
Workshop D1: Gröbner Bases in Cryptography, Coding Theory, and Algebraic Combinatorics
Date: May 01  May 06
Chairmen: Mikhail Klin, Ludovic Perret, Max Sala
The workshop is organized in the framework of the Special Semester on Groebner Bases at RICAM and RISC, Austria
(see www.ricam.oeaw.ac.at/srs/groeb/).
The workshop is divided into three consecutive sessions: Coding (12 May), Cryptography (34 May) and
Algebraic Combinatorics (4 May late afternoon  6 May).
On 30 May, we will be honoured by a starting lecture on Groebner bases by Bruno Buchberger
(founder of the method).
The goal of this workshop is to bring experts in three different areas together with a community of people working in Groebner bases.
All sides need to understand the computational interests and current possibilities of each other.
The Coding part is structured as a twoday tutorial on Algebraic Coding theory and Groebner basis techniques that
can be used in this context. The main research event of this part is the poster session.
The Crypto part mainly consists of a number of invited talks, plus a poster session jointly with the AC part.
It concentrates on all aspects of Groebner bases in Cryptography, including recent advances in this area.
The AC part consists of invited talks covering a wide range of aspects of AC, especially those computational aspects where Groebner
basis techniques might provide significant advances. The poster session is jointly with the Crypto part.
Sunday, April 30, morningafternoon 

  Arrival  
Special Lecture
Sunday, April 30 

Location: HF 9901, Campus Linz. See map. 

18.0018.45   B. Buchberger   Tutorial on Groebner Bases for Newcomers I 
18.4519.15   Coffeebreak 
19.1520.00   B. Buchberger   Tutorial on Groebner Bases for Newcomers II 
Coding Session, First Poster Session:
Monday, May 01, morning: "Groebner bases and Cyclic Codes" 

Location: 'Managment Zentrum' building, Campus Linz. See map. 

09.1509.30   B. Buchberger   KickOff: Salutatory 
09.3010.10   E. Betti, E. Orsini   Introduction to cyclic codes


10.2011.00   T. Mora, E. Orsini   Decoding cyclic codes: the Cooper philosophy



11.0011.30   Coffeebreak 
11.3012.10   M. Sala   A theory for the distance of cyclic codes


12.2013.00   D. Augot   Interpolation based decoding of ReedMuller codes


LUNCH
Monday, May 01, afternoon: "AG Goppa Code" 

15.3016.10   D. Leonard   Introduction to AG Goppa codes


16.1016.30   Coffeebreak 
16.3017.20   J. Little   Groebner bases for encoding of codes from order domains


17.3018.10   O. Geil   Some interesting families of AG Goppa codes


Tuesday, May 02, morning: "Combinatorial approach to zerodimensional ideals" 

Location: 'Uni Centre' building, Campus Linz. See map. 

09.0009.45   S. Sakata   On the BerlekampMasseySakata algorithm


09.5510.35   T. Mora   Moeller's Algorithm



10.3511.00   Coffeebreak 
11.0011.40   J.C. Faugère   Computation of Gb by change of ordering: comparing the efficiency of several algorithms 
11.5012.30   T. Mora  
A survey on combinatorial duality approach: CerlinacoMureddu Algorithm, the AxisofEvil Theorem, Macaulay's Algorithm, Noether Decomposition



LUNCH
Tuesday, May 02, afternoon: "Combinatorial approach to Groebner bases and coding theory" 

14.1515.00   S. Sakata   Application of the BMS algorithm to decoding of codes from algebraic curves


15.1015.50   B. Trager   Burst Error correction for Reed Solomon Codes 
15.5016.20   Coffeebreak 
16.2017.00   H. O'Keeffe, P. Fitzpatrick   A Groebner basis approach to list decoding of ReedSolomon and Algebraic Geometry Codes


17.1017.25   M. Sala   Relations between bounds on the distance of cyclic codes and FGLM decoding 
17.2517.40   D. Leonard   A module view of integral closure


17.4017.55   O. Geil   Two applications of the footprint bound


Cryptography Session:
Wednesday, May 03 

Location: Castle of Hagenberg (the site of RISC), Hagenberg (shuttle busses will be provided free of charge). See RISC webpage. 

