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

• Managing board member of the journal Applicable Algebra in Engineering, Communication and Computing, Springer.
• Editorial board member of the Bulletin of the Institute of Combinatorics and its Applications, ICA (Institute of Combinatorics and its Applications).
• Editorial board member of the Journal of Combinatorial Theory, Series A, Elsevier.
• Editorial board member of the journal Cryptography and Communications Discrete Structures, Boolean Functions and Sequences, 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 of Mathematical Cryptology, de Gruyter.
  
  
• G. Gonnet, D. Panario and A. Viola (eds) of the proceedings of LATIN 2000: Latin American Theoretical INformatics, 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''), Contemporary Mathematics 579, American Mathematical Society, 2012.
• M. Giesbrecht and D. Panario (eds), Special issue in honour of the research and influence of Joachim von zur Gathen Journal of Symbolic Computation, 47 (4), 355-502, 2012.
• H. Niederreiter, A. Ostafe, D. Panario and A. Winterhof (eds), Proceedings of the Special Semester on Applications of Algebra and Number Theory, held in Linz (Austria), October - December, 2013; vol. 16 of the Radon Series on Computational and Applied Mathematics, de Gruyter, 2014.
• A. Canteaut, G. Effinger, S. Huczynska, D. Panario and L. Storme (eds.) of the proceedings of Fq12 Contemporary Developments in Finite Fields and Applications, World Scientific, 2016.
• S. Nikova and D. Panario (eds.) of the proceedings of WAIFI 2024: International Workshop on the Arithmetic of Finite Fields, to appear in Lecture Notes in Computer Science 15176, Springer, 2024.

Recent publications

• Handbook of Finite Fields by Gary L. Mullen and Daniel Panario, ``Discrete Mathematics and Its Applications'' Series, CRC Press, 2013; see also the CRC webpage and the errata.
• Topics in Finite Fields with Applications to Cryptography and Coding Theory (in Portuguese) by Ariane Masuda and Daniel Panario, 26º Colóquio Brasileiro de Matemática, IMPA, Rio de Janeiro (Brazil), 2007.

Papers:

