# Khodakhast Bibak

## Assistant Professor

205T Benton Hall

513-529-0338

bibakk@MiamiOH.edu

www.users.miamioh.edu/bibakk

### Research Interests

- Cryptography, Information Security
- Coding Theory, Information Theory, Communication Theory
- Discrete Mathematics
- Number Theory, Finite Fields
- Mathematics of Quantum Theory
- Algorithms

### Education

**Ph. D., Computer Science**

University of Victoria, Canada

2017**Master of Mathematics**

University of Waterloo, Canada

2013

### Academic Appointments

**Postdoctoral Research Associate**, September 2017 – August 2018

Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, USA

Host: Professor Olgica Milenkovic**Postdoctoral Research Fellow**, May 2017 – August 2017

Department of Computer Science, University of Victoria, Canada

Hosts: Professor Bruce M. Kapron and Professor Venkatesh Srinivasan

### Teaching Certificates

- Fundamentals of University Teaching, Spring 2013

Centre for Teaching Excellence (CTE), University of Waterloo

### Teaching Experiences

Teaching assistant (lab instructor, marker etc) for a variety of courses in computer science and mathematics at

- University of Victoria: CSC 167, CSC 349A, CSC 320
- University of Waterloo: Math 104, Math 106, Math 118, Math 119, Math 135, Math 137, CO 227, CO

250, PMath 352.

### Professional Activities

- Reviewer of
- Designs, Codes and Cryptography
- 28th Annual ACM-SIAM Symposium on Discrete Algorithms — SODA 2017
- Discrete Mathematics
- IEEE Transactions on Information Theory
- IEEE Transactions on Signal Processing
- Neural Computing and Applications
- Linear and Multilinear Algebra
- IEEE Transactions on Information Theory (subreviewer)
- Discussiones Mathematicae Graph Theory
- 8th International Symposium on Foundations & Practice of Security — FPS 2015
- Journal of Number Theory
- IEEE Signal Processing Letters

- Session Chair of 55th Annual Allerton Conference on Communication, Control, and Computing — Allerton 2017 (Allerton Retreat Center, Monticello, IL, USA, October 3–6, 2017)
- Organizing Committee Member of 14th International Symposium on Algorithms and Data Structures — WADS 2015 (University of Victoria, August 5–7, 2015)
- Scientific Committee Member (proposer and marker of problems) of Iranian Mathematics Competitions

for University Students, 2008–2011.

### Fellowships/Awards, Travel Grants, Honours, Other Recognition

#### Fellowships/Awards

- UVic Fellowship, University of Victoria (Fall 2014 – Summer 2016)
- UVic Graduate Award, University of Victoria (Summer 2015, Spring 2016, Summer 2016, Spring 2017)
- RA Support, University of Victoria (Fall 2014 – present)
- Senate Graduate Scholarship Tutte C&O Award, University of Waterloo (Fall 2012)
- Graduate Research Studentship, University of Waterloo (Fall 2011 – Winter 2013)
- Mathematics Graduate Experience Award, University of Waterloo (Fall 2011 – Winter 2013)
- International Master’s Student Award, University of Waterloo (Fall 2011 – Winter 2013)
- Mathematics Faculty Graduate Award, University of Waterloo (Fall 2011 and Fall 2012)

#### Travel Grants

- Travel Grant from the Heidelberg Laureate Forum Foundation (HLFF) for the 4th Heidelberg Laureate Forum, Heidelberg University, September 18–23, 2016
- Travel Grant from the International Association for Cryptologic Research (IACR) for the 36th International Cryptology Conference — CRYPTO 2016, University of California, Santa Barbara, August 14–18, 2016
- Travel Grant from the Fields Institute for the Conference on Geometry, Algebra, Number Theory, and their Information Technology Applications, The Fields Institute, Toronto, June 13–16, 2016
- Travel Grant from NSF for the 2015 Midwest Number Theory Conference, University of Illinois at Chicago, October 16–18, 2015
- Travel Grant from ACM/NSF for the 8th ACM Conference on Security and Privacy in Wireless and Mobile Networks — ACM WiSec 2015, New York Institute of Technology, June 24–26, 2015 (declined)
- Travel Grant from the Pacific Institute for the Mathematical Sciences (PIMS) for the Algorithmic Theory of Networks Workshop, Simon Fraser University, March 27–29, 2015
- Travel Grant from the Mathematical Sciences Research Institute (MSRI) for the Workshop Hot Topics: Kadison-Singer, Interlacing Polynomials, and Beyond, MSRI, Berkeley, March 9–13, 2015
- Travel Grant from the Fields Institute for the Workshop on Number Theory with a view towards Transcendence and Diophantine Approximation, University of Ottawa, June 8–10, 2013
- Travel Grant from the Centre de Recherches Mathématiques (CRM) for the SMS 2012 Summer School: Probabilistic Combinatorics, CRM, Université de Montréal, June 25 – July 6, 2012