09.0009.25   L. Perret   Why Can Groebner Bases Be Used in Cryptology ? 
09.3010.10   O. Billet   Multivariate Cryptography: An Overview


10.1010.35   Coffeebreak 
10.3511.25   J.C. Faugère   The F5 and FGLM algorithms : Applications to HFE and Sflasfh 
11.3512.15   C. Diem   On the Subexponentiality of the Elliptic Curve Discrete Logarithm Problem over Extension Fields 

LUNCH 

14.0014.25   F. LevyditVehel   Algebraic Decoding of Rank Metric Codes


14.3515.15   M. Kreuzer   Grobner Basis Cryptosystems


15.1515.35   Coffeebreak 
15.3516.15   T. Rai, S. Bulygin   Countering ChosenCiphertext Attacks against Noncommutative Polly Crackertype Cryptosystems


16.2517.05   H. Park   Security of GB Cryptosystems and CastelnuovoMumford Regularity 

18.1518.25   B. Buchberger   Short Introduction to RISC and Softwarepark Hagenberg 
18.2519.15   L. Perret   Grobner Bases in Cryptography: A Personal View 

19.15   Buffet Dinner 
Thursday, May 04 

Location: 'Uni Centre' building, Campus Linz. See map. 

09.3010.20   C. Cid   Algebraic Anaysis of the AES 
10.3011.10   R.P. Weinmann   Block Cipher Sensitive to Groebner Bases 
11.1011.35   Coffeebreak 
11.3512.25   F. Armknecht   A Survey of Algebraic Attacks against Stream Ciphers



LUNCH 

14.0014.40   M. Sugita   Implementation of F4 algorithm, and Experimental Cryptanalysis of Toyocrypt and 58round SHA1 using Groebner Bases 
14.5016.00   Panel Discussion on "Groebner Bases in Cryptography: What's the Future?" 
16.0016.30   Coffeebreak 
Algebraic Combinatorics session:
16.3017.30   M. Klin   Tutorial Coherent configurations and association schemes, Part I: Definitions, examples, simple facts


17.4018.30   A. Hulpke   Groebner Bases and related methods in Group Theory

 mov


DINNER 

20.3022.00   Joint poster session on Cryptography and Algebraic Combinatorics 
Friday, May 05 

Location: 'Uni Centre' building, Campus Linz. See map. 

10.0011.00   M. Muzychuk   Tutorial Coherent configurations and association schemes, Part II: Spectral properties and mergings of classes


11.0011.25   Coffeebreak 
11.2512.05   E. Bannai   Spherical packings and association schemes, Part I


12.1013.00   A. Sali   Groebner Bases and Extremal Combinatorics, Part I: Combinatorial aspects



LUNCH 

14.3015.30   C. Pech   Tutorial Coherent configurations and association schemes, Part III: Galois correspondence between permutation groups and coherent configurations


15.4016.30   G. Jones   Computational problems arising from dessins d'enfants 
16.3016.55     Coffeebreak 
16.5517.45   G.E. Moorhouse   Approaching Some Problems in Finite Geometry through Algebraic Geometry


17.5518.35   I. Ponomarenko   Isomorphism problem for finite combinatorial objects via coherent configurations


Saturday, May 06 

Location: 'Uni Centre' building, Campus Linz. See map. 

09.3010.20   V. Welker   Groebner bases with spherical or polytopal initial ideal


10.2010.45    Coffeebreak 
10.4511.25   E. MartinezMoro   MattsonSolomon transform and Groebner bases: applications to association schemes and codes


11.3512.15   E. Bannai   Spherical packings and association schemes, Part II


12.2013.00   S. Reichard   New ideas in enumeration of coherent subalgebras of a prescribed coherent algebra



LUNCH 

14.3015.20   L. Ronyai   Groebner Bases and Extremal Combinatorics, Part II: Algebraic aspects


15.3016.20   A. Jurisic   Classification of trianglefree distance regular graphs (with small application of Groebner bases)


16.2016.45     Coffeebreak 
16.4517.25   I. Miyamoto   Performance of the GAPfunction Normalizer and an attempt of its improvement


17.3018.20   J. Backelin   Noncommutative Gröbner bases, viewed formally or as applied combinatorial algebra. 

18.3019.00   Optional: A short concluding discussion 

END of workshop D1 not later than on 19:15 

