How secret is a secret?. DFF 2014

Abstract

We consider concrete methods to prevent an eavesdropper from obtaining too much infor- mation when he/she wiretaps symbols sent through a data channel. We consider both classic channels and networks. The classic channel problem is related to the problem of secret sharing for which we also present concrete constructions.

Description in Danish

Vi udvikler matematiske metoder ved hjælp af hvilke, man kan beskytte data mod at blive aflyttet. Alt efter i hvilket medie, kommunikationen finder sted, er der brug for forskellige matematiske konstruktioner. Vi betragter to situationer, nemlig en klassisk kanal (eksempelvis et kabel) og et netværk (eksempelvis internettet). De udviklede metoder udmærker sig ved samtidig at kunne beskytte kommunikationen mod støj og hærværk. De matematiske konstruktioner, udviklet til den klassiske kanal, finder også anvendelse i helt andre sammenhænge. Nemlig i secret sharing, hvor en hemmelighed ønskes fordelt blandt en gruppe individer - på en sådan måde, at alene delgrupper af en vis størrelse kan genskabe hemmeligheden. Et sådant system blev eksempelvis benyttet i Sovjetunionen for at modvirke, at atomvåben blev affyret ved en fejl. Secret sharing schemes med yderligere matematisk struktur kan også bruges i den situation, hvor et individ ønsker at udføre en stor beregningsopgave ved hjælp af fremmede computere, men hvor det samtidig er essentielt, at de fremmede computere ikke får adgang til for mange oplysninger. De matematiske metoder anvendt i forbindelse med netværk involverer, at man giver stationerne i netværket frihed til selv at bestemme, hvorledes data skal behandles. Dette øger på overraskende vis den mængde af data, der kan sendes gennem netværket.

Activities and news (since June 2014 to October 2017)

Umberto Martínez-Peñas has been granted an international postdoc from the Independent Research Fund Denmark. Umberto will work for two years at the University of Toronto: Skew polynomials: From Algebra to the Internet.
2nd–4th October 2017: The Dune Workshop on Secrets was held at Klitgården in Skagen.
Tom Høholdt was in Washington in October 2016 to work on the book and the book: A Course in Error-Correcting Codes 2. Edition (J. Justesen and T. Høholdt) was published in July 2017.
Olav Geil has participated in the 5th International Castle Meeting on Coding Theory and Applications, Vihula Manor, Estonia, August 28th-31st to give two contributed talks based on joint works with Ferruh Özbudak and Daniel Lucani, respectively.
Ignacio Cascudo visited CWI Amsterdam, invited by Prof. Ronald Cramer, from 14 to 20 August, 2017.
Olav Geil and Umberto Martínez-Peñas have participated and given a talk in the SIAM AG17 Conference on Applied Algebraic Geometry, July 31st - August 4th, 2017, Atlanta, USA, as invited speakers of the Minisymposium in Coding Theory.
Ignacio Cascudo attended the seminar Aarhus Summer Crypto Days, at the Department of Computer Science of Aarhus University, on 4th and 5th July 2017. He gave the talk "Resource-efficient OT combiners with active security".
Ignacio Cascudo is guest editor of Security and Communication Networks (Special Issue on Secure Multiparty Computation).
Ignacio Cascudo is a member of the program committee of Eurocrypt 2018
Ignacio Cascudo is a member of the program committee of ICITS 2017
Fernando Hernando at Jaume I University (Castellón, Spain) has visited Aalborg University as guest professor for one month, since June 26th 2017.
Peter Beelen participated in the Conference Arithmetic of Function Fields, University Münster, Germany, 26th-30nd June 2017.
Diego Ruano has participated in the Colloquium "Celebrating Contributions of Antonio Campillo to Mathematics", June 23rd, 2017, University of Valladolid, Spain
Peter Beelen participated in the Workshop Arithmetic, Geometry, Cryptography and Coding Theory (AGCT-16), CIRM, Luminy, France, 19th-23nd June 2017.
Olav Geil has participated in the Meeting of the Catalan, Spanish, Swedish Math Societies, June 12th-15th, Umeå, Sweden, as an invited speaker of the session Numerical Semigroups and Applications. He has presented a join work with Kasper Halbak Christensen: "A Gröbner basis approach for counting rational places in algebraic function felds". [Slides]. He also acted as chairman for a subsession of the special session "Numerical Semigroups and Applications".
Ignacio Cascudo has participated in the workshop "Theory and Practice of Multiparty Computation" at the University of Bristol, UK, April 3rd - 7th, 2017.
Ryutaroh Matsumoto at Tokyo Institute of Technology has visited Aalborg University to do research with I. Cascudo, O. Geil and D. Ruano, 14th - 15th March, 2017. Social dinner's photos: [Photo 1], [Photo 2], [Photo 3], [Photo 4], [Photo 5].
Élise Barelli has visitied P. Beelen and J.S.R. Nielsen at DTU, February 13th - March 10th, 2017. She is a Ph.D. student at the project team Grace at Inria Saclay (France), where she is supervised by Alain Couvreur.
Johan P. Hansen has done a research stay at Centre International de Rencontres Mathématiques (CIRM, Luminy, France), February 6th - March 19 2017.
