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Multivariate public key cryptosystems (MPKC) is a fast-developing area in cryptography. This book systematically presents the subject matter for a broad audience and is the first book to focus on this exciting new topic.

Multivariate public key cryptosystems (MPKC) is a fast-developing area in cryptography. This book systematically presents the subject matter for a broad audience and is the first book to focus on this exciting new topic.

DES, the Data Encryption Standard, is the best known and most widely used civilian cryptosystem. It was developed by IBM and adopted as a US national standard in the mid 1970`s, and had resisted all attacks in the last 15 years. This book presents the first successful attack which can break the full 16 round DES faster than via exhaustive search. It describes in full detail, the novel technique of Differential Cryptanalysis, and demonstrates its applicability to a wide variety of cryptosystems and hash functions, including FEAL, Khafre, REDOC-II, LOKI, Lucifer, Snefru, N-Hash, and many modified versions of DES. The methodology used offers valuable insights to anyone interested in data security and cryptography, and points out the intricacies of developing, evaluating, testing, and implementing such schemes. This book was written by two of the field`s leading researchers, and describes state-of-the-art research in a clear and completely contained manner.

Learn to apply abstract algebra to practical real-world problems with TOPICS IN APPLIED ABSTRACT ALGEBRA! With coverage of interesting applications such as designing block designs to conduct statistical experiments for unbiased study of samples and designing secret-key cryptosystems and public-key cryptosystems for secure transmission of sensitive or secret data, this mathematics text makes the study of abstract algebra more exciting and meaningful. The opening chapter provides a brief refresher on the basic algebraic systems so that you are fully prepared to learn.

Complete coverage of the current major public key cryptosystems their underlying mathematics and the most common techniques used in attacking them Public Key Cryptography: Applications and Attacks introduces and explains the fundamentals of public key cryptography and explores its application in all major public key cryptosystems in current use, including ElGamal, RSA, Elliptic Curve, and digital signature schemes. It provides the underlying mathematics needed to build and study these schemes as needed, and examines attacks on said schemes via the mathematical problems on which they are based – such as the discrete logarithm problem and the difficulty of factoring integers. The book contains approximately ten examples with detailed solutions, while each chapter includes forty to fifty problems with full solutions for odd-numbered problems provided in the Appendix. Public Key Cryptography: · Explains fundamentals of public key cryptography · Offers numerous examples and exercises · Provides excellent study tools for those preparing to take the Certified Information Systems Security Professional (CISSP) exam · Provides solutions to the end-of-chapter problems Public Key Cryptography provides a solid background for anyone who is employed by or seeking employment with a government organization, cloud service provider, or any large enterprise that uses public key systems to secure data.

(Key College Publishing) A textbook that is a one-semester introduction to number theory that uses the computer as a tool for motivation and explanation. Covers traditional topics and uses software to explore factoring algorithms, primality testing, the RSA public-key cryptosystem, and more. DLC: Number theory.

This text introduces cryptography, from its earliest roots to cryptosystems used today for secure online communication.Beginning with classical ciphers and their cryptanalysis, this book proceeds to focus on modern public key cryptosystems such as Diffie-Hellman, ElGamal, RSA, and elliptic curve cryptography with an analysis of vulnerabilities of these systems and underlying mathematical issues such as factorization algorithms. Specialized topics such as zero knowledge proofs, cryptographic voting, coding theory, and new research are covered in the final section of this book.Aimed at undergraduate students, this book contains a large selection of problems, ranging from straightforward to difficult, and can be used as a textbook for classes as well as self-study. Requiring only a solid grounding in basic mathematics, this book will also appeal to advanced high school students and amateur mathematicians interested in this fascinating and topical subject.

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. It includes exercises and examples at the end of each section.

A pseudorandom generator is an easy-to-compute function that stretches a short random string into a much longer string that "looks" just like a random string to any efficient adversary. One immediate application of a pseudorandom generator is the construction of a private key cryptosystem that is secure against chosen plaintext attack. There do not seem to be natural examples of functions that are pseudorandom generators. On the other hand, there do seem to be a variety of natural examples of another basic primitive: the one-way function. A function is one-way if it is easy to compute but hard for any efficient adversary to invert on average. The first half of the book shows how to construct a pseudorandom generator from any one-way function. Building on this, the second half of the book shows how to construct other useful cryptographic primitives, such as private key cryptosystems, pseudorandom function generators, pseudorandom permutation generators, digital signature schemes, bit commitment protocols, and zero-knowledge interactive proof systems. The book stresses rigorous definitions and proofs.

This text introduces cryptography, from its earliest roots to cryptosystems used today for secure online communication.Beginning with classical ciphers and their cryptanalysis, this book proceeds to focus on modern public key cryptosystems such as Diffie-Hellman, ElGamal, RSA, and elliptic curve cryptography with an analysis of vulnerabilities of these systems and underlying mathematical issues such as factorization algorithms. Specialized topics such as zero knowledge proofs, cryptographic voting, coding theory, and new research are covered in the final section of this book.Aimed at undergraduate students, this book contains a large selection of problems, ranging from straightforward to difficult, and can be used as a textbook for classes as well as self-study. Requiring only a solid grounding in basic mathematics, this book will also appeal to advanced high school students and amateur mathematicians interested in this fascinating and topical subject.

