Mathematical Methods in Computer Science Essays in Memory of Thomas Beth
This Festschrift volume contains the proceedings of the conference Mathematical Methods in Computer Science, MMICS 2008, held December 2008, in Karlsruhe, Germany, in memory of Thomas Beth. The themes of the conference reflect his many interests.
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| Main Authors | , , |
|---|---|
| Format | eBook |
| Language | English |
| Published |
Berlin, Heidelberg
Springer Berlin / Heidelberg
2008
Springer Berlin Heidelberg Springer |
| Edition | 1 |
| Series | Lecture Notes in Computer Science |
| Subjects | |
| Online Access | Get full text |
| ISBN | 3540899936 9783540899938 |
| ISSN | 0302-9743 1611-3349 |
| DOI | 10.1007/978-3-540-89994-5 |
Cover
Table of Contents:
- Intro -- Preface -- In Memoriam -- Organization -- Table of Contents -- On the Security of Beth's Identification Schemes against Active and Concurrent Adversaries -- Steiner t-Designs for Large t -- New Spatial Configurations -- Construction of Large Constant Dimension Codes with a Prescribed Minimum Distance -- Invited Talk: Embedding Classical into Quantum Computation -- A Criterion for Attaining the Welch Bounds with Applications for Mutually Unbiased Bases -- An Efficient Quantum Algorithm for the Hidden Subgroup Problem over Weyl-Heisenberg Groups -- Computing Equiangular Lines in Complex Space -- Complexity of Comparing Monomials and Two Improvements of the Buchberger-Moller Algorithm -- Invited Talk: Decoding Cyclic Codes: The Cooper Philosophy -- Kernel Dimension for Some Families of Quaternary Reed-Muller Codes -- Coding-Based Oblivious Transfer -- Protection of Sensitive Security Parameters in Integrated Circuits -- On Reconstruction of RC4 Keys from Internal States -- Author Index
- Introduction -- The Weyl-Heisenberg Groups -- Fourier Sampling Approach to HSP -- The Irreducible Representations -- The Quantum Algorithm -- Conclusions -- References -- A QFT for the Weyl-Heisenberg Groups -- Algorithms -- Computing Equiangular Lines in Complex Space -- Introduction -- The General Case -- Weyl-Heisenberg Symmetry -- Zauner's Conjecture -- Modular Techniques for Solving Polynomial Equations -- Conclusions -- References -- Appendix -- Complexity of Comparing Monomials and Two Improvements of the Buchberger-M\"{o}ller Algorithm -- Introduction -- Monomial Manipulations -- Complexity Model -- Monomial Orders -- Comparing Vectors of Integers -- Comparing Monomials with Respect to a Standard Order -- Comparing Monomials with Respect to a Matrix Order -- Merging Sorted Lists of Monomials -- TheBuchberger-M\'{o}ller -Algorithm Revised -- Two Formulations of the BM-Algorithm -- Optimizing the BM-Algorithm -- Applications to the FGLM-Algorithm and for Ideals Defined by Functionals -- Discussion and Future Work -- References -- Coding Theory -- Invited Talk: Decoding Cyclic Codes: The Cooper Philosophy -- References -- Kernel Dimension for Some Families of Quaternary Reed-Muller Codes -- Introduction -- Preliminaries -- Quaternary Linear Codes -- Quaternary Linear Reed-Muller Codes -- Kernel Dimensions for the \RM_s Family with s=0 -- Kernel Dimensions for the \RM_s Families -- Conclusions -- References -- Cryptography II -- Coding-Based Oblivious Transfer -- Introduction -- Preliminaries -- Security Definitions -- Assumptions -- Tools -- Reducing the Gap in Rabin OT -- Rabin Oblivious Transfer -- Security Analysis -- Omitting Trusted Third Party -- 1-out-of-2 String Oblivious Transfer -- References -- Appendix A: Details on Security of Rabin OT -- A.1 Examples of Security Parameters -- A.2 Reaction Attack
- A.3 Proof Details for Receiver's Security -- Protection of Sensitive Security Parameters in Integrated Circuits -- Introduction -- Properties of the IC-Eigenkey -- Physical Uncloneable Functions -- Different Basic Systems for PUFs -- Silicon PUFs Based on Propagation Delays of Gates -- Delay Line Configuration of the IC-Eigenkey Generator -- Configuration Control of the IC-Eigenkey Generator -- Simulation Results and Tests -- Simulation Results -- Test Results -- Conclusion -- References -- On Reconstruction of RC4 Keys from Internal States -- Introduction -- Description of \sf{RC4} and Notations -- Previous Results -- A Hypotheses-Testing Approach to the Problem -- Complexity Analysis -- Simulation Results -- A Bit-by-Bit Approach for Key Recovery -- Conclusion -- References -- A Deriving Optimized Parameters for Tree-Based Bit-by-Bit Search Algorithm -- B Improved Recovery of Sum of the Key Elements -- C Potential Improvements -- Author Index
- Intro -- Title Page -- Preface -- Organization -- Table of Contents -- Cryptography I -- On the Security of Beth's Identification Schemes against Active and Concurrent Adversaries -- Introduction -- Definitions -- Preliminaries -- El-Gamal Signature Scheme -- The Identification Scheme Beth-SI-0 -- The Identification Scheme Beth-SI-1 -- The Identification Scheme Beth-IBI-1 -- References -- Designs -- Steiner t-Designs for Large t -- Introduction -- Combinatorial Designs -- Basic Properties and Existence Results -- Approach via Symmetry -- Non-existence of Block-Transitive Steiner 6-Designs -- References -- New Spatial Configurations -- Introduction and Notation -- New Constructions -- k ≤ 7 -- k = 8 -- k = 9 -- The Existence Table of 2-Configurations -- References -- Construction of Large Constant Dimension Codes with a Prescribed Minimum Distance -- Introduction -- Subspace Codes -- q−Analogues of Designs -- Construction of Constant Dimension Codes -- Constant Dimension Codes with Prescribed Automorphisms -- Example -- Using Singer Cycles -- Results -- References -- Quantum Computing -- Invited Talk: Embedding Classical into Quantum Computation -- Introduction -- Classically Simulatable Quantum Computations -- Extensions of Simulatable Circuits -- Concluding Remarks -- References -- A Criterion for Attaining the Welch Bounds with Applications for Mutually Unbiased Bases -- Mutually Unbiased Bases -- Welch Bounds and Crosscorrelation -- Link between MUBs and the Welch Bounds -- Criterion for Attaining the Welch Bounds -- Application of the Criterion to MUBs -- Homogeneous Systems of MUBs -- Fourier Matrices -- Fourier Matrices in Homogeneous Systems -- Known Constructions -- Related Combinatorial Structures -- Conclusion -- References -- An Efficient Quantum Algorithm for the Hidden Subgroup Problem over Weyl-Heisenberg Groups