This creation to cryptography employs a programming-oriented method of research an important cryptographic schemes in present use and the most cryptanalytic assaults opposed to them. dialogue of the theoretical points, emphasizing targeted protection definitions in response to methodological instruments equivalent to complexity and randomness, and of the mathematical features, with emphasis on number-theoretic algorithms and their purposes to cryptography and cryptanalysis, is built-in with the programming method, hence offering implementations of the algorithms and schemes in addition to examples of real looking size.

A virtue of the author's procedure is using Maple as a programming surroundings during which not only the cryptographic primitives but in addition crucial cryptographic schemes are carried out following the concepts of criteria our bodies equivalent to NIST, with a number of the identified cryptanalytic assaults carried out in addition. the aim of the Maple implementations is to permit the reader test and research, and consequently the writer comprises various examples. The ebook discusses very important contemporary topics akin to homomorphic encryption, identity-based cryptography and elliptic curve cryptography. The algorithms and schemes that are taken care of intimately and applied in Maple comprise AES and modes of operation, CMAC, GCM/GMAC, SHA-256, HMAC, RSA, Rabin, Elgamal, Paillier, Cocks IBE, DSA and ECDSA. furthermore, a few lately brought schemes having fun with robust defense houses, similar to RSA-OAEP, Rabin-SAEP, Cramer--Shoup, and PSS, also are mentioned and carried out. at the cryptanalysis aspect, Maple implementations and examples are used to debate many vital algorithms, together with birthday and man-in-the-middle assaults, integer factorization algorithms comparable to Pollard's rho and the quadratic sieve, and discrete log algorithms equivalent to baby-step giant-step, Pollard's rho, Pohlig--Hellman and the index calculus method.

This textbook is appropriate for complex undergraduate and graduate scholars of laptop technological know-how, engineering and arithmetic, enjoyable the necessities of assorted kinds of classes: a simple introductory direction; a theoretically orientated direction whose concentration is at the particular definition of safeguard thoughts and on cryptographic schemes with reductionist protection proofs; a practice-oriented direction requiring little mathematical heritage and with an emphasis on functions; or a mathematically complex direction addressed to scholars with an improved mathematical heritage. the most prerequisite is a simple wisdom of linear algebra and simple calculus, and whereas a few wisdom of chance and summary algebra will be priceless, it isn't crucial as the publication contains the required history from those topics and, additionally, explores the number-theoretic fabric intimately. The publication can be a complete reference and is acceptable for self-study via practitioners and programmers.