Johan P. Hansen is supervising the master theses "Aspekter af sikkerhed indenfor kryptering med elliptiske kurver" (Merete Hellerup Toft) and "Sikker kryptografi med elliptiske kurver" (Lea Cathrine Crean og Sanna Krabbe Lyngs)
Ignacio Cascudo has given a seminar in the Department of Computer Science of Aalborg University, hosted by Katja Hose, on the 13th of January, 2017. The title was "Multiparty computation and secret sharing".
Peter Beelen has visited IIT-Bombay (India) as visiting professor, January 2017.
The film "Olav Geil: Fejlkorrigerende koder" has been released as part of the series "10 danske matematikere-10 matematiske fort ællinger", Lindhardt og Ringhof, Uddannelse. The film is available from https://www.youtube.com/watch?v=rIszlgH7Exw
Irene Giacomelli has defended her PhD thesis at Aarhus University on January 4th 2017. The thesis has been supervised by Ivan B. Damgård and Johan P. Hansen.
Diego Ruano has visited Jaume I University, Castellón, Spain, to do research with Carlos Galindo and Fernando Hernando, December 18th - 23th, 2016.
Vincent Neiger started working as postdoc at DTU on December 15th 2016. He is supported by a HC-Ørsted grant for two years. He will work on topics related to fast linear algebra for matrices with polynomial entries.
We have organized and participated in the workshop "Secrets", workshop of the research project "How secret is a secret?", DTU Compute, The technical University of Denmark, November 14th 2016.
On November 4, 2016 the film "Fejlkorrigerende koder" was presented in connection with a reception at the publishing house Lindhardt og Rinhof. The film is one out ten in the series "10 danske matematikere -- 10 matematiske fortællinger". In the film Olav Geil lectures on coding theory to an audience of highschool student.
Umberto Martínez-Peñas has visited Frank R. Kschischang at University of Toronto (Canada), November 1st 2016 - March 15th 2017.
U. Martínez-Peñas has given a talk at the Research seminar in coding theory and cryptography. University of Neuchatel, Switzerland, October 26th 2016.
Diego Ruano has supervised the following master thesis at Aalborg University: Secure Multy-Party Computations using Secret Sharing Schemes, Johan M. Sorknæs, October 2016.
René B. Christensen and Jaron Skovsted Gundersen have started a PhD at Aalborg University (4+4 scheme) under the supervision of Ignacio Cascudo and Diego Ruano.
Olav Geil is a member of the Scientific Committee for 5th International Castle Meeting on Coding Theorey and Applications, to take place in Estonia, August 28--31, 2017.
Nurdagül Anbar finished her postdoc at DTU ultimo September 2016. She is now postdoc at Faculty of Mathematics, Otto-von-Gueriche University, Magdeburg, Germany.
U. Martínez-Peñas has participated and given a talk at 54th Annual Allerton Conference on Communication, Control, and Computing. September 27th - 30th , 2016, Allerton Park and Retreat Center, Monticello, IL, USA
Nurdagül Anbar has conducted the project "Polynomials over finite fields", with Alev Topuzoğlu, in the WIN-E2: Women in Numbers Europe-2 25th - 30th September 2016.
Peter Beelen has been keynote speaker and Ignacio Cascudo has been a tutorial speaker at Workshop on Mathematics of Information - Theoretic Cryptography. National University of Singapore and Nanyang Technological University (Singapore), September 19th - 30th, 2016.
Johan P. Hansen has supervised the following master thesis at Aarhus University: Efficient Elliptic Curve Cryptography Twisted Hessian curves and elliptic curves in Montgomery-form and their cryptographic applications, Asger Pilegaard, September 6th 2016.
Peter Beelen visited Aalborg University on August 30th to participate in the inaugural lecture of Olav Geil.
Olav Geil gave an inaugural lecture on August 30th 2016 in connection with his appointment as a professor with special responsibilities. The title of the lecture was "Bounding the number of affine roots - with applications in reliable and secure communication". [Slides].
Associate professor Alp Bassa from Bogazici university, Istanbul has visited Peter Beelen (DTU) in the period August 17th - 25th 2016.
T. Høholdt has participated and U. Martínez-Peñas has participated and given a talk at ISIT 2016-IEEE International Symposium on Information Theory, Barcelona, Spain. July 10th - 15th 2016.
T. Høholdt has participated (invited) and U. Martínez-Peñas has participated and given a talk at WMC 2016-Workshop on Mathematics in Communications, Santander, Spain. July 6th - 8th 2016.
Ignacio Cascudo is publicity co-chair for International Conference on Information-Theoretical Cryptography, August 9-12, 2016.
Ignacio Cascudo participated in Paris Crypto Day, ENS, June 30th, 2016.
Ignacio Cascudo was an invited speaker and had an invited paper at Computability in Europe (CiE 2016). Université Paris 13, Paris, June 27th - July 1st, 2016. [paper]
Olav Geil was invited speaker at Workshop: On the Algebraic and Geometric Classifications of Projective Varieties, June 20-24, 2016 at University of Messina. Title of talk: "Bounding the number of affine roots using algebraic methods", abstract.
