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 Diffie–Hellmann 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.
Read or Download An Introduction to Mathematical Cryptography (Undergraduate Texts in Mathematics) PDF
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