Workshop I: Number Theory and Cryptography – Open Problems - IPAM

Workshop I: Number Theory and Cryptography – Open Problems

Part of the Long Program Securing Cyberspace: Applications and Foundations of Cryptography and Computer Security
October 9 - 13, 2006

Schedule

All times in this Schedule are Pacific Time (PT)

Monday, October 9, 2006

Morning Session

08:00-08:45
Check-In/Light Breakfast (Hosted by IPAM)
08:45-09:00
Welcome and Opening Remarks
09:00-10:00
Antoine Joux (Université Versailles/Saint Quentin-en-Yvelines)
Discrete Logarithm in all finite fields Short
10:00-10:30
Break
10:30-11:30
Ronald Rivest (Massachusetts Institute of Technology)
Controlled Algebras and GII’s
11:30-13:30
Lunch (on your own)

Afternoon Session

13:30-14:30
Pascal Paillier (Gemplus)
Can RSA keys be instance-malleable?
14:30-14:45
Break
14:45-15:45
Peter Montgomery (Microsoft Research)
Searching for Higher-Degree Polynomials for the General Number Field Sieve
15:45-16:15
Break
16:15-17:15
Johannes Buchmann (Technishche Universtitat Darmstadt)
CMSS - An efficient version of the Merkle signature scheme
17:15-19:00
Wine/Cheese Reception (Hosted by IPAM)

Tuesday, October 10, 2006

Morning Session

08:00-09:00
Continental Breakfast
09:00-10:00
()
Primitive subgroups in torus-based and pairing-based cryptography
10:00-10:30
Break
10:30-11:30
Denis Charles (Microsoft Research)
Computing isogenies on elliptic curves
11:30-13:30
Lunch (on your own)

Afternoon Session

13:30-14:30
Tanja Lange (Technische Universiteit Eindhoven)
Open Problems in Pairings
14:30-14:45
Break
14:45-15:45
Igor Shparlinski (Macquarie University)
Group structure of elliptic curves over finite fields
15:45-16:15
Break
16:15-17:15
Neal Koblitz (University of Washington)
Generic Groups
17:30-19:00
Dinner (Hosted by IPAM)

Wednesday, October 11, 2006

Morning Session

08:00-09:00
Continental Breakfast
09:00-10:00
Renate Scheidler (University of Calgary)
Real Hyperelliptic Curves
10:00-10:15
Break
10:15-11:15
Kristin Lauter (Microsoft Research)
Algorithms for computing genus 2 curves for use in cryptography
11:15-11:45
Break
11:45-12:45
Phong Nguyen (École Normale Supérieure)
Hermite's Constant and Lattice Reduction

Afternoon Session

12:45-14:00
Lunch (on your own)
14:00-15:00
Yvo Desmedt (University College London)
Trapdoor-Free RSA Like Assumption
16:00-17:00
Igor Shparlinski, Macquarie University "Inversions " (* talk located in Math Science (MS) Bldg. 6943)
17:15-18:15
Joseph Silverman, Brown University "Dynamical Systems from an Arithmetical Viewpoint "(* talk located in Math Science (MS) Bldg. 6943)

Thursday, October 12, 2006

Morning Session

08:00-09:00
Continental Breakfast
09:00-10:00
Gerhard Frey (Universität Duisburg-Essen)
Duality in Arithmetic Geometry and Applications to Discrete Logarithms
10:00-10:30
Break
10:30-11:30
Wayne Raskind (University of Southern California)
Global duality and the discrete logarithm problem in abelian algebraic groups over finite fields (joint work with Ming-Deh Huang).
11:30-13:30
Lunch (on your own)

Afternoon Session

13:30-14:30
Everett Howe (Center for Communications Research)
Low-genus curves over finite fields
14:30-14:45
Break
14:45-15:45
Jean-Marc Couveignes (Université de Toulouse II (Le Mirail))
Linearizing torsion classes in the Picard group of algebraic curves over finite fields
15:45-16:15
Break
16:15-17:15
Kiran Kedlaya (Massachusetts Institute of Technology)
Recent results on p-adic computation of zeta functions

Friday, October 13, 2006

Morning Session

08:00-09:00
Continental Breakfast
09:00-10:00
Joseph Silverman (Brown University)
Independence of Heegner Points
10:00-10:15
Break
10:15-11:15
Kirsten Eisentraeger (Pennsylvania State University)
On the computation of the Cassels pairing and applications to cryptography
11:15-11:30
Break
11:30-12:30
Daniele Micciancio (University of California, San Diego)
Cyclic lattices: cryptographic applications and open problems

Afternoon Session

12:30-13:30
Lunch (on your own)
13:30-14:30
Alexander May (Technishche Universtitat Darmstadt)
On Solving Number Theoretic Problems with Lattice Reduction
14:45-15:45
Ming-Deh Huang (University of Southern California)
The height function and the elliptic curve discrete logarithm problem
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