Khodakhast Bibak

                                                                            Welcome to My Homepage!

 

Hi! I am a PhD student (since Fall 2014) at the Department of Computer Science, University of Victoria, under the supervision of Professor Bruce Kapron and Professor Venkatesh Srinivasan. Prior to pursuing my PhD, I obtained an MMath degree (Fall 2011-Winter 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 “Codewords in the Varshamov-Tenengolts codes …” studies an arithmetic function and gives several applications to coding theory and combinatorics.

·         My paper “On linear congruences with distinct …” 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.      (with B. M. Kapron, V. Srinivasan) Codewords in the Varshamov-Tenengolts codes with Hamming weight k and several combinatorial applications, submitted.

2.      (with B. M. Kapron, V. Srinivasan) On linear congruences with distinct coordinates: A graph theoretic method, submitted.

3.      (with 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].

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

5.      (with 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].

6.      (with 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].

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

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

9.      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].

 

 

Mathematics of Quantum Theory

10.  (with 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)

11.  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 ≈ 2.2)

 

 

Graph Theory and Combinatorics

12.  (with H. Esfandiari, P. Salehi Nowbandegani, M. H. Shirdareh Haghighi) 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.)

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

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

15.  (with M. H. Shirdareh Haghighi) The number of spanning trees in some classes of graphs, Rocky Mountain Journal of Mathematics 42 (2012), 1183-1195; [journal].

16.  (with M. H. Shirdareh Haghighi) Degree-equipartite graphs, Discrete Mathematics 311 (2011), 888-891; [arXiv], [journal].

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

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

19.  (with M. H. Shirdareh Haghighi) 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

20.  (with 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

21.  Problem # 1884, Mathematics Magazine, Vol. 84, No. 5, December 2011. [The published solution is here.]

22.  Problem # 11590, American Mathematical Monthly, Vol. 118, No. 7, August-September 2011. [The published solution is here.]

 

 

Theses

23.  Contributions at the interface between algebra and graph theory, Master's thesis, Department of Combinatorics and Optimization, University of Waterloo, 2013.

 

 

Technical Reports

24.  (with 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 - 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

 

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

·         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: Department of Computer Science, University of Victoria, 3800 Finnerty Rd, Victoria, BC, Canada V8W 3P6

Office: ECS 521

Theory Lab: ECS 642

Theory Lab Phone Number: 250-472-5738

Email: kbibak at uvic dot ca, khmath at gmail dot com