptographic primitive. The main reason is that no subexponential algorithm for computing discrete logarithms on small genus curves is currently available, except in very special cases. Therefore curve-based cryptosystems require much smaller key sizes than RSA to attain the same security level. This makes them particularly attractive for implementations on memory-restricted devices like smart cards and in high-security applications. The Handbook of Elliptic and Hyperelliptic Curve Cryptography introduces the theory and algorithms involved in curve-based cryptography. After a very detailed exposition of the mathematical background, it provides ready-to-implement algorithms for the group operations and computation of pairings. It explores methods for point counting and constructing curves with the complex multiplication method and provides the algorithms in an explicit manner. It also surveys generic methods to compute discrete logarithms and details index calculus methods for hyperelliptic curves. For some special curves the discrete logarithm problem can be transferred to an easier one; the consequences are explained and suggestions for good choices are given. The authors present applications to protocols for discrete-logarithm-based systems (including bilinear structures) and explain the use of elliptic and hyperelliptic curves in factorization and primality proving. Two chapters explore their design and efficient implementations in smart cards. Practical and theoretical aspects of side-channel attacks and countermeasures and a chapter devoted to (pseudo-)random number generation round off the exposition. The broad coverage of all- important areas makes this book a complete handbook of elliptic and hyperelliptic curve cryptography and an invaluable reference to anyone interested in this exciting field. |
| elliptic curve discrete logarithm problem: Selected Areas in Cryptography Mitsuru Matsui, Robert Zuccherato, 2004-05-17 This book constitutes the thoroughly refereed postproceedings of the 10th Annual International Workshop on Selected Areas in Cryptography, SAC 2003, held in Ottawa, Canada, in August 2003. The 25 revised full papers presented were carefully selected from 85 submissions during two rounds of reviewing and improvement. The papers are organized in topical sections on elliptic and hyperelliptic curves, side channel attacks, security protocols and applications, cryptanalysis, cryptographic primitives, stream ciphers, and efficient implementations. |
| elliptic curve discrete logarithm problem: Mathematics of Public Key Cryptography Steven D. Galbraith, 2012-03-15 This advanced graduate textbook gives an authoritative and insightful description of the major ideas and techniques of public key cryptography. |
| elliptic curve discrete logarithm problem: The Arithmetic of Elliptic Curves Joseph H. Silverman, 2013-03-09 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 approach in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. Following a brief discussion of the necessary algebro-geometric results, the book proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local fields, and global fields. Final chapters deal with integral and rational points, including Siegels theorem and explicit computations for the curve Y = X + DX, while three appendices conclude the whole: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and an overview of more advanced topics. |
| elliptic curve discrete logarithm problem: Guide to Elliptic Curve Cryptography Darrel Hankerson, Alfred J. Menezes, Scott Vanstone, 2006-06-01 After two decades of research and development, elliptic curve cryptography now has widespread exposure and acceptance. Industry, banking, and government standards are in place to facilitate extensive deployment of this efficient public-key mechanism. Anchored by a comprehensive treatment of the practical aspects of elliptic curve cryptography (ECC), this guide explains the basic mathematics, describes state-of-the-art implementation methods, and presents standardized protocols for public-key encryption, digital signatures, and key establishment. In addition, the book addresses some issues that arise in software and hardware implementation, as well as side-channel attacks and countermeasures. Readers receive the theoretical fundamentals as an underpinning for a wealth of practical and accessible knowledge about efficient application. Features & Benefits: * Breadth of coverage and unified, integrated approach to elliptic curve cryptosystems * Describes important industry and government protocols, such as the FIPS 186-2 standard from the U.S. National Institute for Standards and Technology * Provides full exposition on techniques for efficiently implementing finite-field and elliptic curve arithmetic * Distills complex mathematics and algorithms for easy understanding * Includes useful literature references, a list of algorithms, and appendices on sample parameters, ECC standards, and software tools This comprehensive, highly focused reference is a useful and indispensable resource for practitioners, professionals, or researchers in computer science, computer engineering, network design, and network data security. |
