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Aritmetica, crittografia e codici = Arithmetic, cryptography and codes
The basic techniques of algebra and number theory useful in recent applications to cryptography and codes are developed, with the aim of being elementary and self-sufficient. The emphasis is on computational problems. This part of the volume can be useful as a textbook for a first course in algebra for mathematicians, computer scientists or engineers. Important applications of algebra and geometry to cryptography and codes are then illustrated. Both, cryptography and codes have significant applications in daily life which are illustrated here. Cryptography is developed in detail in much of its classic and current aspects, and both private and public key cryptography are developed. Cryptography with the use of elliptic curves on finite fields is also illustrated. A chapter introducing the subject is dedicated to linear codes.
Architecture of computing systems - ARCS 2008 ; 21st International Conference, Dresden, Germany, February 25-28, 2008. Proceedings
This book constitutes the refereed proceedings of the 21st International Conference on Architecture of Computing Systems, ARCS 2008, held in Dresden, Germany, in February 2008.
Applied algebra, algebraic algorithms and error-correcting codes ; 17th International Symposium, AAECC-17, Bangalore, India, December 16-20, 2007, Proceedings
Among the subjects addressed are block codes, including list-decoding algorithms; algebra and codes: rings, fields, algebraic geometry codes; algebra: rings and fields, polynomials, permutations, lattices; cryptography: cryptanalysis and complexity; computational algebra: algebraic algorithms and transforms; sequences and boolean functions.
Algorithmic number theory ; 8th International Symposium, ANTS-VIII Banff, Canada, May 17-22, 2008 Proceedings
This book constitutes the refereed proceedings of the 8th International Algorithmic Number Theory Symposium, ANTS 2008, held in Banff, Canada, in May 2008.
Advances in cryptology – ASIACRYPT 2007 ; 13th International conference on the theory and application of cryptology and information security, Kuching, Malaysia, December 2-6, 2007, Proceedings
The book are organized in topical sections on number theory and elliptic curve, protocol, hash function design, group/broadcast cryptography, mac and implementation, multiparty computation, block ciphers, foundation, public key encryption, and cryptanalysi.
A First Course in Modular Forms
This book introduces the theory of modular forms with an eye toward the Modularity Theorem: All rational elliptic curves arise from modular forms. The topics covered include: • elliptic curves as complex tori and as algebraic curves, • modular curves as Riemann surfaces and as algebraic curves, • Hecke operators and Atkin–Lehner theory, • Hecke eigenforms and their arithmetic properties, • the Jacobians of modular curves and the Abelian varieties associated to Hecke eigenforms, • elliptic and modular curves modulo p and the Eichler–Shimura Relation, • the Galois representations associated to elliptic curves and to Hecke eigenforms. As it presents these ideas, the book states the Modularity Theorem in various forms, relating them to each other and touching on their applications to number theory.
