Daniel Panario - Research

• Research interests
• Awards and grants
• Editorial work
• Research publications
• Organized events
• Education
• Students
• Talks
• Courses (some with webpages)
• Interesting coming conferences

Research interests

• all aspects of finite fields and their applications;
• analysis of algorithms and analytic combinatorics;
• combinatorics;
• analytic, computational and combinatorial number theory;
• cryptography, coding theory and information theory;
• computer algebra and algebraic complexity.

Editorial Work

• Editorial board member of the journal Applicable Algebra in Engineering, Communication and Computing, Springer.
• Editorial board member of the journal Designs, Codes and Cryptography, Springer.
• Editorial board member of the journal Finite Fields and their Applications, Elsevier.
• Editorial board member of the journal International Journal of Combinatorics, Hindawi Publishing Corporation.
• Editorial board member of the journal International Journal of Information and Coding Theory, Inderscience Publishers.
• ``LATIN 2000: Latin American Theoretical INformatics'', G. Gonnet, D. Panario and A. Viola (eds), Lecture Notes in Computer Science 1776 (2000), Springer-Verlag, 480 pages.
• G. Gonnet, D. Panario and A. Viola (eds), Special issue in Theoretical Computer Science, 297(1-3), 510 pages, 2003.
• P. Jacquet, D. Panario and W. Szpankowski (eds), Special issue dedicated to the 10th International Seminar on Analysis of Algorithms in Algorithmica, 46 (3-4), 319 pages, 2006.
• D. Applegate, G. Brodal, D. Panario and R. Sedgewick (eds) of the proceedings of ANALCO'07 (``Analytic Algorithmics and Combinatorics 2007'') and ALENEX'07 (``Algorithm Engineering and Experiments''), SIAM Proceedings in Applied Mathematics 126, 287 pages, 2007.
• G. Mullen, D. Panario and I. Shparlinski (eds) of the proceedings of Fq8 (``8th Finite Fields and their Applications Conference''), Contemporary Mathematics 461, American Mathematical Society, 2008.
• G. McGuire, G. Mullen, D. Panario and I. Shparlinski (eds) of the proceedings of Fq9 (``9th Finite Fields and their Applications Conference''), to appear in Contemporary Mathematics series of the American Mathematical Society.

Recent publications

Papers:

