International Association for Cryptologic Research (IACR)

ECC2016 Computational Algebraic Number Theory School


This school is going to take took place on September 1-4, 2016 just before ECC. It is sponsored by the International Association for Cryptologic Research (IACR). The main topic of this school is the computational, cryptographic, and cryptanalytic aspects of algebraic number theory. The lecturers are as follows:

 

Ravzan Barbulescu

 

 

Omer Kucuksakalli

 

Université Pierre et Marie Curie, Laboratoire IMJ-PRG, Paris, France

Middle East Technical University (METU), Ankara, Turkey

 

Maike Massierer

 

 

Benjamin Smith

 

University of New South Wales (UNSW), Sydney, Australia

Équipe-Projet GRACE, INRIA Saclay–Île-de-France and Laboratoire d'informatique (LIX), École polytechnique, Paris, France

 

Peter Stevenhagen

 

 

Osmanbey Uzunkol

 

Leiden University, Leiden, Netherlands

Mathematical and Computational Sciences, Tubitak, Gebze, Turkey



Date

Time

Talk/Event

Media

Sept 1

09:00 - 09:45

Peter Stevenhagen, "Overview - The history of Algebraic Number Theory"

 

09:45 - 10:00

Break

 

10:00 - 10:45

Razvan Barbulescu, "Overview - Algebraic Number Theory in Cryptography"

[SLIDES]

10:45 - 11:00

Coffee/Tea Break

 

11:00 - 11:45

Omer Kucuksakalli, Part I: "Rings and fields, field extensions, modules, free abelian groups, algebraic numbers, conjugates and discriminants, algebraic integers, integral bases, norms and traces, ring of integers."

[SLIDES]

11:45 - 12:00

Break

 

12:00 - 12:45

Omer Kucuksakalli, Part II: "Rings and fields, field extensions, modules, free abelian groups, algebraic numbers, conjugates and discriminants, algebraic integers, integral bases, norms and traces, ring of integers."

[SLIDES]

12:45 - 14:00

Lunch

 

14:00 - 14:45

Osmanbey Uzunkol, Part I: "Examples of number fields: quadratic fields, cubic fields, cyclotomic fields. Prime ideal decomposition. Class group. Generalization to arbitrary orders."

[SLIDES]

14:45 - 15:00

Break

 

15:00 - 15:45

Osmanbey Uzunkol, Part II: "Examples of number fields: quadratic fields, cubic fields, cyclotomic fields. Prime ideal decomposition. Class group. Generalization to arbitrary orders."

 

15:45 - 16:00

Coffee/Tea Break

 

16:00 - 17:45

Omer Kucuksakalli and Razvan Barbulescu, "Computer Algebra Lab Session @ Room F106"

 

Sept 2

09:00 - 09:45

Peter Stevenhagen, Part I: "Finiteness of class group and Dirichlet's unit theorem"

 

09:45 - 10:00

Break

 

10:00 - 10:45

Peter Stevenhagen, Part II: "Finiteness of class group and Dirichlet's unit theorem"

 

10:45 - 11:00

Coffee/Tea Break

 

11:00 - 11:45

Razvan Barbulescu, "The computation of class groups and units"

[SLIDES]

11:45 - 12:00

Break

 

12:00 - 12:45

Peter Stevenhagen, "Quadratic orders"

 

12:45 - 14:00

Lunch

 

14:00 - 15:45

Omer Kucuksakalli and Razvan Barbulescu, "Computer Algebra Lab Session @ Room F106"

[FILES]

15:45 - 16:00

Coffee/Tea Break

 

16:00 - 20:00

Social Event - Downtown City Tour

 

Sept 3

09:00 - 09:45

Peter Stevenhagen, Part I: "Class field theory; the rational and imaginary quadratic base fields. Complex multiplication"

 

09:45 - 10:00

Break

 

10:00 - 10:45

Peter Stevenhagen, Part II: "Class field theory; the rational and imaginary quadratic base fields. Complex multiplication"

 

10:45 - 11:00

Coffee/Tea Break

 

11:00 - 11:45

Osmanbey Uzunkol, Part I: "Generating various class fields by modular functions"

 

11:45 - 12:00

Break

 

12:00 - 12:45

Osmanbey Uzunkol, Part II: "Generating various class fields by modular functions"

 

12:45 - 14:00

Lunch

 

14:00 - 14:45

Benjamin Smith, Part I: "Constructing elliptic curves over finite fields with "known" Frobenius"

 

14:45 - 15:00

Break

 

15:00 - 15:45

Benjamin Smith, Part II: "Constructing elliptic curves over finite fields with "known" Frobenius"

 

15:45 - 16:00

Coffee/Tea Break

 

16:00 - 17:45

Maike Massierer and Omer Kucuksakalli and Razvan Barbulescu, "Computer Algebra Lab Session @ Room F106"

[FILES]

Sept 4

09:00 - 09:45

Benjamin Smith, Part I: "Point counting for elliptic curves over finite fields"

 

09:45 - 10:00

Break

 

10:00 - 10:45

Benjamin Smith, Part II: "Point counting for elliptic curves over finite fields"

 

10:45 - 11:00

Coffee/Tea Break

 

11:00 - 11:45

Razvan Barbulescu, Part I: "Variants of NFS for fields of p^n elements when n>1"

 

11:45 - 12:00

Break

 

12:00 - 12:45

Razvan Barbulescu, Part II: "Variants of NFS for fields of p^n elements when n>1"

 

12:45 - 14:00

Lunch

 

14:00 - 14:45

Maike Massierer, Part I: "Recent advances in Index Calculus methods"

[SLIDES]

14:45 - 15:00

Break

 

15:00 - 15:45

Maike Massierer, Part II: "Recent advances in Index Calculus methods"

 

15:45 - 16:00

Coffee/Tea Break

 

16:00 -

Closing remarks, open problems (Chair: Peter Stevenhagen)

 

The school will take place at Auditorium A011 F001, Yasar University, Selcuk Yasar Campus, Izmir, Turkey. The auditorium can accommodate a maximum of 154 60 persons. The auditorium is equipped with air-conditioning, overhead projectors, boards, desk per seat, WIFI, HD broadcast to Internet infrastructure, and sound system.