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.
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