MAT 401  Seminar: Mathematical Cryptography  

Fall 2025, TuTh 2:00-3:20pm Physics P125

Instructor: Ljudmila Kamenova

e-mail: kamenova@math.stonybrook.edu
Office: Math Tower 3-115
Office hours:

Syllabus: The seminar topic this semester will be "Mathematical Cryptography". The term cryptography refers to a wide range of security issues in the transmission and safeguarding of information. Many applications of algebra and number theory have arisen as a result of the development of public key cryptography. We'll introduce polynomial algorithms and randomized algorithms. We'll also recall the Euclidean algorithm for polynomials, prove the Hilbert Basis Theorem, and the Nullstellensatz. We'll apply algebraic and number theory methods to study hidden monomial cryptosystems, and combinatorial-algebraic cryprosystems. If time permits, we can also talk about elliptic and hyperelliptic cryptosystems. This course satisfies the SBC SPK requirement; as such, students are required to give presentations. MAT401 and MAT402 may be repeated, since the topic changes every time. All students wishing to receive departmental Honors in Mathematics must take MAT401 or MAT402 at least once (among other requirements).

This seminar course is aimed primarily at third- and fourth-year students majoring in mathematics.

I will start by giving a few initial lectures, but after a week or two the students will start their in-class presentations. During the first week of classes topics will be assigned to students.

Prerequisites: Basic understanding of algebra or number theory as in MAT 311, or MAT 312, or MAT 313 or equivalent.

Required Text: There is no required textbook. We are going to use mostly Neal Koblitz's book "Algebraic Aspects of Cryptography" (you can find a PDF version of this book online).

Here are some further reading materials:

Grading: The grading will be based primarily on class participation (40%), the quality of the student's in-class presentations (30%), and a final term paper consisting of the written version of one of the presentations (30%). The term paper should be typed of length 5 to 10 pages. Not attending regularly will have a negative effect on the grade. Regular attendance is therefore recommended.

The final term papers are due in the last week of classes.

List of topics (Lecture number/ topic) : TBA
  1. (Aug 26) Introduction.

  2. (Aug 28)

  3. (Sept 2)

  4. (Sept 4)

  5. (Sept 9)

  6. (Sept 11)

  7. (Sept 16)

  8. (Sept 18)

  9. (Sept 23)

  10. (Sept 25)

  11. (Sept 30)

  12. (Oct 2)

  13. (Oct 7)

  14. (Oct 9)

  15. (Oct 16)

  16. (Oct 21)

  17. (Oct 23)

  18. (Oct 28)

  19. (Oct 30)

  20. (Nov 4)

  21. (Nov 6)

  22. (Nov 11)

  23. (Nov 13)

  24. (Nov 18)

  25. (Nov 20)

  26. (Nov 25)

  27. (Dec 2)

  28. (Dec 4)


Accessibility Support Center (SASC) Statement: If you have a physical, psychological, medical or learning disability that may impact your course work, please contact the Student Accessibility Support Center (SASC), ECC (Educational Communications Center) Building, room 128, (631) 632-6748. They will determine with you what accommodations, if any, are necessary and appropriate. All information and documentation is confidential.

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