| elliptic curve discrete logarithm problem: The Development of the Number Field Sieve Arjen K. Lenstra, Hendrik W.Jr. Lenstra, 2006-11-15 The number field sieve is an algorithm for finding the prime factors of large integers. It depends on algebraic number theory. Proposed by John Pollard in 1988, the method was used in 1990 to factor the ninth Fermat number, a 155-digit integer. The algorithm is most suited to numbers of a special form, but there is a promising variant that applies in general. This volume contains six research papers that describe the operation of the number field sieve, from both theoretical and practical perspectives. Pollard's original manuscript is included. In addition, there is an annotated bibliography of directly related literature. |
| elliptic curve discrete logarithm problem: Recommendation for Pair-Wise Key Establishment Schemes Using Discrete Logarithm Cryptography Elaine Barker, National Institute of Standards and Technology (U.S.), Don Johnson, Miles Smid, 2007-03-30 This Recommendation specifies key establishment schemes using discrete logarithm cryptography, based on standards developed by the Accredited Standards Committee (ASC) X9, Inc.: ANS X9.42 (Agreement of Symmetric Keys Using Discrete Logarithm Cryptography) and ANS X9.63 (Key Agreement and Key Transport Using Elliptic Curve Cryptography). |
| elliptic curve discrete logarithm problem: Number Theory and Cryptography Marc Fischlin, Stefan Katzenbeisser, 2013-11-21 Johannes Buchmann is internationally recognized as one of the leading figures in areas of computational number theory, cryptography and information security. He has published numerous scientific papers and books spanning a very wide spectrum of interests; besides R&D he also fulfilled lots of administrative tasks for instance building up and directing his research group CDC at Darmstadt, but he also served as the Dean of the Department of Computer Science at TU Darmstadt and then went on to become Vice President of the university for six years (2001-2007). This festschrift, published in honor of Johannes Buchmann on the occasion of his 60th birthday, contains contributions by some of his colleagues, former students and friends. The papers give an overview of Johannes Buchmann's research interests, ranging from computational number theory and the hardness of cryptographic assumptions to more application-oriented topics such as privacy and hardware security. With this book we celebrate Johannes Buchmann's vision and achievements. |
| elliptic curve discrete logarithm problem: Cryptography for Developers Tom St Denis, 2006-12-01 The only guide for software developers who must learn and implement cryptography safely and cost effectively.Cryptography for Developers begins with a chapter that introduces the subject of cryptography to the reader. The second chapter discusses how to implement large integer arithmetic as required by RSA and ECC public key algorithms The subsequent chapters discuss the implementation of symmetric ciphers, one-way hashes, message authentication codes, combined authentication and encryption modes, public key cryptography and finally portable coding practices. Each chapter includes in-depth discussion on memory/size/speed performance trade-offs as well as what cryptographic problems are solved with the specific topics at hand. - The author is the developer of the industry standard cryptographic suite of tools called LibTom - A regular expert speaker at industry conferences and events on this development |
| elliptic curve discrete logarithm problem: Advances in Elliptic Curve Cryptography Ian F. Blake, Gadiel Seroussi, Nigel P. Smart, 2005-04-25 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 protocols that hold great promise. Notions such as provable security, side channel analysis and the Weil descent technique have also grown in importance. This second volume addresses these advances and brings the reader up to date. Prominent contributors to the research literature in these areas have provided articles that reflect the current state of these important topics. They are divided into the areas of protocols, implementation techniques, mathematical foundations and pairing based cryptography. Each of the topics is presented in an accessible, coherent and consistent manner for a wide audience that will include mathematicians, computer scientists and engineers. |