• ``Revisiting linearly extended discrete functions'' (with C. Gravel), to appear in Journal of Mathematical Cryptology.
• ``Quantum quasi-cyclic LDPC codes with column weight at least 3 have girth at most 6'' (with F. Amirzade and M.-R. Sadeghi), to appear in Problemy Peredachi Informatsii.
• ``Quasi-polycyclic and skew quasi-polycyclic codes over F_q^*'' (with T. Bag), Finite Fields and their Applications, 101, Article 102536, 2015.
• ``Stability of binomials over finite fields'' (with A. Fernandes and L. Reis), Finite Fields and their Applications 101, Article 102520, 2025.
• ``Infinitude of palindromic almost-prime numbers'' (with A. Tuxanidy), International Math. Research Notices, 2024, 12466-12503, 2024.
• ``Girth Analysis of Quantum Quasi-Cyclic LDPC Codes'' (with F. Amirzade and M.-R. Sadeghi), Problems of Information Transmission, 60, 71-89, 2024.
• ``Additive codes with few weights'' (with M. Sahin and Q. Wang), Cryptography and Communications, 16, 1077-1102, 2024.
• ``Disjoint difference sets and QC-LDPC codes with girth 10'' (with F. Amirzade and M.-R. Sadeghi), to appear in IWCIT 2024 (12th Iran Workshop on Communication and Information Theory).
• ``Nilpotent linearized polynomials over finite fields, revisited'' (with L. Reis), Finite Fields and their Applications, 97, Article 102442, 2024.
• ``Probabilistic root finding in code-based cryptography'' (with D. Marchiori, R. Custódio and L. Moura), Journal of Cryptographic Engineering, 14, 71-85, 2024.
• ``A concrete LIP-based KEM with simple lattices'' (with G. Biage, G. Zambonin, T. Idalino and R. Custodio), IEEE Access, 12, 16408-16420, 2024.
• ``Construction of protograph-based LDPC codes with chordless short cycles'' (with F. Amirzade and M.-R. Sadeghi), IEEE Transactions on Information Theory, 70, 51-74, 2024.
• ``Linear label code of a root lattice using Gröbner bases'' (with M. Aliasgari and M.-R. Sadeghi), Applicable Algebra in Engineering, Communication and Computing, 35, 3-16, 2024.
• ``Evaluating the generalized Buchstab function and revisiting the variance of the distribution of the smallest components of combinatorial objects'' (with C. Gravel), INTEGERS Electronic Journal of Combinatorial Number Theory, 24, A7, 2024.
• ``Curvas sobre cuerpos finitos'' (in Spanish, with M. Abdon and C. Carvalho), Publicaciones Matemáticas del Uruguay, 18, 1-57, 2023.
• ``Ordered covering arrays and upper bounds on covering codes in NRT spaces'' (with A. Castoldi, E. Carmelo, L. Moura and B. Stevens), Journal of Combinatorial Designs, 31, 304-329, 2023.
• ``One-generator quasi-cyclic codes and their dual codes” (with K. Abdukhalikov and T. Bag), Discrete Mathematics, 346, Article 113369, 2023.
• ``Comparing balanced sequences obtained from ElGamal function to random balanced sequences'' (with L. Perin and B. Stevens), Cryptography and Communications, 15, 675-707, 2023.
• ``Self-dual and LCD double circulant and double negacirculant codes over a family of finite rings Fq[v1,v2,...,vt]'' (with T. Bag, H.Q. Dinh, B.P. Yadav, A.K. Upadhyay), Cryptography and Communications, 15, 529–551, 2023.
• ``Feedback linearly extended discrete functions'' (with C. Gravel), Journal of Algebra and its Applications, 22, Article 2350051, 2023.
• ``Equivalence classes and balance properties of interleaved sequences'' (with K. Nelson and B. Stevens), in IWSDA 2022 (10th International Workshop on Signal Design and its Applications in Communications), IEEE Xplore, 166-170, 2022.
• ``Maximum-length low-density MDS codes and near resolvable designs'' (with O. Al Aboud and B. Stevens), in ISIT 2022 (International Symposium on Information Theory), IEEE Xplore, 2178-2183, 2022.
• ``Trade-based LDPC codes'' (with F. Amirzade and M.-R. Sadeghi), in ISIT 2022 (International Symposium on Information Theory), IEEE Xplore, 542-547, 2022.
• ``Protograph-based LDPC codes with chordless short cycles and large minimum distance'' (with F. Amirzade and M.-R. Sadeghi), in CWIT 2022 (17th Canadian Workshop on Information Theory), IEEE Xplore, 16-20, 2022.
• ``QC-LDPC codes with large column weight and free of small size ETSs'' (with F. Amirzade and M.-R. Sadeghi), IEEE Communications Letters, 26, 500-504, 2022.
• ``Secure one-way relaying scheme based on random difference family (RDF) lattice codes'' (with K. Bagheri, T. Eghlidos and H. Khodaiemehr), Wireless Networks, 27, 4615-4634, 2021.
• ``Faster hash-based signatures with constant-sum Winternitz scheme'' (with L. P. Perin, G. Zambonin, R. Custodio and L. Moura), Journal of Cryptographic Engineering, 11, 329-351, 2021.
• ``Design and practical decoding of full-diversity Construction A lattices for block-fading channels'' (with H. Khodaiemehr and M.-R. Sadeghi), IEEE Transactions on Information Theory, 67, 138-163, 2021.
• ``Towards constant-time probabilistic root finding for code-based cryptography'' (with D. Marchiori, R. Custódio and L. Moura), SBSeg 2021 (XXI Brazilian Symposium on Information and Computational Systems Security).
• ``Quasi-cyclic protograph-based raptor-like LDPC codes with girth 6 and shortest length'' (with F. Amirzade and M.-R. Sadeghi), ISIT 2021 (International Symposium on Information Theory), IEEE Xplore, 368-373, 2021.
• ``An extension of a strength 3 covering array construction'' (with M. Saaltink, B. Stevens and D. Wevrick), Journal of Combinatorial Designs, 28, 842-861, 2020.
• ``Finding linearly generated subsequences'' (with C. Gravel and B. Rigault), WAIFI 2020 (International Workshop on the Arithmetic of Finite Fields), Lecture Notes in Computer Science 12542, Springer, 174-192, 2020.
• ``A joint encryption and coded modulation scheme using QC-LDPC codes'' (with K. Bagheri, T. Eghlidos, M.-R. Sadeghi and H. Khodaiemehr), IEEE Transactions on Communications, 68, 4673-4693, 2020.