• ``Asymptotics of smallest component sizes in decomposable combinatorial structures of alg-log type'' (with L. Dong, B. Richmond and Z. Gao), to appear in Discrete Mathematics and Theoretical Computer Science.
• ``Codes with girth 8 Tanner graph representation'' (with A. Sakzad and M. Sadeghi), to appear in Designs, Codes and Cryptography.
• ``Karatsuba's algorithm for polynomial multiplication in Chebyshev form'' (with J. Bandeira Lima and Q. Wang), to appear in IEEE Transactions on Computers.
• ``Adaptive sampling strategies for Quickselect'' (with C. Martinez and A. Viola), to appear in ACM Transactions on Algorithms.
• ``The number of irreducible polynomials of degree n over F_q with given trace and constant terms'' (with B. Omidi Koma and Q. Wang), Discrete Mathematics, 310, 1282-1292, 2010.
• ``Ambiguity and deficiency in Costas arrays and APN permutations'', to appear in LATIN 2010 (Latin American Theoretical INformatics), 2010.
• ``Bivariate asymptotics for striped plane partitions'' (with B. Richmond and B. Young), ANALCO'10 (Analytic Algorithmics and Combinatorics), SIAM, 18-26, 2010.
• ``Locating errors using ELAs, covering arrays and adaptive testing algorithms'' (with C. Martinez, L. Moura and B. Stevens), SIAM Journal on Discrete Mathematics, 23, 1776-1799, 2009.
• ``Efficient pth root computations in finite fields of characteristic p'' (with D. Thomson), Designs, Codes and Cryptography, 50, 351-358, 2009.
• ``Assinaturas digitais baseadas em polinomios de Chebyshev sobre corpos finitos primos'' (with J. Bandeira Lima and R. Campello de Souza), to appear in SBrT'09 (Simposio Brasileiro de Telecomunicacoes), 2009.
• ``Distribution of the number of encryptions in revocation schemes for stateless receivers'' (with C. Eagle, Z. Gao, M. Omar and B. Richmond), Discrete Mathematics and Theoretical Computer Science, 195-206, 2008.
• ``Enumeration of combinatorial decomposable structures with restricted patterns'' (with L. Dong and Z. Gao), Annals of Combinatorics, 12, 353-368, 2008.
• ``The trace of an optimal normal element and low complexity normal bases'' (with M. Christopoulou, T. Garefalakis and D. Thomson), Designs, Codes and Cryptography, 49, 199-215, 2008.
• ``Low complexity normal elements over finite fields of characteristic two'' (with A. Masuda, L. Moura and D. Thomson), IEEE Transactions on Computers, 57, 990-1001, 2008.
• ``Blind sequence separation based on the eigenstructure of finite fields transforms'' (with J. Bandeira Lima and R. Campello de Souza), SBrT'08 (Simposio Brasileiro de Telecomunicacoes), 2008.
• ``Algorithms to locate errors using covering arrays'' (with C. Martinez, L. Moura and B. Stevens), LATIN 2008, Lecture Notes in Computer Science 4957, Springer, 504-519, 2008.
• ``Security of public-key cryptosystems based on Chebyshev polynomials over prime finite fields'' (with J. Bandeira Lima and R. Campello de Souza), ISIT 2008 (IEEE International Symposium on Information Theory), 504-519, 2008.
• ``The size of the rth smallest component in decomposable structures with a restricted pattern'' (with L. Dong and Z. Gao), Discrete Mathematics and Theoretical Computer Science, 365-384, 2007.
• ``Division of trinomials by pentanomials and orthogonal arrays'' (with M. Dewar, L. Moura, B. Stevens and S. Wang), Designs, Codes and Cryptography, 45, 1-17, 2007.
• ``Sequences of consecutive smooth polynomials over a finite field'' (with A. Masuda), Proceedings of the American Mathematical Society, 135, 1271-1277, 2007.
• ``The trace of an optimal normal element and low complexity normal bases'' (with M. Christopoulou, T. Garefalakis and D. Thomson), extended abstract in Workshop on Coding and Cryptography 2007 (edited by D. Augot, N. Sendrier and J.-P. Tillich), INRIA, 79-88, 2007.
• ``A hybrid of Darboux's method and singularity analysis in combinatorial asymptotics'' (with P. Flajolet, E. Fusy, X. Gourdon and N. Pouyanne), The Electronic Journal of Combinatorics, 13, R103, 2006.
• ``Asymptotics of largest components in combinatorial structures'' (with M. Omar, B. Richmond and J. Whitely), Algorithmica, 46, 493-504, 2006.
• ``Integrating flexible tree searches to the orthogonal matching pursuit algorithm'' (with G. Karabulut, L. Moura and A. Yongacoglu), IEE Proc. on Vision, Image and Signal Processing, 153 (5), 538-548, 2006.
• ``Low density parity check lattices: construction and performance analysis'' (with M. Sadeghi and A. Banihashemi), IEEE Transactions on Information Theory, 52 (10), 4481-4495, 2006.
• ``The number of permutation binomials over F_{4p+1} where p and 4p+1 are primes'' (with A. Masuda and Q. Wang), The Electronic Journal of Combinatorics, 13, R65, 2006.
• ``Degree distribution of the greatest common divisor of polynomials over F_q'' (with Z. Gao), Random Structures and Algorithms, 29, 26-37, 2006.