#### Honours

- Erdős Number: 3. Link: Paul Erdős - Carl Pomerance - Igor Shparlinski - me
- Einstein Number: 4. Link: Albert Einstein - Ernst Straus - Carl Pomerance - Igor Shparlinski - me
- 1st rank (two years) in the Province, and 40th and 20th ranks in the Country, in Iranian Mathematics

Olympiad

#### Other Recognition

- My paper “The number of spanning trees..." has been featured on the cover of International Journal of Quantum Chemistry, Volume 113, Issue 8: http://onlinelibrary.wiley.com/doi/10.1002/qua.v113.8/issuetoc

### Research Highlights

- My paper "Explicit formulas for..." proves a very general result which gives, as consequences, the weight enumerators of several important classes of deletion correcting codes and some of their variants which have been recently used in studying DNA-based data storage systems. Our general results might have more applications/implications in information theory, computer science, and mathematics.
- My paper "Unweighted linear congruences with distinct..." studies an arithmetic function and then, as a consequence, gives the weight distribution of the important Varshamov–Tenengolts codes. There are also interesting connections to combinatorics.
- My paper "A generalization of Schönemann’s theorem..." generalizes a result of Schönemann from 1839 using a graph theoretic method.
- My paper "The Cayley graphs associated with..." using tools from spectral graph theory, character theory, and finite fields, solves a conjecture (stemming from coding theory) appeared in IEEE Trans. Inform. Theory.
- My paper "Counting surface-kernel epimorphisms..." gives, as a corollary, an ‘equivalent’ form of the famous and influential Harvey’s theorem on the cyclic groups of automorphisms of compact Riemann surfaces. There are also motivations from string theory and quantum field theory.
- My paper "On an almost-universal hash function family..." is the first paper that introduces applications of Ramanujan sums, finite Fourier transform, and restricted linear congruences in the study of universal hashing.
- My paper "MMH∗ with arbitrary modulus..." simply generalizes the well-known ∆-universal hash function family, MMH∗.
- My paper "Restricted linear congruences" strongly generalizes a result of Rademacher from 1925 and Brauer from 1926 and many others. There are also direct applications to the “generalized knapsack problem" and many other things.
- My paper "On fully split..." studies a problem in factorizations of sparse polynomials over finite fields using a rather unusual combination of some techniques including some graph theory arguments.
- My paper "Degree-equipartite graphs" solves a problem posed by some leading combinatorialists. This also automatically generalizes the main result of their paper (and another paper published in Trans. Amer. Math. Soc.) too.
- My paper "On the Erdős-Gyárfás conjecture in claw-free graphs" gives some partial results on the

well-known Erdős-Gyárfás conjecture.

### Publications

#### (Mathematics of) Cryptology and Information Theory

1. (**K. Bibak**, O. Milenkovic) Explicit formulas for the weight enumerators of some classes of deletion correcting codes, submitted.

2. (**K. Bibak**, B. M. Kapron, V. Srinivasan) A generalization of Schönemann's theorem via a graph theoretic method, submitted.

3. (**K. Bibak**, O. Milenkovic) Weight enumerators of some classes of deletion correcting codes, In Proceedings of the 2018 IEEE International Symposium on Information Theory --- ISIT 2018, Vail, Colorado, USA, Jun. 17-22, 2018.

4. (**K. Bibak**, B. M. Kapron, V. Srinivasan) Unweighted linear congruences with distinct coordinates and the Varshamov-Tenengolts codes, Designs, Codes and Cryptography 86 (2018), 1893–1904.

5. (**K. Bibak**, B. M. Kapron, V. Srinivasan, L. Tóth) On an almost-universal hash function family with applications to authentication and secrecy codes, International Journal of Foundations of Computer Science 29 (2018), 357-375.

6. (**K. Bibak**, B. M. Kapron, V. Srinivasan, R. Tauraso, L. Tóth) Restricted linear congruences, Journal of Number Theory 171 (2017), 128–144.

7. (**K. Bibak**, B. M. Kapron, V. Srinivasan) The Cayley graphs associated with some quasi-perfect Lee codes are Ramanujan graphs, IEEE Transactions on Information Theory 62 (2016), 6355–6358.

8. (**K. Bibak**, B. M. Kapron, V. Srinivasan, L. Tóth) On a variant of multilinear modular hashing with applications to authentication and secrecy codes, In Proceedings of the International Symposium on Information Theory and Its Applications — ISITA 2016, Monterey, California, USA, Oct. 30 – Nov. 2, 2016, pp. 320–324.