• ``The design of a novel multiple-parameter fractional number-theoretic transform and its application in image encryption'' (with J. Bandeira Lima and J. Neto), IEEE Transactions on Circuits and Systems for Video Technology, 30, 2489-2502, 2020.
• ``Construction of irreducible polynomials through rational transformations'' (with L. Reis and Q. Wang), Journal of Pure and Applied Algebra 224, 106241, 2020.
• ``A construction of F_2-linear cyclic, MDS codes'' (with S.D. Cardell, J.-J. Climent and B. Stevens), Advances in Mathematics of Communications, 14, 437-453, 2020.
• ``QC-LDPC construction free of small size elementary trapping sets based on multiplicative subgroups of a finite field'' (with F. Amirzade and M. Sadeghi), Advances in Mathematics of Communications, 14, 397-411, 2020.
• ``Periods of iterations of mappings over finite fields with restricted preimage sizes'' (with R. Martins, C. Qureshi and E. Schmutz), ACM Transactions on Algorithms, 16, Article 30, 2020.
• ``A trigonometric approach for Dickson polynomials over fields of characteristic two'' (with J. Bandeira Lima), Applicable Algebra in Engineering, Communication and Computing, 31, 253-270, 2020.
• ``Unicyclic strong permutations'' (with C. Gravel and D. Thomson) Cryptography and Communications, 11, 1211-1231, 2019.
• ``A new class of irreducible pentanomials for polynomial based multipliers in binary fields'' (with G. Banegas and R. Custodio), Journal of Cryptographic Engineering, 9, 359-373, 2019.
• ``Fixed points of rational functions satisfying the Carlitz property'' (with K. Chubb and Q. Wang), Applicable Algebra in Engineering, Communication and Computing, 30, 417-439, 2019.
• ``A general construction of ordered orthogonal arrays using LFSRs'' (with M. Saaltink, B. Stevens and D. Wevrick), IEEE Transactions on Information Theory, 65, 4307-4315, 2019.
• ``The functional graph of linear maps over finite fields and applications'' (with L. Reis), Designs, Codes and Cryptography, 87, 437-453, 2019.
• ``The graph structure of Chebyshev polynomials over finite fields and applications'' (with C. Qureshi), Designs, Codes and Cryptography, 87, 393-416, 2019.
• ``A survey on iterations of mappings over finite fields'' (with R. Martins and C. Qureshi), Radon Series on Computational and Applied Mathematics, de Gruyter, 23, 135-172, 2019.
• ``Nonlinear vectorial primitive recursive sequences'' (with S. U. Hasan and Q. Wang), Cryptography and Communications, 10, 1075-1090, 2018.
• ``A generating matrix method for constructing Hermite-Gaussian-like number-theoretic transform eigenvectors'' (with J. de Oliveira Neto and J. Bandeira Lima), Signal Processing, 152, 189-196, 2018.
• ``A non-commutative cryptosystem based on quaternion algebras'' (with K. Bagheri and M.-R. Sadeghi), Designs, Codes and Cryptography, 86, 2345–2377, 2018.
• ``Non-homogeneous conditional recurrences'' (with M. Sahin and Q. Wang), Linear and Multilinear Algebra, 66, 2089-2099, 2018.
• ``Fast modular reduction and squaring in GF(2^m)'' (with L. Boppre Niehues and R. Custodio), Information Processing Letters, 132, 33-38, 2018.
• ``Periods of iterations of mappings over finite fields with restricted preimage sizes'' (with R. Martins, C. Qureshi and E. Schmutz), in 29th International Meeting on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms AofA 2018, LIPICS (Leibniz International Proceedings in Informatics), Vol. 110, Dagstuhl Publishing, 2018.
• ``Normal basis exhaustive search: 10 years later'' (with L. Moura and D. Thomson), in International Workshop on the Arithmetic of Finite Fields WAIFI 2018, Lecture Notes in Computer Science 11321, Springer, 188-206, 2018.
• ``A neural network lattice decoding algorithm'' (with F. Amirzade, A. Sakzad and M.-R. Sadeghi), in Information Theory Workshop ITW 2018, IEEE Xplore, 485-490, 2018.
• ``Secret sharing schemes with hidden sets'' (with R. L. de Souza, M. Vigil, R. Custódio, F. Caullery and L. Moura), 2018 IEEE Symposium on Computers and Communications ISCC 2018, IEEE Xplore, 713-718, 2018.
• ``Modular construction A lattices from cyclotomic number fields and their applications in information security'' (with H. Khodaiemehr and M.-R. Sadeghi), in ISC (Iranian Society of Cryptology) Conference on Information Security and Cryptology ISCISC 2018.
• ``A family of matrices for generating Hermite-Gaussian-like DFT eigenvectors'' (with J. de Oliveira Neto and J. Bandeira Lima), 2018 IEEE International Conference on Acoustics, Speech and Signal Processing ICASSP 2018, IEEE Xplore, 4384-4389, 2018.
• ``Number of t-tuples in arrays from LFSRs'' (with B. Stevens, G. Tzanakis), Electronic Notes in Discrete Mathematics, 65, 17-22, 2018.
• ``Matrices for generating eigenvectors of number-theoretic transforms'' (with J. de Oliveira Neto and J. Bandeira Lima), in IEEE Global Conference on Signal and Information Processing GlobalSIP 2017.
• ``Covering arrays from m-sequences and character sums” (with G. Tzanakis, L. Moura and B. Stevens), Designs, Codes and Cryptography, 85, 437-456, 2017.
• ``Ambiguity, deficiency and differential spectrum of normalized permutation polynomials over finite fields'' (with D. Santana and Q. Wang), Finite Fields and their Applications, 47, 330-350, 2017.
• ``Ordered orthogonal array construction using LFSR sequences'' (with A. Castoldi, L. Moura and B. Stevens), IEEE Transactions on Information Theory, 63, 1336-1347, 2017.
• ``The graph structure of the Chebyshev polynomial over finite fields and applications'' (with C. Qureshi), in Workshop on Coding and Cryptography 2017; available at WCC 2017.
• ``Cycle structure of iterating Redei functions'' (with C. Qureshi and R. Martins), Advances in Mathematics of Communications, 11, 397-407, 2017. Special issue dedicated to the Workshop on Mathematics in Communication WMC 2016.