• ``Polynomial Gauss sums'' (with S. Cohen, M. Dewar, J. Friedlander and I. Shparlinski), Proceedings of the American Mathematical Society, 133, 2225-2231, 2005.
• ``Low density parity check lattices based on Construction D' and cycle-free Tanner graphs'' (with M. Sadeghi), Algebraic Coding Theory and Information Theory, A. Ashikmin and A. Barg (eds.), AMS DIMACS Series 28, 85-90, 2005.
• ``Flexible tree-search based orthogonal matching pursuit algorithm'' (with G. Karabulut, L. Moura and A. Yongacoglu), ICASSP 2005 (IEEE International Conference on Acoustics, Speech, and Signal Processing), 4, 673-676, 2005.
• ``Distribution of exponential functions with $k$-full exponent modulo a prime'' (with M. Dewar and I. Shparlinski), Indagationes Mathematicae, 15, 497-503, 2004.
• ``The degree of the splitting field of a random polynomial over a finite field'' (with J. Dixon), Electronic Journal of Combinatorics, 11, R70, 2004.
• ``Asymptotics of combinatorial structures with large smallest component'' (with E. Bender, A. Mashatan and B. Richmond), Journal of Combinatorial Theory A, 107, 117-125, 2004.
• ``Low complexity normal bases'' (with B. Young), Finite Fields and their Applications, 10, 53-64, 2004.
• ``Mutual irreducibility of certain polynomials'' (with M. Dewar), Proceedings of the Seventh International Conference on Finite Fields: Theory, Applications, and Algorithms, G.L. Mullen, A. Poli and H. Stichtenoth (eds), Lecture Notes in Computer Science 2948, Springer, 59-68, 2004.
• ``What do random polynomials over finite fields look like?'', Proceedings of the Seventh International Conference on Finite Fields: Theory, Applications, and Algorithms, G.L. Mullen, A. Poli and H. Stichtenoth (eds), Lecture Notes in Computer Science 2948, Springer, 89-108, 2004.
• ``Adaptive sampling for Quickselect'' (with C. Martinez and A. Viola), in SODA'04, (Symposium on Discrete Algorithms), SIAM, 440-448, 2004.
• ``A simple primality test and the rth smallest prime factor'' (with B. Richmond and M. Yip), ANALCO'04, (Analytic Algorithmics and Combinatorics), SIAM Proceedings Series 115, 185-193, 2004.
• ``Integer to integer Karhunen Loeve transform over finite fields'' (with G. Karabulut and A. Yongacoglu), ICASSP 2004 (IEEE International Conference on Acoustics, Speech, and Signal Processing), 5, 213-216, 2004.
• ``Construction of lattices from low density parity check codes'' (with M. Sadeghi and A. Banihashemi), in CCECE 2004 (IEEE Canadian Conference on Electrical and Computer Engineering), 3, 1393-1396, 2004
• ``On iterative decoding algorithms of lattices'' (with M. Sadeghi and A. Banihashemi), in CCECE 2004 (IEEE Canadian Conference on Electrical and Computer Engineering), 3, 1417-1420, 2004
• ``Linear transformation shift registers'' (with M. Dewar), IEEE Transactions on Information Theory, 49, 2047-2052, 2003.
• ``Analysis of quickfind with small subfiles'' (with C. Martinez and A. Viola), Colloquium on Mathematics and Computer Science: Algorithms, Trees, Combinatorics and Probabilities, Trends in Mathematics, Birkhauser, 329-340, 2002.
• ``Polynomials over finite fields free from large and small degree irreducible factors'' (with T. Garefalakis), Journal of Algorithms, 44, 98-120, 2002.
• ``A rigorous proof of the Waterloo algorithm for the discrete logarithm problem'' (with M. Drmota), Designs, Codes and Cryptography, 26, 229-241, 2002.
• ``Asymptotics of subtracted singularities for generating functions with small singularities'', Journal of Computational and Applied Mathematics, 142, 197-209, 2002.
• ``Analysis of Rabin's irreducibility test for polynomials over finite fields'' (with B. Pittel, B. Richmond and A. Viola), Random Structures and Algorithms, 19, 525-551, 2001. [Extended abstract in LATIN'98 (Latin American Theoretical INformatics)].
• ``Exact largest and smallest size of components in decomposable structures'' (with B. Richmond), Algorithmica, 31, 413-432, 2001.
• ``The complete analysis of a polynomial factorization algorithm over finite fields'' (with P. Flajolet and X. Gourdon), Journal of Algorithms, 40, 37-81, 2001. [Extended abstract in ICALP'96 (International Colloquium on Automata, Languages and Programming)].
• ``The index calculus method using non-smooth polynomials'' (with T. Garefalakis), Mathematics of Computation, 70, 1253-1264, 2001.
• ``A survey on factoring polynomials over finite fields'' (with J. von zur Gathen), Journal of Symbolic Computation, 31, 3-17, 2001.
• ``Smallest components in decomposable structures: exp-log class'' (with B. Richmond), Algorithmica, 29, 205-226, 2001.
• ``Algorithms for exponentiation in finite fields'' (with S. Gao, J. von zur Gathen and V. Shoup), Journal of Symbolic Computation, 29, 879-889, 2000.

