Seminar: Elliptic curve, isogenies and related topics

Main projects: Elliptic curves, isogenies, related topics and their application in cryptography.

The first part of the seminar (elliptic curves, varieties, …): We follow the book "The Arithmetic of Elliptic Curves" of Silverman -chapters 1, 2, 3

We can also read the note of Stevenhagen

The second part of the seminar (Isogenies and related computational problems): We will follow the lecture notes (from lecture #5) of Andrew Sutherland here

The third part of the seminar: We work in 3 groups and meet once a week for updates.

The schedule for Fall 2022 and Winter 2023 are as below: 7:30am - 9am on Saturday (Edmonton time) on Zoom, see more info on Slack.

September 3: Hang will present "Shape of number fields" (Home's thesis).
November 05: Hang will present the paper "An efficient key recovery attack on SIDH (preliminary version)" (Wouter Castryck and Thomas Decru)
November 26: Thuong will present compact Riemann surfaces and modular functions (in the series "Modular curves, CM methods and applications in crypto".)

The participants are as below:

The schedule for Winter 2022 and Summer 2022 are as below: 7am - 9am on Saturday (Edmonton time) on Zoom, see more info on Slack.

January 28, 2022: Tri Nguyen- ternary forms associated to Endomorphism rings of supersingular elliptic curves- Cervino and Lemurell's papers.
February 11: Discussion Chapter 7 in Kohel’s thesis.
February 18: Lecture 20- Sutherland-The Hilbert class polynomial (Thang Nguyen)
March 11 and 18: Lecture 16 -Sutherland- Complex Multiplication (CM) (Thang Nguyen)
April 2 and April 9: Hang Nguyen presented her thesis - construct an isogeny between 2 given ordinary elliptic curves.
April 16: Tri presented his thesis -Elliptic curves cryptography and attacks.
July 9: Tri will present his project "Ternary forms of supersingular elliptic curves over F_p".
July 30 and August 6: Tri presents the paper "Endomorphism rings of supersingular elliptic curves over F_p" (Li, Ouyang, Xu-2020)".
August 13: Hang will present "Shape of lattices" (Home's thesis).

The participants are as below:

The schedule of Fall 2021 is as below: 8 pm-10 pm on Saturday (Edmonton time) on Zoom, see more info on Slack.

September 7, 2021: Tri Nguyen - Chapter 3.8-Silverman
September 14: No seminar.
September 21: Trinh Le - Chapter 3.9, 3.10-Silverman
September 28: No seminar.
October 9: Trinh Le - Lecture #5 - Isogenies (Sutherland)
October 16: Dat Tran - Lecture #6- Isogeny Kernels and Division Polynomials (PDF) (Sutherland)
October 23: Dat Tran - Lecture #6- Isogeny Kernels and Division Polynomials (PDF) (Sutherland)continued
and Hang Nguyen: Galois theory - review
October 30: Tri Nguyen - Lecture # 7-Endomorphism Rings (PDF) (Sutherland)
November 6: No seminar.
November 13: Tri Nguyen - Lecture # 7-Endomorphism Rings (PDF) (Sutherland) -continued
November 20: Thang Nguyen - Lecture # 13 - Endomorphism Algebras (PDF) (Sutherland)
November 27: Thang Nguyen - Lecture # 13 - Endomorphism Algebras (PDF) (Sutherland)-continued
December 4: Thang Nguyen - Lecture # 14 - Ordinary and Supersingular Curves (PDF) (Sutherland)
December 11: Thang Nguyen - Lecture # 14 - Ordinary and Supersingular Curves (PDF) (Sutherland)-continued
December 17: Tri Nguyen -Lecture #8 - Schoof's algorithm
December 25, 2021: No seminar

The participants are as below:

The schedule for Summer 2021 is as below: 8 pm-10 pm on Tuesday (Edmonton time) on Zoom, see more info on Slack.

The participants are as below: