Jean Chaumine, James Hirschfeld, Robert Rolland's Algebraic Geometry and Its Applications: Dedicated to Gilles PDF

By Jean Chaumine, James Hirschfeld, Robert Rolland

ISBN-10: 9812793429

ISBN-13: 9789812793423

ISBN-10: 9812793437

ISBN-13: 9789812793430

This quantity covers many subject matters together with quantity concept, Boolean services, combinatorial geometry, and algorithms over finite fields. This e-book includes many fascinating theoretical and applicated new effects and surveys provided through the simplest experts in those parts, corresponding to new effects on Serre's questions, answering a question in his letter to best; new effects on cryptographic functions of the discrete logarithm challenge regarding elliptic curves and hyperellyptic curves, together with computation of the discrete logarithm; new effects on functionality box towers; the development of latest sessions of Boolean cryptographic features; and algorithmic purposes of algebraic geometry.

Show description

Read or Download Algebraic Geometry and Its Applications: Dedicated to Gilles Lachaud on His 60th Birthday (Series on Number Theory and Its Applications) PDF

Similar algebraic geometry books

Get Computational Noncommutative Algebra and Applications PDF

The fusion of algebra, research and geometry, and their software to genuine global difficulties, were dominant subject matters underlying arithmetic for over a century. Geometric algebras, brought and categorized by means of Clifford within the overdue nineteenth century, have performed a well-known function during this attempt, as noticeable within the mathematical paintings of Cartan, Brauer, Weyl, Chevelley, Atiyah, and Bott, and in purposes to physics within the paintings of Pauli, Dirac and others.

Download e-book for kindle: A Scrapbook of Complex Curve Theory (University Series in by C. Herbert Clemens

This wonderful booklet via Herb Clemens quick turned a favourite of many complicated algebraic geometers while it used to be first released in 1980. it's been well-liked by newcomers and specialists ever considering. it's written as a e-book of "impressions" of a trip during the conception of advanced algebraic curves. Many themes of compelling attractiveness ensue alongside the way in which.

Grigoriy Blekherman, Pablo A. Parrilo, Rekha Thomas's Semidefinite optimization and convex algebraic geometry PDF

This ebook presents a self-contained, obtainable creation to the mathematical advances and demanding situations as a result of using semidefinite programming in polynomial optimization. This quick evolving examine quarter with contributions from the various fields of convex geometry, algebraic geometry, and optimization is named convex algebraic geometry.

Additional resources for Algebraic Geometry and Its Applications: Dedicated to Gilles Lachaud on His 60th Birthday (Series on Number Theory and Its Applications)

Sample text

We now show that the condition p ∤ [OK : Z[π, π]] is automatically satisfied for all primes p except possibly 2 and 3. 7. Suppose p > 3 and that π ∈ OK corresponds to the Frobenius endomorphism of an ordinary abelian surface A over Fp . Then p ∤ [OK : Z[π, π]]. Proof. Let ∆(R) denote the discriminant of a Z-module R. 4], which shows that ∆(Z[π, π]) = ± NormK/Q (π − π) ∆(Z[π + π]). 4] that any prime that divides ∆(OK0 [π]) the index [OK : Z[π, π]] must divide either [OK0 : Z[π + π]] or ∆(O . 3], the second quantity is prime to p if the abelian surface is ordinary.

G¨ urel. Implementing the Arithmetic of C3,4 Curves. In Algorithmic Number Theory Symposium - ANTS-VI, volume 3076 of LNCS, pages 87–101. Springer, 2004. 5. R. Blache, J. Estrada Sarlabous and M. Petkova. A geometric interpretation of reduction in the Jacobian of Cab curves. preprint. 6. C. Diem and E. Thom´e. Index calculus in class groups of non-hyperelliptic curves of genus three. accepted at J. of Cryptology, 2007. 7. E. W. Howe, K. E. Lauter and J. Top. Pointless curves of genus three and four.

Addition then requires 131M +14SQ+2I and a doubling requires 148M +19SQ+2I. Finally, note that the case of Picard curves has been handled in [8]. However, we point out that thanks to the new remarks made in this paper, we can actually reduce the cost for addition in the case of Picard curves to 116M + 14SQ + 2I and to 133M + 19SQ + 2I for doubling. 4. Examples Fast additions can be useful in modern counting points algorithm and the two following examples are in this trend. The first example illustrates our algorithm in characteristic 2 and in the tangent case.

Download PDF sample

Algebraic Geometry and Its Applications: Dedicated to Gilles Lachaud on His 60th Birthday (Series on Number Theory and Its Applications) by Jean Chaumine, James Hirschfeld, Robert Rolland


by John
4.3

Rated 4.12 of 5 – based on 33 votes