TY - BOOK
AU - Hoffstein,Jeffrey
AU - Pipher,Jill
AU - Silverman,Joseph H.
ED - SpringerLink (Online service)
TI - An Introduction to Mathematical Cryptography
T2 - Undergraduate Texts in Mathematics,
SN - 9781493917112
AV - QA241-247.5
U1 - 512.7 23
PY - 2014///
CY - New York, NY
PB - Springer New York, Imprint: Springer
KW - Mathematics
KW - Data structures (Computer science)
KW - Data encryption (Computer science)
KW - Algebra
KW - Ordered algebraic structures
KW - Information theory
KW - Number theory
KW - Number Theory
KW - Data Structures, Cryptology and Information Theory
KW - Data Encryption
KW - Information and Communication, Circuits
KW - Order, Lattices, Ordered Algebraic Structures
N1 - Preface -- 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
N2 - This 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
UR - http://dx.doi.org/10.1007/978-1-4939-1711-2
ER -