Ferruh Özbudak at Middle East Technical University (Turkey) has visited Aalborg University as guest professor, June 15th - July 15th 2016.
Peter Beelen was invited speaker at SIAM Conference on Discrete Mathematics(DM16). Georgia State University (USA), June 6th - 10th, 2016.
Nurdagül Anbar was invited speaker at the conference N3-Days IV, University of Copenhagen, Denmark, 3rd - 4th June 2016.
Ruud Pellikaan at Eindhoven University of Technology (The Netherlands) has visited Aalborg University as guest professor, June 3rd - 15th 2016.
Mrinmoy Datta started working as postdoc at DTU on June 1st 2016. He is supported by a FNU grant for two years. He will work on topics related to determining the number of solutions of systems of polynomial equations.
Ignacio Cascudo participated in Workshop on Theory and Practice of Secure Multiparty Computation. Aarhus University, May 30- June 3, 2016.
Nurdagül Anbar was invited speaker at the conference Antalya Algebra Days XVIII, Turkey, 18th - 22nd May 2016.
Olav Geil has visited Jaume I University, Castellón, Spain to do research with Carlos Galindo and Fernando Hernando, May 22th - June 5th, 2016. Olav Geil gave an invited talk with the title "Bounding the number of affine roots using algebraic methods".
Diego Ruano has participated and gave a talk at the Third IMAC and Singacom Day on Algebraic Applications to Information Theory, Castellón, Spain, May 9th - 10th, 2016.
Diego Ruano has visited Jaume I University, Castellón, Spain to do research with Carlos Galindo and Fernando Hernando, May 6th - 21th, 2016.
T. Høholdt visited University of Puerto Rico for research collaboration with H. Janwa and F. Pinero.
T. Høholdt visited J. Justesen in Washington, D.C. in May 2016 to work on the revised version of their book.
Alain Couvreur at INRIA Saclay has visited DTU, April 17th - 23rd, 2016.
Johan P. Hansen has supervised the following master thesis at Aarhus University: Secret sharing, lineære koder og algebraiske kurver, Irene Frank Kristensen and Cecilie Bøttern Steffensen, April 2016.
Since April 15th, Olav Geil is a Professor MSO for 5 years.
On April 11th 2016, Peter Beelen visited Aalborg University to do research with Olav Geil and Diego Ruano.
Daniel E. Lucani has given a talk at at the COST Action IC1104 conference Network Coding and Designs, Dubrovnik, Croatia, April 4th - 9th, 2016. "Composite extension fields for (network) coding: Designs and opportunities. Joint work with Olav Geil, Diego Ruano, Janus Heide.
Umberto Martínez-Peñas participated and gave two talks at the COST Action IC1104 conference Network Coding and Designs, Dubrovnik, Croatia, April 4th - 9th, 2016.
Ignacio Cascudo participated and gave a talk and Olav Geil and Umberto Martínez-Peñas participated at the symposium on the 60th birthday of Ivan Damgård, Aarhus, April 1st - 2nd, 2016.
Wilfried Meidl (RICAM), has visited the Technical University of Denmark to do research with Nurdagül Anbar, March 11th - 21st, 2016.
Umberto Martínez-Peñas has received an EliteForsk travel grant of 200.000 kr in connection with his research visit at Massachusetts Institute of Technology - MIT. [Interview]
On February 24th, Olav Geil visited Tom Høholdt at DTU.
Johan P. Hansen has visited CIRM-Centre International de Rencontres Mathématiques (France), February 17th - March 1st 2016.
Peter Beelen has visited IIT-Bombay (India) as visiting professor, January 12th - February 6th, 2016.
Nurdagül Anbar has participated and gave a talk at the Workshop on Finite Fields: Arcs, Curves and Bent Functions. Istanbul, Turkey, 1st - 3rd February, 2016.
Nurdagül Anbar visited Alev Topuzoğlu at Sabanci University, Istanbul, Turkey, 1st - 7th February 2016.
On February 1st, 2016, Tom Høholdt and Olav Geil gave a talk at Information Meeting for The Danish National Research Foundation at Aalborg University.
Stefano Martin started working for Seluxit on February 1st.
Johan P. Hansen has supervised the following master thesis at Aarhus University: Parringsbaseret kryptografi på elliptiske kurver (Weil- og Tate-Lichtenbaum parringen), Diana Christensen and Ingrid Tandberg, February 2016.
Diego Ruano has supervised the following master thesis at Aalborg University: McEliece, kodebaseret kryptografi og matrixprodukt-koder, Camilla Lund Melander and Ida Bentzen-Petersen, January 2016.
Johan P. Hansen has supervised the following master thesis at Aarhus University: Error Correction in Network Coding, Christian Andersen, January 2016.
Wilfried Meidl (RICAM), has visited the Technical University of Denmark to do research with Nurdagül Anbar, January 6th - 17th, 2016.
Olav Geil is participating in the forskningslederkursus at CBS-Copenhagen Business School.
Nurdagül Anbar visited Ferruh Özbudak and gave a talk at Middle East Technical University, Ankara, Turkey on 23rd December 2015.
Peter Beelen is associated editor for IEEE Transactions on Information Theory since December 2015.
On December 14th 2015, Olav Geil has visited the Technical University of Denmark to do research with Peter Beelen.
