Download An Introduction to Mathematical Cryptography (Undergraduate by Jeffrey Hoffstein,Jill Pipher,Joseph H. Silverman PDF

By Jeffrey Hoffstein,Jill Pipher,Joseph H. Silverman

This self-contained advent to fashionable cryptography emphasizes the math at the back of the speculation of public key cryptosystems and electronic signature schemes. The ebook makes a speciality of those key themes whereas constructing the mathematical instruments wanted for the development and safety research of numerous cryptosystems. simply uncomplicated linear algebra is needed of the reader; strategies from algebra, quantity concept, and chance are brought and constructed as required. this article offers a fantastic creation for arithmetic and machine technological know-how scholars to the mathematical foundations of contemporary cryptography. The booklet comprises an intensive bibliography and index; supplementary fabrics can be found online.

The e-book covers numerous issues which are thought of critical to mathematical cryptography. Key issues include:

  • classical cryptographic buildings, similar to DiffieHellmann key alternate, discrete logarithm-based cryptosystems, the RSA cryptosystem, and electronic signatures;
  • fundamental mathematical instruments for cryptography, together with primality checking out, factorization algorithms, likelihood conception, info concept, and collision algorithms;
  • an in-depth remedy of significant cryptographic recommendations, similar to elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem.

The moment variation of An advent

to Mathematical Cryptography features a major revision of the fabric on electronic signatures, together with an past creation to RSA, Elgamal, and DSA signatures, and new fabric on lattice-based signatures and rejection sampling. Many sections were rewritten or extended for readability, particularly within the chapters on details conception, elliptic curves, and lattices, and the bankruptcy of extra subject matters has been accelerated to incorporate sections on electronic money and homomorphic encryption. Numerous new workouts were included.

Show description

Read or Download An Introduction to Mathematical Cryptography (Undergraduate Texts in Mathematics) PDF

Best number theory books

Number Theoretic Methods: Future Trends (Developments in Mathematics)

This quantity includes the court cases of the very profitable moment China-Japan Seminar held in lizuka, Fukuoka, Japan, in the course of March 12-16, 2001 lower than the help of the Japan Society for the promoting of technological know-how (JSPS) and the nationwide technology beginning of China (NSFC), and a few invited papers of eminent number-theorists who visited Japan in the course of 1999-2001 on the party of the convention on the examine Institute of Mathematical Sciences (RIMS), Kyoto college.

Computational Aspects of Modular Forms and Galois Representations: How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime (AM-176) (Annals of Mathematics Studies)

Modular types are vastly very important in numerous parts of arithmetic, from quantity idea and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's tau-function as a regular instance, have deep mathematics importance. sooner than this ebook, the quickest recognized algorithms for computing those Fourier coefficients took exponential time, other than in a few designated circumstances.

Quadratic Forms, Linear Algebraic Groups, and Cohomology: 18 (Developments in Mathematics)

The invited papers accrued during this quantity handle subject matters concerning the learn of Raman Parimala (plenary speaker on the upcoming ICM 2010). those subject matters concentration totally on the interaction among algebra, quantity conception, and algebraic geometry. The incorporated contributions conceal intriguing examine in components corresponding to box patching and an explanation of the Serre's Conjecture II for functionality fields of advanced surfaces.

Mathematical Bridges

Development bridges among classical effects and modern nonstandard difficulties, this hugely correct paintings embraces very important themes in research and algebra from a problem-solving point of view. The publication is dependent to help the reader in formulating and proving conjectures, in addition to devising recommendations to big mathematical difficulties through making connections among quite a few thoughts and ideas from varied parts of arithmetic.

Additional resources for An Introduction to Mathematical Cryptography (Undergraduate Texts in Mathematics)

Example text

Download PDF sample

Rated 4.93 of 5 – based on 46 votes