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Author : Anthony W. Knapp
ISBN : 9780691186900
Genre : Mathematics
File Size : 84.94 MB
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An elliptic curve is a particular kind of cubic equation in two variables whose projective solutions form a group. Modular forms are analytic functions in the upper half plane with certain transformation laws and growth properties. The two subjects--elliptic curves and modular forms--come together in Eichler-Shimura theory, which constructs elliptic curves out of modular forms of a special kind. The converse, that all rational elliptic curves arise this way, is called the Taniyama-Weil Conjecture and is known to imply Fermat's Last Theorem. Elliptic curves and the modeular forms in the Eichler- Shimura theory both have associated L functions, and it is a consequence of the theory that the two kinds of L functions match. The theory covered by Anthony Knapp in this book is, therefore, a window into a broad expanse of mathematics--including class field theory, arithmetic algebraic geometry, and group representations--in which the concidence of L functions relates analysis and algebra in the most fundamental ways. Developing, with many examples, the elementary theory of elliptic curves, the book goes on to the subject of modular forms and the first connections with elliptic curves. The last two chapters concern Eichler-Shimura theory, which establishes a much deeper relationship between the two subjects. No other book in print treats the basic theory of elliptic curves with only undergraduate mathematics, and no other explains Eichler-Shimura theory in such an accessible manner.
Author : Xiaoyun Wang
ISBN : 9783642349614
Genre : Computers
File Size : 84.62 MB
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This book constitutes the refereed proceedings of the 18th International Conference on the Theory and Application of Cryptology and Information Security, Asiacrypt 2012, held in Beijing, China, in December 2012. The 43 full papers presented were carefully reviewed and selected from 241 submissions. They are organized in topical sections named: public-key cryptography, foundation, symmetric cipher, security proof, lattice-based cryptography and number theory, hash function, cryptographic protocol, and implementation issues.
Author : Kan Zhang
ISBN : 9783540232087
Genre : Business & Economics
File Size : 20.24 MB
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This book constitutes the refereed proceedings of the 7th International Information Security Conference, ISC 2004, held in Palo Alto, CA, USA, in September 2004. The 36 revised full papers presented were carefully reviewed and selected from 106 submissions. The papers are organized in topical sections on key management, digital signatures, new algorithms, cryptanalysis, intrusion detection, access control, human authentication, certificate management, mobile and ad-hoc security, Web security, digital rights management, and software security.
Author : K. Srinathan
ISBN : 9783540770268
Genre : Computers
File Size : 73.5 MB
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This book constitutes the refereed proceedings of the 8th International Conference on Cryptology in India, INDOCRYPT 2007, held in Chennai, India, in December 2007. The papers and three invited lectures were carefully reviewed and selected. The papers are organized in topical sections on hashing, elliptic curve, cryptoanalysis, information theoretic security, elliptic curve cryptography, signature, side channel attack, symmetric cryptosystem, asymmetric cryptosystem, and short papers.