• ``Tweaked transformation shift registers'' (with S. U. Hasan and Q. Wang), SEquences and Their Applications SETA 2016.
• ``A secret key encryption scheme based on 1-level QC-LDPC lattices'' (with K. Bagheri, M.-R. Sadeghi and T. Eghlidos), Information Security and Cryptology ISCISC 2016.
• ``Construction of full-diversity 1-level LDPC lattices for block-fading channels'' (with H. Khodaiemehr and M.-R. Sadeghi), IEEE International Symposium on Information Theory ISIT 2016, IEEE Xplore, 2714-2718, 2016.
• ``Computing Grobner bases associated with lattices'' (with I. Alvarez Barrientos, M. Borges-Quintana, M. A. Borges-Trenard), Advances in Mathematics of Communications, 10, 851-860, 2016.
• ``On the heuristic of approximating polynomials over finite fields by random mappings'' (with R. Martins), International Journal of Number Theory, 12, 1987-2016, 2016.
• ``Formulas for p-th root computations in finite fields of characteristic p'' (with L. Perin, R. Custodio and Q. Wang), Electronics Letters, 52, 117-119, 2016.
• ``Fast and simple modular interpolation using factorial representations'' (with G. Mullen and D. Thomson), American Mathematical Monthly, 123, 471-480, 2016.
• ``Finite field constructions of combinatorial arrays'' (with L. Moura and G. Mullen), Designs, Codes and Cryptography, 78, 197-219, 2016.
• ``Constructing new covering arrays from LFSR sequences over finite fields'' (with G. Tzanakis, L. Moura, and B. Stevens), Discrete Mathematics, 339, 1158-1171, 2016.
• ``Redei actions on finite fields and multiplication map in cyclic groups'' (with C. Qureshi), SIAM Journal on Discrete Mathematics, 29, 1486-1503, 2015.
• ``Linear complexity profile and correlation measure of interleaved sequences'' (with J. He, Q. Wang and A. Winterhof), Cryptography and Communications, 7, 497-508, 2015.
• ``An asymptotic formula for the number of irreducible transformation shift registers'' (with S. D. Cohen, S. U. Hasan and Q. Wang), Linear Algebra and Its Applications, 484, 46-62, 2015.
• ``Locating modifications in signed data for partial data integrity'' (with T. Bardini Idalino, L. Moura and R. Custodio), Information Processing Letters 115, 731–737, 2015.
• ``A trigonometric approach for Chebyshev polynomials over finite fields'' (with J. Bandeira Lima and R. Campello de Souza), Chapter 15 of Applied Algebra and Number Theory: Essays in Honour of Harald Niederreiter (on the occasion of his 70th birthday), Cambridge University Press, 255-279, 2015.
• ``Open problems for polynomials over finite fields and applications'', Chapter 5 of Proceedings on the Open Problems in Mathematics and Computer Science Conference, Springer, 111-126, 2015.
• ``Ambiguity and deficiency of reversed Dickson permutations'' (with A. Sakzad and D. Thomson), Fq11 (11th Finite Fields and their Applications Conference), Contemporary Mathematics 632, AMS, 345-356, 2015.
• ``General conditional recurrences'' (with M. Sahin, Q. Wang and W. Webb), Applied Mathematics and Computation 243, 220-231, 2014.
• ``The rth smallest part size of a random integer partition'' (with Z. Gao, C. Martinez and B. Richmond), INTEGERS Electronic Journal of Combinatorial Number Theory, 14A, A3, 2014.
• ``Approximating the number of irreducible polynomials over GF(2) with several prescribed coefficients'' (with B. Omidi Koma), Journal of Combinatorial Mathematics and Combinatorial Computing, 90, 255-284, 2014.
• ``A family of Fibonacci-like conditional sequences'' (with M. Sahin and Q. Wang), INTEGERS Electronic Journal of Combinatorial Number Theory, 13, A78, 2013.
• ``Ambiguity and deficiency of permutations over finite fields with linearized difference map'' (with A. Sakzad, B. Stevens, D. Thomson and Q. Wang), IEEE Transactions on Information Theory, 59, 5616-5626, 2013.
• ``Solving sparse linear systems of equations over finite fields using bit-flipping algorithm'' (with A. Abolpour and M. Sadeghi), Linear Algebra and Its Applications, 439, 1815-1824, 2013.
• ``Existence and properties of k-normal elements over finite fields'' (with S. Huczynska, G. Mullen and D. Thomson), Finite Fields and their Applications, 24, 170-183, 2013.
• ``Grobner bases for lattices and an algebraic decoding algorithm'' (with M. Aliasgari and M. Sadeghi), IEEE Transactions on Communications, 61, 1222-1230, 2013.
• ``Subfield value sets of polynomials over finite fields'' (with W.S. Chou, J. Gomez-Calderon, G. Mullen and D. Thomson), Functiones et Approximatio, Commentarii Mathematici, 48, 147-165, 2013.
• ``Generalized Alcuin's sequence'' (with M. Sahin and Q. Wang), The Electronic Journal of Combinatorics, 19, P55, 2012.
• ``Cycle structure of permutation functions over finite fields and their applications'' (with A. Sakzad and M. Sadeghi), in Advances in Mathematics of Communications, 6, 347-361, 2012.
• ``Divisibility of polynomials over finite fields and combinatorial applications'' (with O. Sosnovski, B. Stevens and Q. Wang), Designs, Codes and Cryptography, 63, 425-445, 2012.
• ``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.
• ``Random mappings with restricted preimages'' (with Andrew MacFie), Proceedings of LatinCrypt 2012 (Second International Conference on Cryptology and Information Security in Latin America), Lecture Notes in Computer Science 7533, Springer, 254-270, 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.
• ``Grobner bases for lattices and an algebraic decoding algorithm'' (with M. Aliasgari and M. Sadeghi), Allerton 2011, IEEE Xplore, 1414-1415, 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, IEEE Xplore, 22-28, 2010.
• ``Construction of turbo lattices'' (with A. Sakzad and M. Sadeghi), Allerton 2010, IEEE Xplore, 14-21, 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), Proceedings 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 online seminars and coming conferences

