By Jeffrey Hoffstein,Jill Pipher,Joseph H. Silverman
This self-contained creation to trendy cryptography emphasizes the math in the back of the idea of public key cryptosystems and electronic signature schemes. The ebook makes a speciality of those key subject matters whereas constructing the mathematical instruments wanted for the development and safeguard research of various cryptosystems. in basic terms simple linear algebra is needed of the reader; recommendations from algebra, quantity thought, and chance are brought and built as required. this article offers a fantastic advent for arithmetic and machine technological know-how scholars to the mathematical foundations of recent cryptography. The publication contains an in depth bibliography and index; supplementary fabrics can be found online.
The ebook covers various issues which are thought of primary to mathematical cryptography. Key themes include:
- classical cryptographic buildings, resembling 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 concept, details concept, and collision algorithms;
- an in-depth therapy of significant cryptographic recommendations, resembling elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem.
The moment version of An creation
to Mathematical Cryptography contains a major revision of the cloth on electronic signatures, together with an past advent to RSA, Elgamal, and DSA signatures, and new fabric on lattice-based signatures and rejection sampling. Many sections were rewritten or improved for readability, specifically within the chapters on details conception, elliptic curves, and lattices, and the bankruptcy of extra subject matters has been increased to incorporate sections on electronic funds and homomorphic encryption. Numerous new routines were included.
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Additional 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