Ph.D. Nhut Nguyen (supervisor Peter Beelen) has defended his Ph.D. thesis at DTU on the 14th of December 2015. Olav Geil was a member of the committee.
Nurdagül Anbar has participated and gave a talk at the conference Arithmetic Geometry: Explicit Methods and Applications. Moscow, Russia, 7th - 11th December, 2015.
On November 27th 2015, Vitaly Skachek (University of Tartu, Estonia) has visited Aalborg university.
Olav Geil and Diego Ruano have participated in the workshop DARNEC'15 Design and Application of Random Network Codes, Istanbul Technical University, Turkey, 4th - 6th November 2015.
On October 28th 2015, Ignacio Cascudo (Aarhus University) has visited Aalborg university to do research. [Photo 1] [Photo 2]
Umberto Martínez-Peñas has given a talk at the Young Researchers Conference of the Royal Spanish Mathematical Society Murcia, Spain, September 7th - 11th, 2016.
Nurdagül Anbar visited Wilfried Meidl and gave a talk at Johann Radon Institute (RICAM), Linz, Austria, 1st - 25th September 2015.
Ignacio Cascudo will join the Mathematics for communication research group on April 2016 as an Assistant professor.
Johan P. Hansen has visited the University of Tromsø (Norway), September 7th - July 9th 2016.
Diego Ruano has participated and presented a work at the Workshop on Algebra and Geometry 2015, University of Valladolid, Spain 2nd - 4th September 2015.
Stefano Martin and Diego Ruano have participated and presented a work at ACA 2015-Applications of Computer Algebra. Kalamata, Greece, July 20th - 23rd, 2015.
Peter Beelen has been invited speaker at WITMSE 2015 (Workshop on Information Theoretic Methods in Science and Engineering 2015). Organized by Peter Harremoes, Copenhagen, June 24th - 26th, 2015.
On June 19th 2015, Olav Geil has visited the Technical University of Denmark to do research with Peter Beelen.
On June 18th 2015, Peter Beelen has visited Aalborg University to do research with Diego Ruano.
Fernando Hernando at Jaume I University (Castellón, Spain) has visited Aalborg University as guest professor, June 18th - July 18th 2015.
Peter Beelen was invited speaker at the N³ Days II conference. University of Copenhagen, June 16th - 17th, 2015.
Ruud Pellikaan from Eindhoven University of Technology, The Netherlands, has visited Aalborg University, May 29th - June 16th, 2015.
Sudhir R. Ghorpade from IIT-Bombay, Mumbai India, has visited Peter Beelen at DTU, May 31st - June 5th 2015.
Sudhir R. Ghorpade from IIT-Bombay, Mumbai India, has visited Aalborg University, May 28th - 31st, 2015. Social dinner's photos: [Photo 1], [Photo 2].
Nurdagül Anbar, Peter Beelen and Johan P. Hansen participated and presented a work in the workshop Arithmetics, Geometry, Cryptography and Coding Theory. Centre International de Rencontres Mathématiques (CIRM, Luminy, France) May 18th - 22nd, 2015.
On May 5th 2015, Peter Beelen has visited Aalborg University Copenhagen (Sydhavn campus) to do research with Diego Ruano.
Umberto Martínez-Peñas participated and presented a poster in the 2015 European School of Information Theory (ESIT), IEEE Information Theory Society, Zandvoort, The Netherlands, April 20th - 24th, 2015
On April 14th 2015, Peter Beelen has visited Aalborg University Copenhagen (Sydhavn campus) to do research with Diego Ruano.
Olav Geil participated, and Nurdagül Anbar and Umberto Martínez-Peñas participated and presented a work at WCC 2015-The Ninth International Workshop on Coding and Cryptography. Paris, France, April 13th - 17th, 2015.
Tom Høholdt is a member of the program committee of the workshop WCC 2015-The Ninth International Workshop on Coding and Cryptography. Paris, France, April 13th - 17th, 2015.
Johan P. Hansen participated in the workshop Geometric Langlands and derived algebraic geometry. Centre International de Rencontres Mathématiques (CIRM, Luminy, France) March 30th - April 3rd, 2015.
Nurdagül Anbar, postdoc at the Technical University of Denmark, has been associated to this project.
Johan P. Hansen has visited the Institute de Mathématique, Luminy (France), March 2015.
On February 24th 2015, Peter Beelen has visited Aalborg university to do research with Olav Geil.
Diego Ruano has visited Ryutaroh Matsumoto at the Tokyo Institute of Technology (Japan), February 21st - March 10th 2015. Partly supported by the "Program for promoting the enhancement of research universities" at Tokyo Institute of Technology.
On February 10th 2014, Peter Beelen has visited Aalborg University Copenhagen (Sydhavn campus) to do research with Diego Ruano.
Stefano Martin, research assistant at Aalborg University, has been associated to this project.
Umberto Martínez-Peñas has participated and presented a poster in the SP Coding and Information School. Campinas, Brazil. January 19th - 30th 2015.
Peter Beelen has been a visiting professor of the Mathematics Institute at IIT-Bombay, Mumbai, India from January 15th-31st 2015.