• Carleton Finite Fields eSeminar.
• ACCESS (Algebraic Coding and Cryptography on the East coast Seminar Series).
• Galois Geometries and their Applications
• SFU Discrete Math Seminar.
• Swiss eSeminar on Coding Theory and Cryptography.
• Mathematics online research seminars (all areas).
  

• 2024 CMS (Canadian Mathematical Society) Winter Meeting: November 29 - December 2, 2024, Richmond (Canada).
• 36th International Meeting on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms AofA 2025: May 5-9, 2025, Toronto (Canada).
• CanaDAM 2025: May 20-23, 2025, Ottawa (Canada).
• 8th Workshop on Design Theory, Hadamard Matrices and Applications: Hadamard 2025, May 26-30, 2025, Seville (Spain).
• The 5th Pythagorean Conference: June 1-5, 2025, Kalamata (Greece).
• 2025 CMS (Canadian Mathematical Society) Summer Meeting: June 6-9, 2025, Quebec City (Canada).
• 2025 IEEE International Symposium on Information Theory: ISIT 2025, June 22-27, 2025, Ann Arbor (USA).
• 16th International Conference on Finite Fields and Applications: Fq16, July 7-11, 2025, Sao Carlos (Brazil).
• Applications of Computer Algebra ACA 2025: July 14-18, 2025, Heraklion (Greece).
• Mathematical Congress of the Americas: MCA 2025, July 21-25, 2025, Miami (USA).
• Selected Areas in Cryptography SAC 2025: August 11–15, 2025, Toronto (Canada).
• Graduate Workshop on Linear Algebra over Finite Fields and Applications: August 18-29, 2025, Providence (USA).
• Latin and American Algorithms, Graphs and Optimization Symposium LAGOS 2025: November 10-14, 2025, Buenos Aires (Argentina).

Here are the LATIN Conference Website (Latin American Theoretical INformatics) and the Latincrypt Conference Website.