- Office hours: Tuesday, Wednesday, Thursday 12-1 in Evans 847
- Here is our syllabus.
- Our textbook is ''An Introduction to Mathematical Cryptography" (2014 edition, Springer) by Hoffstein, Pipher, and Silverman. You can buy this book directly from Springer or on Amazon. You can also download digital copies from the SpringerLink website using the UC Berkeley institutional access.
- There are two editions of this book: the 2009 edition and the 2014 edition. The content we will cover is contained in both editions. However, please make sure you are using the 2014 edition for the homework, as the numbering in the exercises is sometimes different.
- To do many of the homework problems, you will need to use computational mathematics software, such as Sage, Magma, or Mathematica. I recommend using Sage, which is free and open source. You can download it for yourself here, or use it in your browser with cocalc.
- Solutions to the first midterm (class average: ~43.3 out of 55, or ~78%. Standard deviation: 6)
- Documentation for elliptic curves over finite fields in Sage.
- Solutions to the second midterm (class average: ~50.9 out of 65, or ~78.1%. Standard deviation: 5.5)
- First midterm: October 4
- Second Midterm: November 8
- Final Exam: December 12, 3-6 PM
- Homework 1 (due September 4)
Do the following problems from the textbook: 1.7, 1.8, 1.9c,d (try using the method of 1.8, and check your work with Sage), 1.10c,d (check your work with Sage!), 1.11, 1.17, 1.22
- Homework 2 (due September 11)
Do the following problems from the textbook: 1.24, 1.32, 1.36, 2.4, 2.6, 2.8. I recommend using Sage to help with the computations on the last two problems.
- Homework 3 (due September 18)
Do the following problems from the textbook: 2.17, 2.27, 2.28c, 2.29, 2.35d, 2.38, 2.39
Make sure you are using the 2014 edition of the book!
- Homework 4 (due September 25)
Do the following problems from the textbook: 3.1, 3.2, 3.4, 3.7, 3.8, 3.9ab
- Homework 5 (due October 2)
Do the following problems from the textbook: 3.14a, 3.15a,b,f,g, 3.37, 3.39
Using quadratic reciprocity and the method we went over in class (see section 3.9 of the book), decide whether 1103 is a square modulo 2999 (hint: both of these numbers are prime)
- Homework 6 (due October 18) (solutions)
Do the following problems from the textbook: 6.1, 6.2, 6.3, 6.4cd, 6.5ab
See the resources for some information on working with elliptic curves in Sage.
- Homework 7 (due October 25) (solutions)
Do the following problems from the textbook: 6.7, 6.8, 6.11cd, 6.14, 6.16
- Homework 8 (due November 1) (solutions)
Do the following problems from the textbook: 6.24 (we will discuss the Frobenius map on Tuesday), 6.26
Also, do the following three problems.
- Homework 9 (this is a smaller homework, due November 6) (solutions)
Do problems 6.31 and 6.39 from the textbook.
- Homework 10 (due date changed to Tuesday, November 27) (solutions)
Do problems 5.4, 5.21, 5.22, 5.24, 5.25, 5.28, 5.29, and 5.30 from the textbook.
- Homework 11 (due December 4) (solutions)
Do problems 5.34, 5.35, 5.37, 5.38, 5.39, and 5.40 from the textbook.