| elliptic curve discrete logarithm problem: Information Security Applications Hyoungshick Kim, 2021-10-26 This book constitutes the revised selected papers from the 22nd International Conference on Information Security Applications, WISA 2021, which took place on Jeju Island, South Korea, during August 2021. The 23 papers included in this book were carefully reviewed and selected from 66 submissions. They were organized in topical sections as follows: machine learning security; cryptography; hardware security; and application security. |
| elliptic curve discrete logarithm problem: EC Cryptography Tutorials - Herong's Tutorial Examples Herong Yang, 2019-04-20 This EC (Elliptic Curve) cryptography tutorial book is a collection of notes and sample codes written by the author while he was learning cryptography technologies himself. Topics include rule of chord and point addition on elliptic curves; Abelian groups with additive/multiplicative notations; EC as Abelian groups; DLP (Discrete Logarithm Problem) and trapdoor function; Galois fields or finite fields with Additive/Multiplicative Abelian Group; Prime fields, binary fields, and polynomial fields; EC fields reduced with modular arithmetic; EC subgroup and base points; EC private key and public key pairs; ECDH (Elliptic Curve Diffie-Hellman) protocol; ECDSA (Elliptic Curve Digital Signature Algorithm); ECES (Elliptic Curve Encryption Scheme) protocol; Java tool/program to generate EC keys. Updated in 2024 (Version v1.03) with minor changes. For latest updates and free sample chapters, visit https://www.herongyang.com/EC-Cryptography. |
| elliptic curve discrete logarithm problem: Advances in Cryptology – ASIACRYPT 2017 Tsuyoshi Takagi, Thomas Peyrin, 2017-11-17 The three-volume set LNCS 10624, 10625, 10626 constitutes the refereed proceedings of the 23rd International Conference on the Theory and Applications of Cryptology and Information Security, ASIACRYPT 2017, held in Hong Kong, China, in December 2017.The 65 revised full papers were carefully selected from 243 submissions. They are organized in topical sections on Post-Quantum Cryptography; Symmetric Key Cryptanalysis; Lattices; Homomorphic Encryptions; Access Control; Oblivious Protocols; Side Channel Analysis; Pairing-based Protocols; Quantum Algorithms; Elliptic Curves; Block Chains; Multi-Party Protocols; Operating Modes Security Proofs; Cryptographic Protocols; Foundations; Zero-Knowledge Proofs; and Symmetric Key Designs. |
| elliptic curve discrete logarithm problem: Security in Communication Networks Stelvio Cimato, Clemente Galdi, Giuseppe Persiano, 2003-07-01 This book constitutes the thoroughly refereed post-proceedings of the Third International Conference on Security in Communication Networks, SCN 2002, held in Amalfi, Italy in September 2002. The 24 revised full papers presented together with two invited papers were carefully selected from 90 submissions during two rounds of reviewing and revision. The papers are organized in topical sections on forward security, foundations of cryptography, key management, cryptanalysis, systems security, digital signature schemes, zero knowledge, and information theory and secret sharing. |
| elliptic curve discrete logarithm problem: Advances in Cryptology — ASIACRYPT 2001 Colin Boyd, 2003-06-30 The origins of the Asiacrypt series of conferences can be traced back to 1990, when the ?rst Auscrypt conference was held, although the name Asiacrypt was ?rst used for the 1991 conference in Japan. Starting with Asiacrypt 2000, the conference is now one of three annual conferences organized by the Inter- tional Association for Cryptologic Research (IACR). The continuing success of Asiacrypt is in no small part due to the e?orts of the Asiacrypt Steering C- mittee (ASC) and the strong support of the IACR Board of Directors. There were 153 papers submitted to Asiacrypt 2001 and 33 of these were accepted for inclusion in these proceedings. The authors of every paper, whether accepted or not, made a valued contribution to the success of the conference. Sending out rejection noti?cations to so many hard working authors is one of the most unpleasant tasks of the Program Chair. The review process lasted some 10 weeks and consisted of an initial refe- eing phase followed by an extensive discussion period. My heartfelt thanks go to all members of the Program Committee who put in extreme amounts of time to give their expert analysis and opinions on the submissions. All papers were reviewed by at least three committee members; in many cases, particularly for those papers submitted by committee members, additional reviews were obt- ned. Specialist reviews were provided by an army of external reviewers without whom our decisions would have been much more di?cult. |
| elliptic curve discrete logarithm problem: Guide to Pairing-Based Cryptography Nadia El Mrabet, Marc Joye, 2017-01-06 This book is devoted to efficient pairing computations and implementations, useful tools for cryptographers working on topics like identity-based cryptography and the simplification of existing protocols like signature schemes. As well as exploring the basic mathematical background of finite fields and elliptic curves, Guide to Pairing-Based Cryptography offers an overview of the most recent developments in optimizations for pairing implementation. Each chapter includes a presentation of the problem it discusses, the mathematical formulation, a discussion of implementation issues, solutions accompanied by code or pseudocode, several numerical results, and references to further reading and notes. Intended as a self-contained handbook, this book is an invaluable resource for computer scientists, applied mathematicians and security professionals interested in cryptography. |
| elliptic curve discrete logarithm problem: Elliptic Curves and Their Applications to Cryptography Andreas Enge, 1999-08-31 Since their invention in the late seventies, public key cryptosystems have become an indispensable asset in establishing private and secure electronic communication, and this need, given the tremendous growth of the Internet, is likely to continue growing. Elliptic curve cryptosystems represent the state of the art for such systems. Elliptic Curves and Their Applications to Cryptography: An Introduction provides a comprehensive and self-contained introduction to elliptic curves and how they are employed to secure public key cryptosystems. Even though the elegant mathematical theory underlying cryptosystems is considerably more involved than for other systems, this text requires the reader to have only an elementary knowledge of basic algebra. The text nevertheless leads to problems at the forefront of current research, featuring chapters on point counting algorithms and security issues. The Adopted unifying approach treats with equal care elliptic curves over fields of even characteristic, which are especially suited for hardware implementations, and curves over fields of odd characteristic, which have traditionally received more attention. Elliptic Curves and Their Applications: An Introduction has been used successfully for teaching advanced undergraduate courses. It will be of greatest interest to mathematicians, computer scientists, and engineers who are curious about elliptic curve cryptography in practice, without losing the beauty of the underlying mathematics. |
| elliptic curve discrete logarithm problem: Modern Cryptography and Elliptic Curves Thomas R. Shemanske, 2017-07-31 This book offers the beginning undergraduate student some of the vista of modern mathematics by developing and presenting the tools needed to gain an understanding of the arithmetic of elliptic curves over finite fields and their applications to modern cryptography. This gradual introduction also makes a significant effort to teach students how to produce or discover a proof by presenting mathematics as an exploration, and at the same time, it provides the necessary mathematical underpinnings to investigate the practical and implementation side of elliptic curve cryptography (ECC). Elements of abstract algebra, number theory, and affine and projective geometry are introduced and developed, and their interplay is exploited. Algebra and geometry combine to characterize congruent numbers via rational points on the unit circle, and group law for the set of points on an elliptic curve arises from geometric intuition provided by Bézout's theorem as well as the construction of projective space. The structure of the unit group of the integers modulo a prime explains RSA encryption, Pollard's method of factorization, Diffie–Hellman key exchange, and ElGamal encryption, while the group of points of an elliptic curve over a finite field motivates Lenstra's elliptic curve factorization method and ECC. The only real prerequisite for this book is a course on one-variable calculus; other necessary mathematical topics are introduced on-the-fly. Numerous exercises further guide the exploration. |
