Computational and combinatorial group theory and cryptography : AMS Special Sessions : Computational Algebra, Groups, and Applications, April 30-May 1, 2011, University of Nevada, Las Vegas, Nevada, NV : Mathematical Aspects of Cryptography and Cyber Security, September 10-11, 2011, Cornell University, Ithaca, New York / Benjamin Fine, Delaram Kahrobaei, Gerhard Rosenberger, editors.

Format:

Book

Conference/Event

Contributor:

Fine, Benjamin, 1948- editor.

Kahrobaei, Delaram, 1975- editor.

Rosenberger, Gerhard, editor.

Conference Name:

AMS Special Session on Computational Algebra, Groups, and Applications (2011 : University of Nevada), issuing body.

AMS Special Session on Mathematical Aspects of Cryptography and Cyber Security (2011 : Cornell University), issuing body.

Series:

Contemporary mathematics (American Mathematical Society). 0271-4132 582

Contemporary mathematics, 582 0271-4132

Language:

English

Subjects (All):

Group theory--Congresses.

Group theory.

Cryptography--Congresses.

Cryptography.

Physical Description:

1 online resource (210 pages).

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2012]

Language Note:

English

Contents:

Intro

Preface

Weyl Gröbner Basis Cryptosystems

1. Introduction

2. Gröbner Bases in Weyl Algebras

3. Weyl Gröbner Basis Cryptosystems

4. Security of Weyl Gröbner Basis Cryptosystems

5. Two-Sided Weyl Gröbner Basis Cryptosystems

References

A New Look at Finitely Generated Metabelian Groups

1. Introductory remarks

2. Philip Hall's approach

3. A few properties of finitely generated metabelian groups

4. The Bieri-Strebel invariant

5. The geometry of the Cayley graph and metabelian presentations

6. Hilbert functions

7. Where to go from here

8. Affine algebraic sets, localization and completions

9. A new approach to the isomorphism problem for finitely generated metabelian groups

10. Localization of finitely generated, residually nilpotent, metabelian groups and the Telescope Theorem

11. Embedding groups and localization

12. Some of the implications of the use of localization

13. Classifying para-equivalent metabelian groups

14. Examples

15. Further examples and Dedekind domains

-Automorphisms of Groups with Almost Constant Upper Central Series

2. Preliminary discussion

3. Proof of the main result

4. Examples

5. Acknowledgements

A Proposed Alternative to the Shamir Secret Sharing Scheme

2. The Shamir Secret Sharing Scheme

3. An Alternative Based on the Closest Vector Theorem

Improving Latin Square Based Secret Sharing Schemes

2. Cryptographic hash functions

3. Secret sharing schemes

4. Latin square

5. Application of critical set in secret sharing

6. Limitations of Latin square based schemes

7. Apply hash function to Latin square based schemes

8. Conclusion and Future Research

References.

A Hand-Computation Involving Surface Groups, the Reidemeister-Schreier Rewriting Process and Kurosh Subgroup Theorem

2. Surface Groups

3. The Reidemeister-Schreier Rewriting Process

Adjunction of Roots in Exponential A-Groups

2. Preliminaries

3. Results

Logspace Computations in Coxeter Groups and Graph Groups

2. Notation

3. Coxeter groups

4. Mazurkiewicz traces and graph groups

5. Right-angled Coxeter groups

6. Free partially commutative inverse monoids

7. Concluding remarks and open problems

Collection by Polynomials in Finite -groups

2. Existence of polynomials

3. Computing the polynomials

5. The Complexity of multiplication

All Finite Generalized Tetrahedon Groups II

The Classification of One Relator Limit Groups and the Surface Group Conjecture

2. Surface Groups and The Surface Group Conjecture

3. Cyclically Pinched and Conjugacy Pinched One Relator Groups

4. Fully Residually Free Groups

5. Property IF and Results on the Surface Group Conjecture

6. Baumslag Doubles and a Question of Gromov

7. The Free-by-Cyclic Conjectures

8. Approaches to the Classification of One Relator Limit Groups

9. The Lyndon Properties

10. The Classification of One Relator CSA Groups

Discrimination and Separation in the Metabelian Variety

2. Relativization to the Metabelian Variety

3. A Counterexample to the Codiscrimination Theorem and Corollary

4. Failure of Free Constructions

5. Epilogue

6. Questions

A Secret Sharing Scheme Based on Group Presentations and the Word Problem

2. Very Brief Background on Group Theory.

3. An ( , )-threshold Scheme

4. A ( , )-threshold Scheme

5. Why Use Groups?

6. Platform Group

7. Tietze transformations: elementary isomorphisms

8. Conclusions

Authenticated Key Agreement with Key Re-Use in the Short Authenticated Strings Model

3. Communication and Adversarial Model

4. Encryption-based SAS Message Authentication Protocol

5. Encryption-based SAS Authenticated Key Agreement Protocol

Appendix A. IND-CCA Encryption

Appendix B. Difficulty in Extending the General Compilation Theorem of Pasini-Vaudenay

Appendix C. Reductions ℬ_{ }[1-3] in the Proof of Theorem 1

Publicly Verifiable Secret Sharing Using Non-Abelian Groups

1. Introduction to Publicly Verifiable Secret Sharing

2. New schemes

A Note on the Hyperbolicity of Strict Pride Groups

1. Introduction and basic definitions

2. Small Cancellation Theory

3. Strict Pride groups with sufficiently high-powered relators are hyperbolic

An Algorithm to Express Words as a Product of Conjugates of Relators

2. Generating Set

3. The Cayley graph of

4. Generating

5. Rewriting

6. Construction of

7. Rewriting Without Computing

8. Original Relators

9. Conclusions

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references.

Description based on print version record.