A collection of articles and monographs on cryptography ranges from a technical study of the spy cipher used by Reino Hayhanen to an argument against a government-sponsored computer cryptosystem

Complete coverage of the current major public key cryptosystems their underlying mathematics and the most common techniques used in attacking them Public Key Cryptography: Applications and Attacks introduces and explains the fundamentals of public key cryptography and explores its application in all major public key cryptosystems in current use, including ElGamal, RSA, Elliptic Curve, and digital signature schemes. It provides the underlying mathematics needed to build and study these schemes as needed, and examines attacks on said schemes via the mathematical problems on which they are based – such as the discrete logarithm problem and the difficulty of factoring integers. The book contains approximately ten examples with detailed solutions, while each chapter includes forty to fifty problems with full solutions for odd-numbered problems provided in the Appendix. Public Key Cryptography: · Explains fundamentals of public key cryptography · Offers numerous examples and exercises · Provides excellent study tools for those preparing to take the Certified Information Systems Security Professional (CISSP) exam · Provides solutions to the end-of-chapter problems Public Key Cryptography provides a solid background for anyone who is employed by or seeking employment with a government organization, cloud service provider, or any large enterprise that uses public key systems to secure data.

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 of the reader; techniques from algebra, number theory, and probability are introduced and developed as required. This text provides an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. The book includes an extensive bibliography and index; supplementary materials are available online.The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include:classical cryptographic constructions, such as Diffie–Hellmann key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem, and digital signatures;fundamental mathematical tools for cryptography, including primality testing, factorization algorithms, probability theory, information theory, and collision algorithms;an in-depth treatment of important cryptographic innovations, such as elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem.The second edition of An Introduction to Mathematical Cryptography includes a significant revision of the material on digital signatures, including an earlier introduction to RSA, Elgamal, and DSA signatures, and new material on lattice-based signatures and rejection sampling. Many sections have been rewritten or expanded for clarity, especially in the chapters on information theory, elliptic curves, and lattices, and the chapter of additional topics has been expanded to include sections on digital cash and homomorphic encryption. Numerous new exercises have been included.

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. It includes exercises and examples at the end of each section.

Learn to apply abstract algebra to practical real-world problems with TOPICS IN APPLIED ABSTRACT ALGEBRA! With coverage of interesting applications such as designing block designs to conduct statistical experiments for unbiased study of samples and designing secret-key cryptosystems and public-key cryptosystems for secure transmission of sensitive or secret data, this mathematics text makes the study of abstract algebra more exciting and meaningful. The opening chapter provides a brief refresher on the basic algebraic systems so that you are fully prepared to learn.

In the modern age of almost universal computer usage, practically every individual in a technologically developed society has routine access to the most up-to-date cryptographic technology that exists, the so-called RSA public-key cryptosystem. A major component of this system is the factorization of large numbers into their primes. Thus an ancient number-theory concept now plays a crucial role in communication among millions of people who may have little or no knowledge of even elementary mathematics. The independent structure of each chapter of the book makes it highly readable for a wide variety of mathematicians, students of applied number theory, and others interested in both study and research in number theory and cryptography.

In the modern age of almost universal computer usage, practically every individual in a technologically developed society has routine access to the most up-to-date cryptographic technology that exists, the so-called RSA public-key cryptosystem. A major component of this system is the factorization of large numbers into their primes. Thus an ancient number-theory concept now plays a crucial role in communication among millions of people who may have little or no knowledge of even elementary mathematics. The independent structure of each chapter of the book makes it highly readable for a wide variety of mathematicians, students of applied number theory, and others interested in both study and research in number theory and cryptography.

Contents Unit-I: Introduction to Cryptosystem Introduction to Cryptosystem Classical Encryption Technique Modern Block Cipher Principle Data Encryption Standard Unit-II: Introduction to Algorithms and Public Key Cryptosystem Group Ring and Fields Algorithms and Remainder Theorem Public Key Cryptosystem Unit-III: Message Authentication and Hash Function Message Authentication and Hash Function Digital Signature Unit-IV: Authenetication Applications Authentication Applications Unit-V: Introduction to Cryptography IP Security Web Security System Security Advanced Algorithm and Standards Model Test Papers Previous Years Examination Papers Index

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 of the reader; techniques from algebra, number theory, and probability are introduced and developed as required. This text provides an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. The book includes an extensive bibliography and index; supplementary materials are available online.The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include:classical cryptographic constructions, such as Diffie–Hellmann key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem, and digital signatures;fundamental mathematical tools for cryptography, including primality testing, factorization algorithms, probability theory, information theory, and collision algorithms;an in-depth treatment of important cryptographic innovations, such as elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem.The second edition of An Introduction to Mathematical Cryptography includes a significant revision of the material on digital signatures, including an earlier introduction to RSA, Elgamal, and DSA signatures, and new material on lattice-based signatures and rejection sampling. Many sections have been rewritten or expanded for clarity, especially in the chapters on information theory, elliptic curves, and lattices, and the chapter of additional topics has been expanded to include sections on digital cash and homomorphic encryption. Numerous new exercises have been included.

Cryptology, the art and science of 'secret writing', provides ideal methods to solve the problems of transmitting information secretly and securely. The first half of this book studies and analyzes classical cryptosystems. The second half looks at the exciting new directions of public-key cryptology. The book is fun to read, and the author presents the material clearly and simply. Many exercises and references accompany each chapter.