Overview
Employs a programming-oriented approach to study the most important cryptographic schemes and cryptanalytic attacks
Provides implementations of the algorithms and schemes and examples of realistic size
Suitable for advanced undergraduate and graduate students of computer science, engineering and mathematics, and is also a comprehensive reference for self-study by practitioners
Includes supplementary material: sn.pub/extras
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (11 chapters)
Keywords
About this book
This introduction to cryptography employs a programming-oriented approach to study the most important cryptographic schemes in current use and the main cryptanalytic attacks against them. Discussion of the theoretical aspects, emphasizing precise security definitions based on methodological tools such as complexity and randomness, and of the mathematical aspects, with emphasis on number-theoretic algorithms and their applications to cryptography and cryptanalysis, is integrated with the programming approach, thus providing implementations of the algorithms and schemes as well as examples of realistic size.
A distinctive feature of the author's approach is the use of Maple as a programming environment in which not just the cryptographic primitives but also the most important cryptographic schemes are implemented following the recommendations of standards bodies such as NIST, with many of the known cryptanalytic attacks implemented as well. The purpose of the Maple implementations is to let the reader experiment and learn, and for this reason the author includes numerous examples. The book discusses important recent subjects such as homomorphic encryption, identity-based cryptography and elliptic curve cryptography. The algorithms and schemes which are treated in detail and implemented in Maple include AES and modes of operation, CMAC, GCM/GMAC, SHA-256, HMAC, RSA, Rabin, Elgamal, Paillier, Cocks IBE, DSA and ECDSA. In addition, some recently introduced schemes enjoying strong security properties, such as RSA-OAEP, Rabin-SAEP, Cramer--Shoup, and PSS, are also discussed and implemented. On the cryptanalysis side, Maple implementations and examples are used to discuss many important algorithms, including birthday and man-in-the-middle attacks, integer factorization algorithms such as Pollard's rho and the quadratic sieve, and discrete log algorithms such as baby-step giant-step, Pollard's rho, Pohlig--Hellman and the index calculus method.
This textbook is suitable for advanced undergraduate and graduate students of computer science, engineering and mathematics, satisfying the requirements of various types of courses: a basic introductory course; a theoretically oriented course whose focus is on the precise definition of security concepts and on cryptographic schemes with reductionist security proofs; a practice-oriented course requiring little mathematical background and with an emphasis on applications; or a mathematically advanced course addressed to students with a stronger mathematical background. The main prerequisite is a basic knowledge of linear algebra and elementary calculus, and while some knowledge of probability and abstract algebra would be helpful, it is not essential because the book includes the necessary background from these subjects and, furthermore, explores the number-theoretic material in detail. The book is also a comprehensive reference and is suitable for self-study by practitioners and programmers.
Reviews
From the reviews:
“A valuable guide to the practical applications and intricate workings of modern cryptographic systems. … 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. This is an important resource for those interested in learning how to apply and implement cryptosystems within Maple … . Summing Up: Highly recommended. Graduate students, researchers/faculty, and professionals/practitioners.” (T. D. Richardson, Choice, Vol. 50 (11), August, 2013)
“In this book, the authors make a significant contribution to the explanation of cryptographic algorithms using Maple code. … 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.” (Zheng Gong, Computing Reviews, May, 2013)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Introduction to Cryptography with Maple
Authors: José Luis Gómez Pardo
DOI: https://doi.org/10.1007/978-3-642-32166-5
Publisher: Springer Berlin, Heidelberg
eBook Packages: Computer Science, Computer Science (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2013
Hardcover ISBN: 978-3-642-32165-8Published: 19 December 2012
Softcover ISBN: 978-3-642-44621-4Published: 29 January 2015
eBook ISBN: 978-3-642-32166-5Published: 19 December 2012
Edition Number: 1
Number of Pages: XXX, 706
Topics: Data Structures and Information Theory, Number Theory, Software Engineering/Programming and Operating Systems, Algebra