9. (**K. Bibak**, B. M. Kapron, V. Srinivasan) On a restricted linear congruence, International Journal of Number Theory 12 (2016), 2167–2171.

10. (**K. Bibak**, B. M. Kapron, V. Srinivasan) MMH∗ with arbitrary modulus is always almost-universal, Information Processing Letters 116 (2016), 481–483.

11. (**K. Bibak**) Additive combinatorics with a view towards computer science and cryptography, Number Theory and Related Fields: In Memory of Alf van der Poorten (J. M. Borwein, I. E. Shparlinski and W. Zudilin, eds.), Springer Proceedings in Mathematics & Statistics, Vol. 43, Springer, New York, 2013, pp. 99–128. (The most downloaded Chapter of the Book.)

#### Mathematics of Quantum Theory

12. (**K. Bibak**, B. M. Kapron, V. Srinivasan) Counting surface-kernel epimorphisms from a co-compact Fuchsian group to a cyclic group with motivations from string theory and QFT, Nuclear Physics B 910 (2016), 712–723. (IF ≈ 4)

13. (**K. Bibak**) The number of spanning trees in an (r, s)-semiregular graph and its line graph, International Journal of Quantum Chemistry 113 (2013), 1209–1212. (IF ≈ 3)

#### Graph Theory and Combinatorics

14. (P. Salehi Nowbandegani, H. Esfandiari, M. H. Shirdareh Haghighi, **K. Bibak**) On the Erdős-Gyárfás conjecture in claw-free graphs, Discussiones Mathematicae Graph Theory 34 (2014), 635–640. (Among the most downloaded papers of the Journal.)

15. (**K. Bibak**) On the determinant of bipartite graphs, Discrete Mathematics 313 (2013), 2446–2450.

16. (**K. Bibak**, R. Tauraso) Determinants of grids, tori, cylinders and Mobius ladders, Discrete Mathematics 313 (2013), 1436–1440.

17. (M. H. Shirdareh Haghighi, **K. Bibak**) The number of spanning trees in some classes of graphs, Rocky Mountain Journal of Mathematics 42 (2012), 1183–1195.

18. (**K. Bibak**, M. H. Shirdareh Haghighi) Degree-equipartite graphs, Discrete Mathematics 311 (2011), 888–891.

19. (**K. Bibak**, M. H. Shirdareh Haghighi) Some trigonometric identities involving Fibonacci and Lucas numbers, Journal of Integer Sequences 12 (2009), Article 09.8.4.

20. (M. H. Shirdareh Haghighi, **K. Bibak**) Recursive relations for the number of spanning trees, Applied Mathematical Sciences 3 (2009), 2263–2269.

21. (M. H. Shirdareh Haghighi, **K. Bibak**) Distribution of cycle lengths in graphs with minimum degree at least three, In Proceedings of the 39th Annual Iranian Mathematics Conference, Shahid Bahonar University of Kerman, Kerman, Iran, Aug. 24–27, 2008.

#### Number Theory

22. (**K. Bibak**, I. E. Shparlinski) On fully split lacunary polynomials in finite fields, Bulletin of the Polish Academy of Sciences, Mathematics 59 (2011), 197–202.

#### Problems

23. (**K. Bibak**) Problem # 1884, Mathematics Magazine, Vol. 84, No. 5, December 2011.

24. (**K. Bibak**) Problem # 11590, American Mathematical Monthly, Vol. 118, No. 7, August-September 2011.

#### Theses

25. (**K. Bibak**) Number theoretic methods and their significance in computer science, information theory, combinatorics, and geometry, PhD thesis, Department of Computer Science, University of Victoria, 2017.

26. (**K. Bibak**) Contributions at the interface between algebra and graph theory, Master’s thesis, Depart- ment of Combinatorics and Optimization, University of Waterloo, 2013.

#### Technical Reports

27. (**K. Bibak**, C. Liu, H. Vosoughpour, G. Yao, Z. AlMeraj, A. Pytel, W. Cowan, S. Mann) Implicit surfaces seminar, Spring 2012, Technical Report CS-2013-08, David R. Cheriton School of Computer Science, University of Waterloo, 2013 (40 pages).

### Conference Talks

- International Symposium on Information Theory and Its Applications — ISITA 2016, Monterey, California, USA, Oct. 30 – Nov. 2, 2016.
- Conference on Geometry, Algebra, Number Theory, and their Information Technology Applications, The Fields Institute, Toronto, June 13–16, 2016.
- 2015 Midwest Number Theory Conference, University of Illinois at Chicago, October 16–18, 2015.
- International Conference IPM 20 — Combinatorics 2009, IPM, Tehran, Iran, May 15–21, 2009.