An Introduction to Mathematical Cryptography (Undergraduate - download pdf or read online

By Jeffrey Hoffstein,Jill Pipher,Joseph H. Silverman

This self-contained creation to fashionable cryptography emphasizes the maths in the back of the idea of public key cryptosystems and electronic signature schemes. The ebook specializes in those key issues whereas constructing the mathematical instruments wanted for the development and protection research of numerous cryptosystems. simply simple linear algebra is needed of the reader; ideas from algebra, quantity thought, and likelihood are brought and built as required. this article presents an amazing creation for arithmetic and computing device technological know-how scholars to the mathematical foundations of recent cryptography. The booklet comprises an intensive bibliography and index; supplementary fabrics can be found online.

The booklet covers numerous themes which are thought of principal to mathematical cryptography. Key issues include:

  • classical cryptographic structures, 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 idea, details idea, and collision algorithms;
  • an in-depth remedy of vital cryptographic techniques, comparable to elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem.

The moment variation of An creation

to Mathematical Cryptography incorporates a major revision of the fabric on electronic signatures, together with an prior advent to RSA, Elgamal, and DSA signatures, and new fabric on lattice-based signatures and rejection sampling. Many sections were rewritten or elevated for readability, in particular within the chapters on details conception, elliptic curves, and lattices, and the bankruptcy of extra themes has been improved to incorporate sections on electronic money and homomorphic encryption. Numerous new workouts were included.

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An Introduction to Mathematical Cryptography (Undergraduate Texts in Mathematics) by Jeffrey Hoffstein,Jill Pipher,Joseph H. Silverman

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