Johan P. Hansen has participated in the ATV-Møde: "Cybersikkerhed - hvordan ruster vi os i Danmark?". ATV, Innovationsnetværket for Finans IT og DTU. January 15th 2015.
Ph.D. Fernando Piñero (supervisors Peter Beelen and Tom Høholdt) has defended his Ph.D. thesis at DTU on the 16th of December 2014. Olav Geil was a member of the committee.
Stefano Martin (supervisor Olav Geil and co-supervisor Diego Ruano) has defended his Ph.D. thesis at Aalborg University on the 8th of December 2014. Tom Høholdt was a member of the committee.
Peter Beelen has visited Alp Bassa, 6th-11th December 2014 at Bogazici university, Istanbul, Turkey.
On December 3rd 2014, Olav Geil, VELUX visiting professor Ryutaroh Matsumoto and Diego Ruano have visited the Technical University of Denmark to do research with Peter Beelen.
Stefano Martin's contract at Aalborg University has been extended. He will continue working as Research assistant with the Mathematics for communication group until January 2016.
Peter Beelen, on the occasion on having obtained a professor (MSO) position at DTU, has given an inaugural lecture on the 28th of November 2014.
VELUX visiting professor Ryutaroh Matsumoto from the Tokyo Institute of Technology has given a PhD course at Aalborg University. Title: Welcome to Quantum Information Processing. November 21st - December 1st 2014. [Slides] [Group photo] [Almost a group photo...]
VELUX visiting professor Ryutaroh Matsumoto from the Tokyo Institute of Technology has given a talk at Aarhus University. Title: Quantum Ramp Secret Sharing. November 19th 2014. [Slides]
On November 10th 2014, Peter Beelen has visited Aalborg university to do research with Olav Geil, VELUX visiting professor Ryutaroh Matsumoto and Diego Ruano.
Olav Geil has participated and gave a talk in the IEEE Information Theory Workshop-ITW2014, Hobart, Tasmania, Australia, November 2nd - 5th 2014.
Postdoctoral researcher Nurdagül Anbar has started at DTU to work with Peter Beelen (funded by the H.C.Ørsted-COFUND foundation). She will work at DTU between 1st November 2014 – 31st October 2016.
On October 9th 2014, Olav Geil and VELUX visiting professor Ryutaroh Matsumoto have visited the Technical University of Denmark to do research with Peter Beelen.
Diego Ruano has been a member of the committee for the PhD defense of Wilson Olaya-León: Hamming weights' of castle codes. Advisor: Carlos Munuera. University of Valladolid (Spain), October 1st 2014.
Stefano Martin has started at Aalborg University to work with the Mathematics for communication group as Research Assistant. He will work at Aalborg University between 1st October 2014 – 31st December 2014.
Ryutaroh Matsumoto from the Tokyo Institute of Technology has visited Aalborg University during fall 2014 as VELUX Visiting Professor. [Photo with Network Coding Focus Group]
Olav Geil has participated in the 4th International Castle Meeting on Coding Theory and Applications, Castle of Palmela, Portugal, September 15th - 18th, 2014.
Peter Beelen has participated in the Workshop Finite Geometries Fourth Irsee Conference (IRSEE4), Irsee, Germany, September 14th - 20th, 2014.
Diego Ruano has participated and gave a talk in the INdAM meeting: International meeting on numerical semigroups - Cortona 2014, Cortona, Italy, September 8th - 13th, 2014.
J.S.R. Nielsen, Ulm University, has visited Peter Beelen at DTU, September 1st - 5th, 2014.
On September 1st 2014, Umberto Martínez-Peñas has started a PhD at Aalborg University funded by this project. His supervisor is Olav Geil and his co-supervisor is Diego Ruano.
Diego Ruano has visited Carlos Galindo and Fernando Hernando at Jaume I University (Castellón, Spain), July 2014.
Diego Ruano participated and gave a talk in the Second IMAC and Singacom Day on Algebraic Applications to Information Theory. Castellón, Spain, July 17th, 2014.
Stefano Martin participated and gave a talk in The 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014). Groningen, The Netherlands, July 7th - 11th, 2014.
We participated and gave a talk in the Workshop on Applications of Algebraic Geometry in Secret Sharing and Coding Theory, Aalborg, June 30th 2014.
Olav Geil and Diego Ruano have participated in NetCod 2014 - International Symposium on Network Coding. Aalborg, Denmark, June 27th - 28th, 2014. Olav Geil was a member of the Technical program committee.
Peter Beelen has visited Alp Bassa at Bogazici University, Istanbul, Turkey, June 14th - 17th, 2014.
Peter Beelen participated and gave a talk in the Workshop on Function Field Arithmetic in Sirince, Turkey, June 9th - 13th 2014.

Publications (since June 2014 to October 2017).

Papers submitted for publication:

C. Galindo, F. Hernando, D. Ruano: Classical and Quantum Evaluation Codes at the Trace Roots. [preprint] .
C. Galindo, O. Geil, F. Hernando, D. Ruano: New binary and ternary LCD codes. [preprint] .
I. Cascudo: On squares of cyclic codes. [preprint] .
J.P. Hansen: Asymmetric Quantum Codes on Toric Surfaces. [preprint]
O. Geil, U. Martínez-Peñas: Bounding the number of common zeros of multivariate polynomials and their consecutive derivatives", 26 pages. [preprint].
