Introduction to Cryptography with Maple

Introduction to Cryptography with Maple ed. Computer science Algebra Software engineering.

This introduction to cryptography uses a programming-oriented approach to study important current cryptographic schemes and the main cryptanalytic attacks against them. The Maple implementations include many examples with parameters of realistic size. Show more Show less. The work is most useful for those interested in the deep mechanics and mathematics of cryptosystems.

Pardo does an excellent job of considering the algorithmic properties and conversions required for practical use of each cryptosystem within the Maple environment.

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This is an important resource for those interested in learning how to apply and implement cryptosystems within Maple The book is well structured and easy to follow. It is a good self-study book for computer science or mathematics students, and for engineers who work in cryptography.

Pseudo-Random Generators and One-way Functions 16 3. HMAC 3 5. Primality, Factoring and Discrete Logarithms 6.

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• About the Book :.

Cryptography is a key technology in electronic key systems. It is used to keep data secret, digitally sign documents, access control, and so forth.

Users therefore should not only know how its techniques work, but they must also be able to estimate their efficiency and security. Based on courses taught by the author, this book explains the basic methods of modern cryptography.

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It is written for readers with only basic mathematical knowledge who are interested in modern cryptographic algorithms and their mathematical foundation. Several exercises are included following each chapter. This revised and extended edition includes new material on the AES encryption algorithm, the SHA-1 Hash algorithm, on secret sharing, as well as updates in the chapters on factoring and discrete logarithms.

Due to the rapid growth of digital communication and electronic data exchange, information security has become a crucial issue in industry, business, and administration. Modern cryptography provides essential techniques for securing information and protecting data.

In the first part, this book covers the key concepts of cryptography on an undergraduate level, from encryption and digital signatures to cryptographic protocols. Essential techniques are demonstrated in protocols for key exchange, user identification, electronic elections and digital cash.

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In the second part, more advanced topics are addressed, such as the bit security of one-way functions and computationally perfect pseudorandom bit generators. The security of cryptographic schemes is a central topic. Typical examples of provably secure encryption and signature schemes and their security proofs are given. Though particular attention is given to the mathematical foundations, no special background in mathematics is presumed.

The necessary algebra, number theory and probability theory are included in the appendix. Each chapter closes with a collection of exercises.

The second edition contains corrections, revisions and new material, including a complete description of the AES, an extended section on cryptographic hash functions, a new section on random oracle proofs, and a new section on public-key encryption schemes that are provably secure against adaptively-chosen-ciphertext attacks.

The theory of algebraic function fields over finite fields has its origins in number theory. The use of function fields often led to better results than those of classical approaches. This book presents survey articles on some of these new developments. Most of the material is directly related to the interaction between function fields and their various applications; in particular the structure and the number of rational places of function fields are of great significance.

The topics focus on material which has not yet been presented in other books or survey articles.