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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 (1-2 May), Cryptography (3-4 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 two-day 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, morning-afternoon |
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| | Arrival | |
Special Lecture
| Sunday, April 30 |
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| Location: HF 9901, Campus Linz. See map. |
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| 18.00-18.45 | | B. Buchberger | | Tutorial on Groebner Bases for Newcomers I |
| 18.45-19.15 | | Coffee-break |
| 19.15-20.00 | | B. Buchberger | | Tutorial on Groebner Bases for Newcomers II |
Coding Session, First Poster Session:
| Monday, May 01, morning: "Groebner bases and Cyclic Codes" |
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| Location: 'Managment Zentrum' building, Campus Linz. See map. |
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| 09.15-09.30 | | B. Buchberger | | Kick-Off: Salutatory |
| 09.30-10.10 | | E. Betti, E. Orsini | | Introduction to cyclic codes
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| 10.20-11.00 | | T. Mora, E. Orsini | | Decoding cyclic codes: the Cooper philosophy
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| 11.00-11.30 | | Coffee-break |
| 11.30-12.10 | | M. Sala | | A theory for the distance of cyclic codes
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| 12.20-13.00 | | D. Augot | | Interpolation based decoding of Reed-Muller codes
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LUNCH
| Monday, May 01, afternoon: "AG Goppa Code" |
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| 15.30-16.10 | | D. Leonard | | Introduction to AG Goppa codes
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| 16.10-16.30 | | Coffee-break |
| 16.30-17.20 | | J. Little | | Groebner bases for encoding of codes from order domains
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| 17.30-18.10 | | O. Geil | | Some interesting families of AG Goppa codes
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| Tuesday, May 02, morning: "Combinatorial approach to zero-dimensional ideals" |
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| Location: 'Uni Centre' building, Campus Linz. See map. |
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| 09.00-09.45 | | S. Sakata | | On the Berlekamp-Massey-Sakata algorithm
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| 09.55-10.35 | | T. Mora | | Moeller's Algorithm
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| 10.35-11.00 | | Coffee-break |
| 11.00-11.40 | | J.C. Faugère | | Computation of Gb by change of ordering: comparing the efficiency of several algorithms |
| 11.50-12.30 | | T. Mora | |
A survey on combinatorial duality approach: Cerlinaco--Mureddu Algorithm, the Axis-of-Evil Theorem, Macaulay's Algorithm, Noether Decomposition
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LUNCH
| Tuesday, May 02, afternoon: "Combinatorial approach to Groebner bases and coding theory" |
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| 14.15-15.00 | | S. Sakata | | Application of the BMS algorithm to decoding of codes from algebraic curves
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| 15.10-15.50 | | B. Trager | | Burst Error correction for Reed Solomon Codes |
| 15.50-16.20 | | Coffee-break |
| 16.20-17.00 | | H. O'Keeffe, P. Fitzpatrick | | A Groebner basis approach to list decoding of Reed-Solomon and Algebraic Geometry Codes
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| 17.10-17.25 | | M. Sala | | Relations between bounds on the distance of cyclic codes and FGLM decoding |
| 17.25-17.40 | | D. Leonard | | A module view of integral closure
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| 17.40-17.55 | | O. Geil | | Two applications of the footprint bound
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Cryptography Session:
| Wednesday, May 03 |
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| Location: Castle of Hagenberg (the site of RISC), Hagenberg (shuttle busses will be provided free of charge). See RISC web-page. |
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| 09.00-09.25 | | L. Perret | | Why Can Groebner Bases Be Used in Cryptology ? |
| 09.30-10.10 | | O. Billet | | Multivariate Cryptography: An Overview
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| 10.10-10.35 | | Coffee-break |
| 10.35-11.25 | | J.-C. Faugère | | The F5 and FGLM algorithms : Applications to HFE and Sflasfh |
| 11.35-12.15 | | C. Diem | | On the Subexponentiality of the Elliptic Curve Discrete Logarithm Problem over Extension Fields |
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| LUNCH |
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| 14.00-14.25 | | F. Levy-dit-Vehel | | Algebraic Decoding of Rank Metric Codes
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| 14.35-15.15 | | M. Kreuzer | | Grobner Basis Cryptosystems
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| 15.15-15.35 | | Coffee-break |