O. Geil, F. Özbudak: On affine variety codes from the Klein quartic, 27 pages. [preprint].
O. Geil, F. Özbudak, D. Ruano: Constructing sequences with high nonlinear complexity from Hermitian function fields, 10 pages.
J.P. Hansen: Toric Codes, Multiplicative Structure and Decoding. Sumbitted to Discrete Mathematics. [preprint]
U. Martínez-Peñas: Communication efficient and strongly secure secret sharing schemes based on algebraic geometry codes. [preprint]
N. Anbar, W. Meidl: Modified planar functions and their components.
D.E. Lucani, M.V. Pedersen, D. Ruano, C.W. Sørensen, F.H.P. Fitzek, J. Heide, O. Geil: Fulcrum Network Codes: A Code for Fluid Allocation of Complexity. [preprint]

Papers in Journals:

P. Beelen, M. Datta, S.R. Ghorpade: Maximum number of common zeros of homogeneous polynomials over finite fields. To appear in Proceedings of the AMS. [postprint] [paper]
U. Martínez-Peñas, R. Matsumoto: Relative generalized matrix weights of matrix codes for universal security on wire-tap networks. To appear in IEEE Transactions on Information Theory. [postprint] [paper]
C. Galindo, O. Geil, F. Hernando, D. Ruano: Improved constructions of nested code pairs. To appear in IEEE Transactions on Information Theory. [postprint] [paper]
U. Martínez-Peñas: Generalized rank weights of reducible codes, optimal cases and related properties. IEEE Transactions on Information Theory, Volume 64, Issue 1, (2018). [postprint] [paper]
O. Geil, S. Martin, U. Martínez-Peñas, R. Matsumoto, D. Ruano: On asymptotically good ramp secret sharing schemes. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences. Vol.E100-A, No.12, pages 2699-2708 (2017) [postprint] [paper]
P. Beelen, D.Glynn, T. Høholdt, K.V.Kaipa: Counting generalized Reed-Solomon codes, Advances in Mathematics of Communication. Volume 11, Issue 4 (2017). [postprint] [paper]
N. Anbar, A. Bassa, P. Beelen: A complete characterization of Galois subfields of the generalized Giulietti-Korchmáros function field. Finite Fields and their Applications, vol. 48, pages 318-330 (2017). [postprint] [paper]
U. Martínez-Peñas: Rank equivalent and rank degenerate skew cyclic codes, Advances in Mathematics of Communications, 11 (2), pages 267-282, (2017). [postprint] [paper]
U. Martínez-Peñas: On the roots and minimum rank distance of skew cyclic codes, Designs, Codes and Cryptography, 83 (3), pages 639-660 (2017). [postprint] [paper]
U. Martínez-Peñas, R. Pellikaan: Rank error-correcting pairs, Designs, Codes and Cryptography, 84 (1-2), pages 261-281, (2017). [postprint] [paper]
O. Geil, S. Martin: Relative generalized Hamming weights of q-ary Reed-Muller codes, Advances in Mathematics of Communications. Volume 11, Issue 3, pages 503-531 (2017). [postprint] [paper]
N. Anbar, P. Beelen: A Note on a Tower by Bassa, Garcia and Stichtenoth. Functiones et Appoximatio Commentarii Mathematici 57 (1), pages 47-60 (2017). [postprint] [paper]
N. Anbar, P. Beelen, N. Nguyen: A new tower meeting Zink's bound with good p-rank. Acta Arithmetica vol. 177 (4), pages 347-374 (2017). [postprint] [paper]
N. Anbar, W. Meidl, A. Topuzoğlu: Idempotent and p-potent quadratic functions: Distribution of nonlinearity and co-dimension. Design, Codes and Cryptography 82 (no. 1-2), pages 265-291 (2017). [postprint] [paper]
J.P. Hansen: Secret sharing schemes with a large number of players from toric varieties. Arithmetic, Geometry, Cryptography and Coding Theory. Contemporary Mathematics. Volume 686, editors: A. Bassa, A. Couvreur, D. Kohel (2017) [postprint] [paper]
C. Galindo, O. Geil, F. Hernando, D. Ruano: On the distance of stabilizer quantum codes from J-affine variety codes. Quantum Information Processing, Volumen 16, Issue 4, 16:111 (2017). [postprint] [paper]
O. Geil, C. Thomsen: More results on the number of zeros of multiplicity at least r. Discrete Mathematics. Vol. 340, Issue 5, pages 1028-1038 (2017). [postprint] [paper]
O. Geil, S. Martin, U. Martínez-Peñas, D. Ruano: Refined analysis of RGHWs of code pairs coming from Garcia-Stichtenoth's second tower. Journal of Algebra Combinatorics Discrete Structures and Applications, Volume 4, Issue 1, pages 37-47 (2017) [postprint] [paper]