| elliptic curve discrete logarithm problem: Advances on Smart and Soft Computing Faisal Saeed, Tawfik Al-Hadhrami, Fathey Mohammed, Errais Mohammed, 2020-10-19 This book gathers high-quality papers presented at the First International Conference of Advanced Computing and Informatics (ICACIn 2020), held in Casablanca, Morocco, on April 12–13, 2020. It covers a range of topics, including artificial intelligence technologies and applications, big data analytics, smart computing, smart cities, Internet of things (IoT), data communication, cloud computing, machine learning algorithms, data stream management and analytics, deep learning, data mining applications, information retrieval, cloud computing platforms, parallel processing, natural language processing, predictive analytics, knowledge management approaches, information security, security in IoT, big data and cloud computing, high-performance computing and computational informatics. |
| elliptic curve discrete logarithm problem: Cryptography and Secure Communication Richard E. Blahut, 2014-03-27 This fascinating book presents the timeless mathematical theory underpinning cryptosystems both old and new, written specifically with engineers in mind. Ideal for graduate students and researchers in engineering and computer science, and practitioners involved in the design of security systems for communications networks. |
| elliptic curve discrete logarithm problem: Algebraic Function Fields and Codes Henning Stichtenoth, 2009-02-11 This book links two subjects: algebraic geometry and coding theory. It uses a novel approach based on the theory of algebraic function fields. Coverage includes the Riemann-Rock theorem, zeta functions and Hasse-Weil's theorem as well as Goppa' s algebraic-geometric codes and other traditional codes. It will be useful to researchers in algebraic geometry and coding theory and computer scientists and engineers in information transmission. |
| elliptic curve discrete logarithm problem: Rational Points on Modular Elliptic Curves Henri Darmon, 2004 The book surveys some recent developments in the arithmetic of modular elliptic curves. It places a special emphasis on the construction of rational points on elliptic curves, the Birch and Swinnerton-Dyer conjecture, and the crucial role played by modularity in shedding light on these two closely related issues. The main theme of the book is the theory of complex multiplication, Heegner points, and some conjectural variants. The first three chapters introduce the background and prerequisites: elliptic curves, modular forms and the Shimura-Taniyama-Weil conjecture, complex multiplication and the Heegner point construction. The next three chapters introduce variants of modular parametrizations in which modular curves are replaced by Shimura curves attached to certain indefinite quaternion algebras. The main new contributions are found in Chapters 7-9, which survey the author's attempts to extend the theory of Heegner points and complex multiplication to situations where the base field is not a CM field. Chapter 10 explains the proof of Kolyvagin's theorem, which relates Heegner points to the arithmetic of elliptic curves and leads to the best evidence so far for the Birch and Swinnerton-Dyer conjecture. |
| elliptic curve discrete logarithm problem: Random Curves Neal Koblitz, 2009-05-03 Neal Koblitz is a co-inventor of one of the two most popular forms of encryption and digital signature, and his autobiographical memoirs are collected in this volume. Besides his own personal career in mathematics and cryptography, Koblitz details his travels to the Soviet Union, Latin America, Vietnam and elsewhere; political activism; and academic controversies relating to math education, the C. P. Snow two-culture problem, and mistreatment of women in academia. These engaging stories fully capture the experiences of a student and later a scientist caught up in the tumultuous events of his generation. |
| elliptic curve discrete logarithm problem: A Course in Number Theory and Cryptography Neal Koblitz, 2012-09-05 This is a substantially revised and updated introduction to arithmetic topics, both ancient and modern, that have been at the centre of interest in applications of number theory, particularly in cryptography. As such, no background in algebra or number theory is assumed, and the book begins with a discussion of the basic number theory that is needed. The approach taken is algorithmic, emphasising estimates of the efficiency of the techniques that arise from the theory, and one special feature is the inclusion of recent applications of the theory of elliptic curves. Extensive exercises and careful answers are an integral part all of the chapters. |