| 15.35-16.15 | | T. Rai, S. Bulygin | | Countering Chosen-Ciphertext Attacks against Noncommutative Polly Cracker-type Cryptosystems
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| 16.25-17.05 | | H. Park | | Security of GB Cryptosystems and Castelnuovo-Mumford Regularity |
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| 18.15-18.25 | | B. Buchberger | | Short Introduction to RISC and Softwarepark Hagenberg |
| 18.25-19.15 | | L. Perret | | Grobner Bases in Cryptography: A Personal View |
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| 19.15 | | Buffet Dinner |
| Thursday, May 04 |
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| Location: 'Uni Centre' building, Campus Linz. See map. |
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| 09.30-10.20 | | C. Cid | | Algebraic Anaysis of the AES |
| 10.30-11.10 | | R.-P. Weinmann | | Block Cipher Sensitive to Groebner Bases |
| 11.10-11.35 | | Coffee-break |
| 11.35-12.25 | | F. Armknecht | | A Survey of Algebraic Attacks against Stream Ciphers
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| LUNCH |
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| 14.00-14.40 | | M. Sugita | | Implementation of F4 algorithm, and Experimental Cryptanalysis of Toyocrypt and 58-round SHA-1 using Groebner Bases |
| 14.50-16.00 | | Panel Discussion on "Groebner Bases in Cryptography: What's the Future?" |
| 16.00-16.30 | | Coffee-break |
Algebraic Combinatorics session:
| 16.30-17.30 | | M. Klin | | Tutorial Coherent configurations and association schemes, Part I: Definitions, examples, simple facts
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| 17.40-18.30 | | A. Hulpke | | Groebner Bases and related methods in Group Theory
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| DINNER |
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| 20.30-22.00 | | Joint poster session on Cryptography and Algebraic Combinatorics |
| Friday, May 05 |
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| Location: 'Uni Centre' building, Campus Linz. See map. |
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| 10.00-11.00 | | M. Muzychuk | | Tutorial Coherent configurations and association schemes, Part II: Spectral properties and mergings of classes
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| 11.00-11.25 | | Coffee-break |
| 11.25-12.05 | | E. Bannai | | Spherical packings and association schemes, Part I
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| 12.10-13.00 | | A. Sali | | Groebner Bases and Extremal Combinatorics, Part I: Combinatorial aspects
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| LUNCH |
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| 14.30-15.30 | | C. Pech | | Tutorial Coherent configurations and association schemes, Part III: Galois correspondence between permutation groups and coherent configurations
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| 15.40-16.30 | | G. Jones | | Computational problems arising from dessins d'enfants |
| 16.30-16.55 | | | | Coffee-break |
| 16.55-17.45 | | G.E. Moorhouse | | Approaching Some Problems in Finite Geometry through Algebraic Geometry
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| 17.55-18.35 | | I. Ponomarenko | | Isomorphism problem for finite combinatorial objects via coherent configurations
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| Saturday, May 06 |
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| Location: 'Uni Centre' building, Campus Linz. See map. |
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| 09.30-10.20 | | V. Welker | | Groebner bases with spherical or polytopal initial ideal
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| 10.20-10.45 | | | Coffee-break |
| 10.45-11.25 | | E. Martinez-Moro | | Mattson-Solomon transform and Groebner bases: applications to association schemes and codes
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| 11.35-12.15 | | E. Bannai | | Spherical packings and association schemes, Part II
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| 12.20-13.00 | | S. Reichard | | New ideas in enumeration of coherent subalgebras of a prescribed coherent algebra
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| LUNCH |
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| 14.30-15.20 | | L. Ronyai | | Groebner Bases and Extremal Combinatorics, Part II: Algebraic aspects
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| 15.30-16.20 | | A. Jurisic | | Classification of triangle-free distance regular graphs (with small application of Groebner bases)
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| 16.20-16.45 | | | | Coffee-break |
| 16.45-17.25 | | I. Miyamoto | | Performance of the GAP-function Normalizer and an attempt of its improvement
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| 17.30-18.20 | | J. Backelin | | Non-commutative Gröbner bases, viewed formally or as applied combinatorial algebra. |
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| 18.30-19.00 | | Optional: A short concluding discussion |
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| END of workshop D1 not later than on 19:15 |
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