
THEMATIC PROGRAMS 

December 7, 2023  
Fall
2006
Thematic Program in Cryptography Workshop on Computational challenges arising in algorithmic number
theory and Cryptography

Audio of talks  Confirmed Participants  Visitor Information 
Schedule  Speaker Abstracts  Hotels and Housing 
back to Thematic Program page 
Despite intense research over many decades and sometimes even centuries, there are numerous number theoretic problems for which efficient solutions continue to elude us. Moreover, such solutions are generally not even known to exist. For example, it is unkown whether it is possible to find solutions to Pell equations and other norm equations quickly. Furthermore, to date, no efficient algorithm for factoring a large randomly chosen number into its prime factors is known, and the true complexity of the integer factorization problem is not even clear. Nevertheless, the popular RSA cryptosystem is based on the assumed difficulty of this problem.
In general, the security of most publickey cryptographic systems relies on the believed difficulty of a certain number theoretic problem. In exploring such problems, researchers face mathematical as well as computational and algorithmic difficulties. This workshop is intended to address the manifold computational challenges arising in number theoretic algorithms and cryptographic applications. Questions to be explored may include, but are by no means limited to:
Monday,
October 30 (Banquet tickets on sale Monday and Tuesday) 

8:30  8:45  Registration 
8:45  9:00  Opening Remarks 
9:00  10:00  VICTOR S. MILLER, Center
for Communications Research The weil pairing, and its efficient calculation 
10:00  10:30  Coffee Break 
10:30  11:20  STEVEN GALBRAITH,
Royal Holloway University of London Some open problems in elliptic curve cryptography 
11:25  12:15  FLORIAN HESS, Technische Universitt
Berlin The ate pairing  computational aspects of pairings in cryptography 
12:15  2:10  Lunch 
2:10  3:00  KIRAN KEDLAYA, Massachusetts
Institute of Technology Recent results on padic computation of zeta functions 
3:00  3:30  Coffee Break 
3:30  4:20 
ALINA COJOCARU, University of Illinois at Chicago 
4:25  4:45  HUGH WILLIAMS, University
of Calgary My reminiscences of Emma Lehmer 
4:45  Reception at Fields 
Tuesday,
October 31 (Banquet tickets on sale Monday and Tuesday) 

9:00  10:00  FRANCOIS MORAIN, Ecole Polytechnique,
LIX Recent improvements to the SEA algorithm in genus 1 
10:00  10:30  Coffee Break 
10:30  11:20  ALLISON M. PACELLI, Williams
College Constructing number fields and function fields with prescribed class group properties 
11:25  12:15  RACHEL PRIES, Colorado State
University Computing the invariants of ptorsion of Jacobians in characteristic p 
12:15  2:00  Lunch 
2:00  2:50  YOONJIN LEE, Simon Fraser
University Construction of cubic function fields from quadratic infrastructure 
2:50  3:15  Coffee Break 
3:15  4:05 
ERICH KALTOFEN, North Carolina State University 
4:054:55  DANIELE MICCIANCIO, University of California San Diego Ideal lattices: cryptographic applications and open problems 
Wednesday, November 1  
9:00  10:00  PIERRICK GAUDRY, Ecole Polytechnique Variants of the montgomery form based on theta functions 
10:00  10:30  Coffee Break 
10:30  11:20 
ALFRED MENEZES, University of Waterloo 
11:25  12:15 
JOHANNES BUCHMANN, Technische Universitat Darmstad 
Rest of the day free  
Thursday, November 2  
9:00  10:00  PETER STEVENHAGEN, Universiteit
Leiden Computational challenges arising in complex multiplication 
10:00  10:30  Coffee Break 
10:30  11:20  ELISA GORLA, University of
Zurich Computational challenges arising in torusbased cryptography 
11:25  12:15  JINTAI DING, Technical University
of Darmstadt Multivariate public key cryptography 
12:15  2:10  Lunch 
2:10  3:00  DAVID JAO, University of Waterloo The discrete logarithm problem on algebraic curves 
3:00  3:30  Coffee Break 
3:30  4:20  MARK BAUER, University of
Calgary Relating the ECDLP to other curves 
6:00  Banquet at L'Expresso Restaurant, corner of St. George & Bloor, 321 Bloor Street 
Friday, November 3  
9:00  10:00  TAKAKAZU SATOH, Tokyo Institute
of Technology On Euclid prime sequences (joint work with Nobushige Kurokawa) 
10:00  10:30  Coffee Break 
10:30  11:20  NILS BRUIN, Simon Fraser University Deciding the existence of rational points on curves 
11:25  12:15 
MICHAEL JACOBSON, University of Calgary 
12:15  2:10  Lunch 
2:10  3:00  MARK GIESBRECHT AND ARNE STORJOHANN,
University of Waterloo Speedy new algorithms for solving integer linear systems 
3:00  3:30  Coffee Break 
3:30  4:20  ROGER OYONO, University of
Waterloo Computation of nonhyperelliptic modular Jacobians of dimension 3 
Banquet:
There will be a conference banquet on Thursday November 2. Tickets
will be on sale Monday and Tuesday ($60 includes one drink) . All
additional drinks are available at the cash bar.
The banquet will take place Thursday night 6 pm at the L'Expresso
Restaurant at the corner of St. George and Bloor, 321 Bloor
Street. The menu is as follows:
Canopies  Assorted mini pizza served as guests arrive 
Primo  Arugola Salad with asiago cheese, tomato in vinaigrette 
Secondo Choice of 
 Linguine ai Frutti di mare with mussels, calamari, shrimp,
sea scallops and salmon or  Alberta AAA Black Angus Strip loin served with house frites, asparagus and mushroom jus or  a vegetarian choice,Truffled Risotto with Mushrooms 
Dessert 
Assorted biscotti and fruit platter/table Expresso, cappucino, latte 