Topic
Kummer surface
About: Kummer surface is a research topic. Over the lifetime, 234 publications have been published within this topic receiving 3654 citations.
Papers published on a yearly basis
Papers
18 Apr 1996
TL;DR: The number theoretic properties of curves of genus 2 are attracting increasing attention as mentioned in this paper, and the results exemplify the power of computer algebra in diophantine contexts, but computer expertise is not assumed in the main text.
Abstract: The number theoretic properties of curves of genus 2 are attracting increasing attention. This book provides new insights into this subject; much of the material here is entirely new, and none has appeared in book form before. Included is an explicit treatment of the Jacobian, which throws new light onto the geometry of the Kummer surface. The Mordell–Weil group can then be determined for many curves, and in many non-trivial cases all rational points can be found. The results exemplify the power of computer algebra in diophantine contexts, but computer expertise is not assumed in the main text. Number theorists, algebraic geometers and workers in related areas will find that this book offers unique insights into the arithmetic of curves of genus 2.
309 citations
Book•
26 Oct 1990
TL;DR: In this article, Kummer's configuration and quadratic complex and congruence are used to define a quadratically complex surface and a set of sets of nodes, and the index plate is used to represent the singular Kummer surface.
Abstract: 1. Kummer's configuration 2. The quartic surface 3. The orthogonal matrix of linear forms 4. Line geometry 5. The quadratic complex and congruence 6. Plucker's complex surface 7. Sets of nodes 8. Equations of Kummer's surface 9. Special forms of Kummer's surface 10. The wave surface 11. Reality and topology 12. Geometry of four dimensions 13. Algebraic curves on the surface 14. Curves of different orders 15. Weddle's surface 16. Theta functions 17. Applications of Abel's theorem 18. Singular Kummer surfaces Index Plate.
295 citations
TL;DR: This work derives fast formulae for the scalar multiplication in the Kummer surface associated to a genus 2 curve, using a Montgomery ladder, which can be used to design very efficient genus 2 cryptosystems that should be faster than elliptic curve cryptosSystems in some hardware configurations.
Abstract: In 1986, D. V. Chudnovsky and G. V. Chudnovsky proposed to use formulae coming from Theta functions for the arithmetic in Jacobians of genus 2 curves. We follow this idea and derive fast formulae for the scalar multiplication in the Kummer surface associated to a genus 2 curve, using a Montgomery ladder. Our formulae can be used to design very efficient genus 2 cryptosystems that should be faster than elliptic curve cryptosystems in some hardware configurations.
134 citations
Posted Content•
TL;DR: In this article, fast formulae for scalar multiplication in the Kummer surface associated to a genus 2 curve, using a Montgomery ladder, were derived for the arithmetic in Jacobians of genus 2 curves.
Abstract: In 1986, D. V. Chudnovsky and G. V. Chudnovsky proposed to use formulae coming from Theta functions for the arithmetic in Jacobians of genus 2 curves. We follow this idea and derive fast formulae for the scalar multiplication in the Kummer surface associated to a genus 2 curve, using a Montgomery ladder. Our formulae can be used to design very efficient genus 2 cryptosystems that should be faster than elliptic curve cryptosystems in some hardware configurations.
96 citations
1 Jan 1982
TL;DR: In this article, the authors present a collection of musings about several questions related to crystalline cohomology that have plagued me for the past few years, and their justification for publishing is the hope that others will find the problems as intriguing as I did but perhaps have more success in solving them.
Abstract: This paper is a collection of musings about several questions related to crystalline cohomology that have plagued me for the past few years. It contains many more conjectures than proofs, and my justification for publishing is the hope that others will find the problems as intriguing as I did but perhaps have more success in solving them.
78 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 12 |
| 2020 | 9 |
| 2019 | 12 |
| 2018 | 8 |
| 2017 | 15 |
| 2016 | 13 |