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 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''), Contemporary Mathematics 518, American Mathematical Society, 2010.
• Ph. Flajolet and D. Panario (eds) of the proceedings of ANALCO'11 (2011 Analytic Algorithmics and Combinatorics), SIAM Proceedings, 2011.
• M. Lavrauw, G. Mullen, S. Nikova, D. Panario and L. Storme (eds) of the proceedings of Fq10 (``10th Finite Fields and their Applications Conference''), (tentatively) to appear in Contemporary Mathematics, American Mathematical Society, 2012.
• M. Giesbrecht and D. Panario (eds), Special issue in honour of the research and influence of Joachim von zur Gathen to appear in Journal of Symbolic Computation.

Recent publications

Papers:

• ``Cycle structure of permutation functions over finite fields and their applications'' (with A. Sakzad and M. Sadeghi), to appear in Advances in Mathematics of Communications.
• ``Subfield value sets of polynomials over finite fields'' (with W.S. Chou, J. Gomez-Calderon, G. Mullen and D. Thomson), to appear in Functiones et Approximatio, Commentarii Mathematici.
• ``Divisibility of polynomials over finite fields and combinatorial applications'' (with O. Sosnovski, B. Stevens and S. Wang), to appear in Designs, Codes and Cryptography.
• ``A generalization of the Hansen-Mullen conjecture on irreducible polynomials over finite fields" (with G. Tzanakis), Finite Fields and their Applications, 18, 303-315, 2012.
• ``Interval partitions and polynomial factorization'' (with J. von zur Gathen and B. Richmond), Algorithmica, 63, 363-397, 2012.
• ``Gauss periods as constructions of low complexity normal bases'' (with M. Christopoulou, T. Garefalakis and D. Thomson), Designs, Codes and Cryptography, 62, 43-62, 2012.
• ``Sets of orthogonal hypercubes of class r'' (with J. Ethier, G. Mullen, B. Stevens, and D. Thomson), Journal of Combinatorial Theory A, 119, 430-439, 2012.
• ``Word-oriented transformation shift registers and their linear complexity'' (with S. U. Hasan and Q. Wang), in Proceedings of SETA 2012 (SEquences and Their Applications), Lecture Notes in Computer Science 7280, Springer, 190-202, 2012.
• ``Two new measures for permutations: ambiguity and deficiency'' (with A. Sakzad, B. Stevens and Q. Wang), IEEE Transactions on Information Theory, 57, 7648-7657, 2011.
• ``Swan-like results for binomials and trinomials over finite fields of odd characteristic'' (with B. Hanson and D. Thomson), Designs, Codes and Cryptography, 61, 273-283, 2011.
• ``Counting words by number of occurrences of some patterns'' (with Z. Gao and A. MacFie), The Electronic Journal of Combinatorics, 18, P143, 2011.
• ``The eigenstructure of finite field trigonometric transforms'' (with J. Bandeira Lima and R. Campello de Souza), Linear Algebra and Its Applications, 435, 1956-1971, 2011.
• ``Ambiguity and deficiency of permutations from finite fields'' (with A. Sakzad, B. Stevens and Q. Wang), ITW 2011 (Information Theory Workshop), IEEE Xplore, 165-169, 2011.
• ``Extended bit-flipping algorithm for solving large sparse linear systems of equations modulo a prime number p'' (with A. Abolpour and M.-R. Sadeghi), ITW 2011 (Information Theory Workshop), IEEE Xplore, 688-692, 2011.
• ``Public-key encryption based on Chebyshev polynomials over GF(q)'' (with J. Bandeira Lima and R. Campello de Souza), Information Processing Letters, 111, 51-56, 2010.
• ``Asymptotics of decomposable combinatorial structures of alg-log type with positive log exponent'' (with Z. Gao and D. Laferriere), Discrete Mathematics and Theoretical Computer Science, Proc. AM, 289-302, 2010.
• ``Codes with girth 8 Tanner graph representation'' (with A. Sakzad and M. Sadeghi), Designs, Codes and Cryptography, 57, 71-81, 2010.
• ``Adaptive sampling strategies for Quickselect'' (with C. Martinez and A. Viola), ACM Transactions on Algorithms, 6, Article 53, 2010.
• ``Karatsuba's algorithm for polynomial multiplication in Chebyshev form'' (with J. Bandeira Lima and Q. Wang), IEEE Transactions on Computers, 59, 835-841, 2010.
• ``Asymptotics of smallest component sizes in decomposable combinatorial structures of alg-log type'' (with L. Dong, Z. Gao and B. Richmond), Discrete Mathematics and Theoretical Computer Science, 12, 197-222, 2010.
• ``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.
• ``Self-inverse interleavers based on permutation functions for turbo codes'', (with A. Sakzad, M. Sadeghi and N. Eshghi), Allerton 2010, 2010.
• ``Construction of turbo lattices'' (with A. Sakzad and M. Sadeghi), Allerton 2010, 2010.
• ``Ambiguity and deficiency in Costas arrays and APN permutations'', LATIN 2010 (Latin American Theoretical INformatics), Lecture Notes in Computer Science 6034, Springer, 397-406, 2010.
• ``A Family of binary sequences from interleaved construction and their cryptographic properties'' (with J. He and Q. Wang), Fq9 (9th Finite Fields and their Applications Conference), Contemporary Mathematics 518, AMS, 209-223, 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), 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

• Ontario Combinatorics Workshop OCW 2012: May 18-19, 2012, Fields Institute, Toronto (Canada).
• SEquences and Their Applications SETA 2012: June 4-8, 2012, Waterloo (Canada).
• 2012 International Meeting on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms AofA'12: June 17-22, 2012, Montreal (Canada).
• 2012 IEEE International Symposium on Information Theory ISIT 2012: July 1-6, 2012, Cambridge (USA).
• Third Workshop on Mathematical Cryptology WMC2012: July 9-11, 2012, Santander (Spain).
• XXII Escola de Algebra: July 15-20, 2012, Salvador (Brazil).
• RICAM-Workshop on Finite Fields and Their Applications: Character Sums and Polynomials: September 2-7, 2012, Strobl (Austria).
• Combinatorics 2012: September 9-15, 2012, Perugia (Italy).
• International Conference on Applied and Computational Mathematics ICACM: October 3-6, 2012, Ankara (Turkey).
• LatinCrypt 2012: October 7-10, 2012, Santiago (Chile).
• Canadian Discrete and Algorithmic Mathematics Conference CanaDAM 2013: June 10 - 13, 2013, St. John's (Canada).
• 2013 British Combinatorial Conference BCC 24: June 30 - July 5, 2013, London (England).
• Mathematical Congress of the Americas 2013 MCA 2013: August 5 - 9, 2013, Guanajuato (Mexico).

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