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 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 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.
Read or Download An Introduction to Mathematical Cryptography (Undergraduate Texts in Mathematics) PDF
Best number theory books
This contemporary creation to the rules of good judgment and arithmetic not just takes thought into consideration, but in addition treats in a few element functions that experience a considerable effect on daily life (loans and mortgages, bar codes, public-key cryptography). a primary college-level creation to common sense, proofs, units, quantity thought, and graph idea, and a very good self-study reference and source for teachers.
Bridges the space among theoretical and computational points of best numbersExercise sections are a goldmine of fascinating examples, tips to the literature and capability examine projectsAuthors are recognized and highly-regarded within the box
This publication provides a unified treatise of the idea of degree and integration. within the surroundings of a common degree house, each suggestion is outlined accurately and each theorem is gifted with a transparent and whole facts with all of the appropriate information. Counter-examples are supplied to teach that yes stipulations within the speculation of a theorem can't be easily dropped.
A classical theorem of Jordan states that each finite transitive permutation workforce includes a derangement. This lifestyles end result has attention-grabbing and unforeseen functions in lots of components of arithmetic, together with graph conception, quantity thought and topology. a variety of generalisations were studied in additional fresh years, with a selected specialise in the lifestyles of derangements with unique homes.
- The Arithmetic of Fundamental Groups: PIA 2010 (Contributions in Mathematical and Computational Sciences)
- Arithmetische Funktionen (German Edition)
- Mathematical Problems in Elasticity and Homogenization (Studies in Mathematics and its Applications)
- Number Theory: Volume II: Analytic and Modern Tools: 240 (Graduate Texts in Mathematics)
- Basiswissen Zahlentheorie: Eine Einführung in Zahlen und Zahlbereiche (Mathematik für das Lehramt) (German Edition)
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