** Khodakhast
Bibak**

**
Welcome to My Homepage!**

Hi! I am a Postdoctoral Research Associate
(since September 2017) in the Coordinated Science Laboratory
at the University of Illinois at Urbana-Champaign,
hosted by Professor Olgica Milenkovic.
Previously, I was a Postdoctoral Research Fellow (May-August 2017) at the Department of Computer Science, University of Victoria,
from where I also received my PhD (April 2017) under the supervision of
Professor Bruce Kapron and
Professor Venkatesh Srinivasan. Prior
to that, I obtained a Master of Mathematics degree (April 2013) at the Department of Combinatorics
& Optimization, University of Waterloo,
where I was also a member of the Centre for Applied
Cryptographic Research (CACR).

Research Interests

My work is highly interdisciplinary and is at the
intersection of mathematics, computer science, and electrical engineering. More
specifically, my research interests lie in the following areas (and their
interactions):

·
Cryptography,
Information Security

·
Coding
Theory, Information Theory, Communication Theory

·
Discrete
Mathematics

·
Number
Theory, Finite Fields

·
Mathematics
of Quantum Theory

·
Algorithms

Research Highlights

·
My paper “*Weight
enumerators* …” 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
Delta-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)
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.

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

3.
(K. Bibak, B. M. Kapron, V. Srinivasan) Unweighted linear congruences with distinct coordinates and the Varshamov-Tenengolts codes, *Designs, Codes and
Cryptography*, to appear; [journal].

4.
(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*,
to appear; [arXiv], [IACR].

5.
(K. Bibak, B. M. Kapron, V. Srinivasan, R. Tauraso, L. Tóth)
Restricted linear congruences, *Journal of Number
Theory* 171 (2017), 128-144; [arXiv], [IACR], [journal].

6.
(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; [journal].

7.
(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; [conference].

8.
(K. Bibak, B. M. Kapron, V. Srinivasan) On a
restricted linear congruence, *International Journal of Number Theory* 12
(2016), 2167-2171; [arXiv], [journal].

9.
(K. Bibak, B. M. Kapron, V. Srinivasan) MMH* with arbitrary modulus is
always almost-universal, *Information Processing Letters* 116 (2016),
481-483; [journal].

10. (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; [arXiv], [chapter]. (**The most downloaded Chapter of
the Book**.)

Mathematics of Quantum Theory

11. (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; [arXiv], [journal]. (**IF ≈
4**)

12. (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; [journal]. (**IF ≈
3**)

Graph Theory and Combinatorics

13. (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; [arXiv], [journal]. (**Among
the most downloaded papers of the
Journal**.)

14. (K. Bibak) On the determinant of bipartite graphs, *Discrete
Mathematics* 313 (2013), 2446-2450; [journal].

15. (K. Bibak, R. Tauraso)
Determinants of grids, tori, cylinders and Mobius ladders, *Discrete
Mathematics* 313 (2013), 1436-1440; [arXiv], [journal].

16. (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; [journal].

17. (K. Bibak, M. H. Shirdareh Haghighi) Degree-equipartite
graphs, *Discrete Mathematics* 311 (2011), 888-891; [arXiv], [journal].

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

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

20. (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

21. (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; [arXiv], [journal].

Problems

22. **(**K. Bibak) Problem # 1884, *Mathematics Magazine*,
Vol. 84, No. 5, December 2011. [The published solution is here.]

23. (K. Bibak) Problem # 11590, *American
Mathematical Monthly*, Vol. 118, No. 7, August-September 2011. [The
published solution is here.]

Theses

24. (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.

25. (K. Bibak) Contributions at the interface between algebra and
graph theory, Master's thesis, Department of Combinatorics and
Optimization, University of Waterloo, 2013.

Technical Reports

26. (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.

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 - Spring
2017)

·
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

·
1* ^{st}* rank (two years) in the
Province, and 40

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

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

Ø *Designs,
Codes and Cryptography*

Ø *28th Annual
ACM-SIAM Symposium on Discrete Algorithms --- SODA 2017*

Ø
*Discrete Mathematics*

Ø
*IEEE Transactions on Information Theory*

Ø
*IEEE Transactions on Signal Processing *

Ø
*Neural Computing and Applications*

Ø
*Linear and Multilinear Algebra*

Ø
*IEEE Transactions on Information Theory * (subreviewer)

Ø
*Discussiones** Mathematicae
Graph Theory*

Ø
*8th International Symposium on Foundations
& Practice of Security --- FPS 2015*

Ø
*Journal of Number Theory*

Ø
*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. The invaluable book Iranian Mathematics Competitions, 1973-2007
(by Bamdad R. Yahaghi),
presents a collection of problems appeared in these competitions, together with
their solutions. A copy of this book is available here.

Contact Information

Address:
Coordinated Science Laboratory, University of Illinois at Urbana-Champaign,
1308 W. Main St., Urbana, Illinois, 61801

Office: CSL
127

Email: kbibak at illinois
dot edu, khmath at gmail dot com