| elliptic curve discrete logarithm problem: Algorithmic Cryptanalysis Antoine Joux, 2009-06-15 Illustrating the power of algorithms, Algorithmic Cryptanalysis describes algorithmic methods with cryptographically relevant examples. Focusing on both private- and public-key cryptographic algorithms, it presents each algorithm either as a textual description, in pseudo-code, or in a C code program.Divided into three parts, the book begins with a |
| elliptic curve discrete logarithm problem: Advances in Cryptology - Crypto '88 Shafi Goldwasser, 2014-01-15 |
| elliptic curve discrete logarithm problem: Post-Quantum Cryptography Jintai Ding, Jean-Pierre Tillich, 2020-03-27 This volume constitutes the proceedings of the 11th International Conference on post-quantum cryptography, PQCrypto 2020, held in Paris, France in April 2020. The 29 full papers presented in this volume were carefully reviewed and selected from 86 submissions. They cover a broad spectrum of research within the conference's scope, including code-, hash-, isogeny-, and lattice-based cryptography, multivariate cryptography, and quantum cryptanalysis. |
| elliptic curve discrete logarithm problem: Rational Points on Elliptic Curves Joseph H. Silverman, John Tate, 2013-04-17 The theory of elliptic curves involves a blend of algebra, geometry, analysis, and number theory. This book stresses this interplay as it develops the basic theory, providing an opportunity for readers to appreciate the unity of modern mathematics. The book’s accessibility, the informal writing style, and a wealth of exercises make it an ideal introduction for those interested in learning about Diophantine equations and arithmetic geometry. |
| elliptic curve discrete logarithm problem: Selected Areas in Cryptography Roberto Avanzi, Liam Keliher, Francesco Sica, 2009-08-22 This volume constitutes the selected papers of the 15th Annual International Workshop on Selected Areas in Cryptography, SAC 2008, held in Sackeville, New Brunswick, Canada, in August 14-15, 2008. From a total of 99 technical papers, 27 papers were accepted for presentation at the workshop. They cover the following topics: elliptic and hyperelliptic arithmetic, block ciphers, hash functions, mathematical aspects of applied cryptography, stream ciphers cryptanalysis, cryptography with algebraic curves, curve-based primitives in hardware. |
| elliptic curve discrete logarithm problem: Algebraic Aspects of Cryptography Neal Koblitz, 2012-12-06 From the reviews: This is a textbook in cryptography with emphasis on algebraic methods. It is supported by many exercises (with answers) making it appropriate for a course in mathematics or computer science. [...] Overall, this is an excellent expository text, and will be very useful to both the student and researcher. Mathematical Reviews |
| elliptic curve discrete logarithm problem: Elliptic Curves Lawrence C. Washington, 2003-05-28 Elliptic curves have played an increasingly important role in number theory and related fields over the last several decades, most notably in areas such as cryptography, factorization, and the proof of Fermat's Last Theorem. However, most books on the subject assume a rather high level of mathematical sophistication, and few are truly accessible to |
| elliptic curve discrete logarithm problem: Elliptic Curves S. Lang, 2013-06-29 It is possible to write endlessly on elliptic curves. (This is not a threat.) We deal here with diophantine problems, and we lay the foundations, especially for the theory of integral points. We review briefly the analytic theory of the Weierstrass function, and then deal with the arithmetic aspects of the addition formula, over complete fields and over number fields, giving rise to the theory of the height and its quadraticity. We apply this to integral points, covering the inequalities of diophantine approximation both on the multiplicative group and on the elliptic curve directly. Thus the book splits naturally in two parts. The first part deals with the ordinary arithmetic of the elliptic curve: The transcendental parametrization, the p-adic parametrization, points of finite order and the group of rational points, and the reduction of certain diophantine problems by the theory of heights to diophantine inequalities involving logarithms. The second part deals with the proofs of selected inequalities, at least strong enough to obtain the finiteness of integral points. |
Blockchain Analytics & Crypto Compliance Solutions | Elliptic
Elliptic has been our trusted partner since 2015, helping strengthen our AML program and create a new standard for compliance in the crypto industry. We value their emphasis on data precision, …
Elliptic's copilot - Powered by AI | Elliptic
Elliptic's copilot streamlines compliance decisions, saving time and enhancing efficiency for teams managing risk alerts and investigations in the digital asset space.
