04349nam a22005775i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001600172072001600188072002300204082001400227100003300241245013100274250001800405264006700423300004500490336002600535337002600561338003600587347002400623490005100647505037600698520194101074650001703015650004003032650004003072650001303112650003403125650002403159650001903183650001703202650001903219650005603238650002103294650004503315650005103360700002703411700003403438710003403472773002003506776003603526830005103562856004803613912001403661999001903675952007703694978-1-4939-1711-2DE-He21320180115171539.0cr nn 008mamaa140911s2014 xxu| s |||| 0|eng d a97814939171129978-1-4939-1711-27 a10.1007/978-1-4939-1711-22doi 4aQA241-247.5 7aPBH2bicssc 7aMAT0220002bisacsh04a512.72231 aHoffstein, Jeffrey.eauthor.13aAn Introduction to Mathematical Cryptographyh[electronic resource] /cby Jeffrey Hoffstein, Jill Pipher, Joseph H. Silverman. a2nd ed. 2014. 1aNew York, NY :bSpringer New York :bImprint: Springer,c2014. aXVII, 538 p. 32 illus.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aUndergraduate Texts in Mathematics,x0172-60560 aPreface -- Introduction -- 1 An Introduction to Cryptography -- 2 Discrete Logarithms and Diffie-Hellman -- 3 Integer Factorization and RSA -- 4 Digital Signatures -- 5 Combinatorics, Probability, and Information Theory -- 6 Elliptic Curves and Cryptography -- 7 Lattices and Cryptography -- 8 Additional Topics in Cryptography -- List of Notation -- References -- Index. aThis self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required. This text provides an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. The book includes an extensive bibliography and index; supplementary materials are available online. The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include: classical cryptographic constructions, such as Diffieâ€“Hellmann key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem, and digital signatures; fundamental mathematical tools for cryptography, including primality testing, factorization algorithms, probability theory, information theory, and collision algorithms; an in-depth treatment of important cryptographic innovations, such as elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem. The second edition of An Introduction to Mathematical Cryptography includes a significant revision of the material on digital signatures, including an earlier introduction to RSA, Elgamal, and DSA signatures, and new material on lattice-based signatures and rejection sampling. Many sections have been rewritten or expanded for clarity, especially in the chapters on information theory, elliptic curves, and lattices, and the chapter of additional topics has been expanded to include sections on digital cash and homomorphic encryption.Â Numerous new exercises have been included. 0aMathematics. 0aData structures (Computer science). 0aData encryption (Computer science). 0aAlgebra. 0aOrdered algebraic structures. 0aInformation theory. 0aNumber theory.14aMathematics.24aNumber Theory.24aData Structures, Cryptology and Information Theory.24aData Encryption.24aInformation and Communication, Circuits.24aOrder, Lattices, Ordered Algebraic Structures.1 aPipher, Jill.eauthor.1 aSilverman, Joseph H.eauthor.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9781493917105 0aUndergraduate Texts in Mathematics,x0172-605640uhttp://dx.doi.org/10.1007/978-1-4939-1711-2 aZDB-2-SMA c370905d370905 001040708EBookaelibbelibd2018-01-15r2018-01-15w2018-01-15yEBOOK