By Jeffrey Hoffstein,Jill Pipher,Joseph H. Silverman
This self-contained creation to fashionable cryptography emphasizes the math in the back of the idea of public key cryptosystems and electronic signature schemes. The publication specializes in those key subject matters whereas constructing the mathematical instruments wanted for the development and safeguard research of numerous cryptosystems. purely simple linear algebra is needed of the reader; thoughts from algebra, quantity conception, and likelihood are brought and constructed as required. this article presents a fantastic advent for arithmetic and laptop technological know-how scholars to the mathematical foundations of recent cryptography. The publication contains 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 themes include:
- classical cryptographic buildings, comparable to Diffie–Hellmann key trade, 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 thought, and collision algorithms;
- an in-depth remedy of vital cryptographic options, similar 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 contains a major revision of the fabric on electronic signatures, together with an previous 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 info concept, elliptic curves, and lattices, and the bankruptcy of extra subject matters has been multiplied to incorporate sections on electronic money and homomorphic encryption. Numerous new routines were included.
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Extra info for An Introduction to Mathematical Cryptography (Undergraduate Texts in Mathematics)
An Introduction to Mathematical Cryptography (Undergraduate Texts in Mathematics) by Jeffrey Hoffstein,Jill Pipher,Joseph H. Silverman