About Us | Elliptic - Crypto Exchange Monitor
Founded in 2013, Elliptic pioneered the use of blockchain analytics for financial crime compliance. We are the leading provider of crypto compliance solutions globally.
Start Exploring Elliptic
Monitor, investigate, and prevent financial crime with Elliptic's crypto compliance solutions. Get started today.
Blockchain AML & Crypto Compliance Platform | Elliptic
Elliptic provides blockchain AML analytics for cryptoasset compliance, enabling compliance teams to manage risk across crypto assets and fulfil regulations.
Elliptic in Action: Uncloaking Garantex for law enforcement and ...
Mar 7, 2025 · Elliptic's blockchain analysis aids the US Secret Service in exposing Garantex's illicit activities, leading to asset seizures and enhanced sanctions compliance. Discover how advanced …
VASP Screening & Due Diligence | Elliptic Discovery
Elliptic Discovery Assess financial crime risk when engaging VASPs and other crypto businesses, empowering you to take a risk-based approach to onboarding new customers and …
Elliptic redefines industry leading coverage to 50+ blockchains as …
Apr 11, 2025 · Elliptic delivers the most extensive blockchain coverage in the industry, offering real-time monitoring across more than 50 networks, sophisticated cross-chain tracing capabilities, …
Wallet Screening & Transactions Screening for AML Compliance
Streamline compliance and AML workflows with Elliptic’s wallet and transaction screening—detect risks and trace funds effortlessly.
Meet The Elliptic Executive Leadership Team & Board Members
Simone is the CEO of Elliptic and serves to guide its vision to create a freer, fairer, and safer financial system for all.
Blockchain Analytics & Crypto Compliance Solutions | Elliptic
Elliptic has been our trusted partner since 2015, helping strengthen our AML program and create a new standard for compliance in the crypto industry. We value their emphasis on data …
Elliptic's copilot - Powered by AI | Elliptic
Elliptic's copilot streamlines compliance decisions, saving time and enhancing efficiency for teams managing risk alerts and investigations in the digital asset space.
About Us | Elliptic - Crypto Exchange Monitor
Founded in 2013, Elliptic pioneered the use of blockchain analytics for financial crime compliance. We are the leading provider of crypto compliance solutions globally.
Start Exploring Elliptic
Monitor, investigate, and prevent financial crime with Elliptic's crypto compliance solutions. Get started today.
Blockchain AML & Crypto Compliance Platform | Elliptic
Elliptic provides blockchain AML analytics for cryptoasset compliance, enabling compliance teams to manage risk across crypto assets and fulfil regulations.
Elliptic in Action: Uncloaking Garantex for law enforcement and ...
Mar 7, 2025 · Elliptic's blockchain analysis aids the US Secret Service in exposing Garantex's illicit activities, leading to asset seizures and enhanced sanctions compliance. Discover how …
VASP Screening & Due Diligence | Elliptic Discovery
Elliptic Discovery Assess financial crime risk when engaging VASPs and other crypto businesses, empowering you to take a risk-based approach to onboarding new customers and …
Elliptic redefines industry leading coverage to 50+ blockchains as …
Apr 11, 2025 · Elliptic delivers the most extensive blockchain coverage in the industry, offering real-time monitoring across more than 50 networks, sophisticated cross-chain tracing …
Wallet Screening & Transactions Screening for AML Compliance
Streamline compliance and AML workflows with Elliptic’s wallet and transaction screening—detect risks and trace funds effortlessly.
Meet The Elliptic Executive Leadership Team & Board Members
Simone is the CEO of Elliptic and serves to guide its vision to create a freer, fairer, and safer financial system for all.