N. Anbar, A. Bassa, P.Beelen: A modular interpretation of various cubic towers. Journal of Number Theory, Volume 171, pages 341-357 (2017). [postprint] [paper]
R. Matsumoto, D. Ruano, O. Geil: List decoding algorithm based on voting in Gröbner bases for general one-point AG codes. Journal of Symbolic Computation Volume 79, Part 2, pages 384–410 (2017). [postprint] [paper]
U. Martínez-Peñas: On the similarities between rank and Hamming weights and their applications to network coding. IEEE Transaction on Information Theory, 62 (7) : 4081-4095 (2016) [postprint] [paper]
P. Beelen, F. Piñero: The structure of dual Grassmann codes. Designs, Codes and Cryptography, vol. 79 (3), pages 451-470 (2016). [paper]
J.P. Hansen: Forms and Linear Network Codes. International Journal of Mathematics and Computer Science, Vol. 10, no. 2 (2015). [postprint] [paper]
A. Bassa, P. Beelen, N. Nguyen: Good families of Drinfeld modular curves. LMS Journal of Computation and Mathematics, Volume 18, Issue 01 (2015). [postprint] [paper]
C. Galindo, F. Hernando, D. Ruano: Stabilizer quantum codes from J-affine variety codes and a new Steane-like enlargement. Quantum Information Processing, Volume 14, Issue 9, pages 3211-3231 (2015). [postprint] [paper]
C. Galindo, F. Hernando, D. Ruano: New quantum codes from evaluation and matrix-product codes. Finite Fields and their Applications. Volume 36, pages 98-120 (2015). [postprint] [paper]
J.S.R. Nielsen, P. Beelen: Sub-quadratic Decoding of One-point Hermitian Codes. IEEE Transactions on Information Theory, Volume 61, Issue 6, pages 3225-3240 (2015). [postprint] [paper]
O. Geil, S. Martin: An improvement of the Feng-Rao bound for primary codes. Designs, Codes and Cryptography, Volume 76, Issue 1, pages 49-79 (2015), [postprint] [paper]
T. Høholdt, F. Piñero, P. Zeng: Optimal codes as Tanner codes with cyclic component codes. Designs, Codes and Cryptography, Volume 76, Issue 1, pages 37-47 (2015). [paper]
P. Beelen, S. R. Ghorpade, S. Ul Hasan: Linear Codes associated to Determinantal Varieties. Discrete Mathematics 338, no. 8, pages 1493-1500 (2015). [postprint] [paper]
J.P. Hansen: Riemann-Roch Spaces and Linear Network Codes. International Journal of Mathematics and Computer Science, 10 no. 1 (2015). [postprint] [paper]
O. Geil: Roots and coefficients of multivariate polynomials over finite fields. Finite Fields and Their Applications, Volume 34, pages 36-44 (2015). [postprint] [paper]
A. Bassa, P. Beelen, A. Garcia, H. Stichtenoth: Towers of Function Fields over Non-prime Finite Fields. Moscow Mathematical Journal, Volume 15, Number 1, pages 1-29 (2015). [postprint] [paper]
O. Geil, S. Martin, R. Matsumoto, D. Ruano, Y. Luo: Relative generalized Hamming weights of one-point algebraic geometric codes. IEEE Transactions on Information Theory, vol.60, no. 10, pages 5938-5949 (2014). [postprint] [paper]
A. Bassa, P. Beelen, A. Garcia and H. Stichtenoth: An Improvement of the Gilbert--Varshamov Bound over Non-prime Fields. IEEE Transactions on Information Theory, Volume 60, Issue 7, pages 3859-3861 (2014). [paper]
A. Bassa, P.Beelen, A.Garcia and H.Stichtenoth: Galois towers over non-prime finite fields. Acta Arithmetica 164.2, pages 163-179 (2014). [postprint] [paper]
O. Geil, S. Martin: Further improvements on the Feng-Rao bound for dual codes. Finite Fields and their Applications, Volume 30, pages 33-48 (2014). [postprint] [paper]
T. Høholdt, J. Justesen: On the sizes of expander graphs and minimum distances of graph codes. Discrete Mathematics, Volume 325, pages 38-46 (2014) [paper]

Peer Reviewed Conference Papers:

I. Cascudo, B. David: SCRAPE: Scalable Randomness Attested by Public Entities. Applied Cryptography and Network Security (ACNS 2017), Springer Lecture Notes in Computer Science, Volume 10355, pages 537-556 (2017) [postprint] [paper].
I. Cascudo, I. Damgård, O. Farràs and Samuel Ranellucci: Resource-efficient OT combiners with active security. Theory of Cryptography (TCC 2017), pages 461-486 (2017) [postprint] [paper].
