MA 1580: Cryptography

Instructor

  • Reinier Bröker
  • Office: Room 117, Math Building
  • Phone: (401) 863-7959
  • E-mail: reinier@math.brown.edu

    • Times and Places

    Text book

    An introduction to mathematical cryptography by J. Hoffstein, J. Pipher, J. Silverman. This book is available at the Brown bookstore and online. The `homepage' of this book contains a list of errata.

    Contents

    Topics include classical cryptographic constructions, such as Diffie-Hellman key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem and digital signatures. To explore the full potential of these systems, we cover fundamental mathematical tools, such as primality testing and factorization algorithms. We will make a selection from various advanced cryptosystems based on e.g. elliptic curves, lattices or convolution polynomial rings.

    Midterm

    Click here for a copy of the midterm.

    Exams

    The final exam will be December 9, 9am -- noon. The room is Barus and Holley 141.

    Grade

    Your grade is based on the homework, midterm and final. I will weigh these as follows. Homework: 30%, Midterm: 30%, Final: 40%. If any curving is done (it need not be), it will only be done on your averaged grade.

    News (11/1/2010): you can earn a max. 7 point improvement on your midterm grade by doing extra work. Everything needs to be handed in before class ends on Monday November 22.

    Homework

    I will assign homework every week, see below. The exercises fall into three categories: (1) easy exercises, (2) hard exercises, (3) obligatory exercises. Easy exercises are worth 2 points, hard and obligatory exercises are worth 3 points. Your homework score is your total number of points. If you decide to do mostly easy exercises, then you should expect that you're at `B-level' for the course. The hard exercises are mostly on `A-level'. You have the freedom to choose the exercises you do yourselves. I will tell you how many exercises you should hand in and a set of exercises you may pick from.

    Calculators

    Calculators are not required for this course, and they are not allowed on any exam. You make your own life easier if you do not use them for the homework exercises either.

    Homework

    Due date Number of exercises Easy exercises Hard exercises Obligatory exercises
    9-8-2010 4 1.1, 1.2, 1.3, 1.6, 1.7 1.4, 1.5, 1.8, 1.11, 1.13 Compute the extended gcd of your birthday and phone number
    9-15-2010 4 1.14, 1.15, 1.16, 1.21, 1.28 1.18, 1.19, 1.20, 1.22, 1.27 1.25
    9-22-2010 4 1.32 (a-d), 1.34 (a-c), 1.38, 1.43, 1.44 1.31, 1.33, 1.35, 1.36, 1.39, 1.46, 1.47 (a-c) 1.30(a)
    9-29-2010 4 2.3, 2.4, 2.11, 2.14 (allowed to use 2.13), 2.16 2.5, 2.7, 2.9, 2.12, 2.13, 2.15 (a-d) 2.8
    10-6-2010 4 2.21, 2.26 2.20, 2.22, 2.23, 2.24 2.17a, 2.18(a,d), 2.28(a)
    10-13-2010 4 3.1(a-b), 3.3(a-b), 3.8 3.4, 3.9 3.10, 3.12 3.6, 3.7
    10-20-2010 2 none none 3.13(a), 3.14(a)
    10-28-2010 2 3.37, 3.38(a) 3.18, 3.36 3.21(a)
    11-3-2010 2 3.41, 6.1
    11-10-2010 3 6.3, 6.13, Additional exercise
    11-17-2010 3 6.17, 6.18, 6.22(b,c)
    12-1-2010 5 7.1, 7.4 7.6, 7.7 6.28, 6.32, 7.2, 7.5