If you are interested in receiving a copy of some of these papers (or the ones before the year 2000), send mail to: daniel@math.carleton.ca

Education

After my PhD was completed, I spent some few months at the Department of Combinatorics and Optimization of the University of Waterloo. At Waterloo, I had a posdoc position with Bruce Richmond.

My master's degree was done under the supervision of Arnaldo Mandel at the Department of Computer Science, Institute of Mathematics and Statistics, Universidade de Sao Paulo, Sao Paulo, Brazil.

I did my undergraduate studies at the Institute of Computing of the Faculty of Engineering, and at the Center of Mathematics of the Faculty of Sciences, both of the Universidad de la Republica, Montevideo, Uruguay.

Interesting coming conferences

• Latin American Theoretical INformatics LATIN 2010: April 19-23, 2010, Oaxaca (Mexico).
• Ontario Combinatorics Workshop OCW: May 7-8, 2010, St. Catharines (Canada).
• Discrete Math Days DMD: May 14-15, 2010, Carleton University, Ottawa (Canada).
• Antalya Algebra Days XII AAD XII: May 19-22, 2010, Antalya (Turkey).
• A Modern Computer Algebraist: Joachim von zur Gathen at 60: May 27-29, 2010, Bonn (Germany).
• Canadian Mathematical Society Summer 2010 Meeting: June 4-6, 2010, Fredericton (Canada).
• 2010 International Symposium on Information Theory ISIT'10: June 12-18, 2010, Austin (USA).
• SIAM Conference on Discrete Mathematics: June 14-17, 2010, Austin (USA).
• 2010 International Meeting on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms AofA'10: June 28 - July 2, 2010, Vienna (Austria).
• Carleton Finite Fields Workshop: July 20-23, 2010, Carleton University, Ottawa (Canada).
• XXI Brazilian Algebra School: July 25-31, 2010, Brasilia (Brazil).
• LatinCrypt 2010: August 8-11, 2010, Puebla (Mexico).
• SEquences and Their Applications SETA 2010: September 12-17, 2010, Paris (France).
• Canadian Mathematical Society Winter 2010 Meeting: December 4-6, 2010, Vancouver (Canada).
• Analytic Algorithms and Combinatorics ANALCO'11: January 22, 2011, San Francisco (USA).
• ACM-SIAM Symposium on Discrete Algorithms SODA'11: January 23-25, 2011, San Francisco (USA).
• 10th International Conference on Finite Fields and Applications Fq10: July 11-15, 2011, Ghent (Belgium).

Here is the LATIN Conference Website (Latin American Theoretical INformatics) and the LatinTCS mailing list.