R. Matsumoto, D. Ruano: Geometric and Computational Approach to Classical and Quantum Secret Sharing. In: Applications of Computer Algebra. ACA 2015. Kotsireas I., Martínez-Moro E. (eds). Springer Proceedings in Mathematics & Statistics, vol 198. Springer (2017). [paper]
O. Geil, F. Özbudak: Bounding the minimum distance of affine variety codes using symbolic computations of footprints. Lecture Notes in Computer Science. 5th International Castle Meeting on Coding Theory and Applications. ICMCTA 2017: Coding Theory and Applications, pages 128-138 (2017). [paper]
O. Geil, D. Lucani: Random network coding over composite fields. Lecture Notes in Computer Science. 5th International Castle Meeting on Coding Theory and Applications. ICMCTA 2017: Coding Theory and Applications, pages 118-127 (2017). [paper]
U. Martínez-Peñas: Universal secure rank-metric coding schemes with optimal communication overheads. Accepted for publication and presentation in ISIT 2017-The IEEE International Symposium on Information Theory, June 25-30, Aachen, Germany. [postprint]
N. Anbar, P. Beelen, N. Nguyen: The exact limit of some cubic towers. Proceedings of AGCT-15, Contemporary Mathematics, vol. 686, pages 1-15 (2017). [paper]
I. Cascudo, I. Damgård, F. Lacerda, S. Ranellucci: Oblivious Transfer from any Non-Trivial Elastic Noisy Channels via Secret Key Agreement. TCC2016-B. Proceedings, Part I. Springer-Verlag Lecture Notes in Computer Science, Volume 9985, pages 204-234, (2016). [postprint] [paper]
I. Cascudo, I. Damgård, B. David, N. Döttling and J. Buus Nielsen: Rate-1, Linear Time and Additively Homomorphic UC Commitments. CRYPTO 2016 . Advances in Cryptology-CRYPTO 2016, Part III, Springer-Verlag Lecture Notes in Computer Science, Volume 9816, pages 179-207 (2016) [postprint] [paper]
U. Martínez-Peñas, R. Matsumoto: Unifying Notions of Generalized Weights for Universal Security on Wire-Tap Networks. 54th Annual Allerton Conference on Communication, Control, and Computing. September 27th - 30th , 2016, Allerton Park and Retreat Center, Monticello, IL, USA
U. Martínez-Peñas: Generalized rank weights of reducible codes, optimal cases and related properties. IEEE International Symposium on Information Theory, Barcelona, Spain, July 10-15, 2016. [postprint] [paper]
U. Martínez-Peñas: Rank equivalent and rank degenerate skew cyclic codes. Workshop on Mathematics and Communications, Santander, Spain, July 6-8, 2016. [postprint]
J. Hansen: Secret Sharing Schemes with Strong Multiplication and a Large Number of Players from Toric Varieties. Proceedings of AGCT 15. AMS Contemporary mathematics, 2016.
O. Geil, S. Martin, U. Martínez-Peñas, D. Ruano: Refined analysis of RGHWs of code pairs coming from Garcia-Stichtenoth's second tower. Accepted for publication and presentation at ACA 2015-Applications of Computer Algebra. Kalamata, Greece, July 20th - 23rd, 2015. [paper]
C. Galindo, F. Hernando, D. Ruano: Quantum codes with bounded minimum distance. Accepted for publication and presentation at ACA 2015-Applications of Computer Algebra. Kalamata, Greece, July 20th - 23rd, 2015. [paper]
R. Matsumoto, D. Ruano: Geometric and Computational Approach to Classical and Quantum Secret Sharing. Accepted for publication and presentation at ACA 2015-Applications of Computer Algebra. Kalamata, Greece, July 20th - 23rd, 2015. [paper]
D.Gomez-Perez, O. Moreno,T. Høholdt, I. Rubio, A.Z. Tirkel: Linear Complexity for Multidimensional Arrays-a Numerical Invariant. Information Theory Proceedings (ISIT), 2015 IEEE International Symposium on, pages 86-90 (2015). [paper]
M.A. Abdelraheem, P. Beelen, A.Bogdanov, E. Tischhauser: Twisted Polynomials: Revisiting Polynomial-based Authenticated Encryption. Advances in Cryptology-EUROCRYPT 2015, 34th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Sofia, Bulgaria, April 26-30 2015. Editors: Oswald, Elisabeth, Fischlin, Marc. Proceedings, Part I, pages 762-786 (2015).
O. Geil, S. Martin, U. Martínez-Peñas, R. Matsumoto, D. Ruano: On asymptotically good ramp secret sharing schemes. Accepted for publication and presentation in WCC-2015. The Ninth International Workshop on Coding and Cryptography (2015).
P. Beelen, S.R. Ghorpade, S. Ul Hasan: Linear Codes associated to Determinantal Varieties. In: Proceedings of the ACCT-XIV Fourteenth International Workshop on Algebraic and Combinatorial Coding Theory. September 7--13 2014 Svetlogorsk (Kaliningrad region), ISBN: 978-5-901158-26-5. Institute for Information Transmission Problems, Moscow, Russia, pages 68-75 (2014).
O. Geil, S. Martin, R. Matsumoto, D. Ruano, Y. Luo: Relative generalized Hamming weights of one-point algebraic geometric codes. In Proceedings of Information Theory Workshop (ITW), 2014 IEEE, pages 137-141 (2014). [paper]
O. Geil, S. Martin: Affine variety codes are better than their reputation. Proceedings of The 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014). Groningen, The Netherlands, 4 pages (2014).
A. Bassa, P. Beelen and N. Nguyen: Good towers of function fields. Algebraic Curves and Finite Fields: Codes, Cryptography, and other Emergent Applications (H. Niederreiter, A. Ostafe, D. Panario, and A. Winterhof, eds.), de Gruyter, Berlin, pages 23-40 (2014). [postprint] [paper]

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