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International Symposium on Mathematics, Quantum Theory, and Cryptography : Proceedings of MQC 2019.

Bibliographic Details
Main Author: Takagi, Tsuyoshi.
Other Authors: Wakayama, Masato., Tanaka, Keisuke., Kunihiro, Noboru., Kimoto, Kazufumi., Ikematsu, Yasuhiko.
Format: eBook
Language:English
Published: Singapore : Springer Singapore Pte. Limited, 2020.
Edition:1st ed.
Series:Mathematics for Industry Series
Subjects:
Electronic books.
Online Access:Click to View
Table of Contents:
  • Intro
  • Foreword
  • Preface
  • Contents
  • About the Editors
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  • Keynote
  • Sustainable Cryptography
  • What Kind of Insight Provide Analytical Solutions of Quantum Models?
  • References
  • Emerging Ultrastrong Coupling Between Light and Matter Observed in Circuit Quantum Electrodynamics
  • References
  • Summary
  • Verified Numerical Computations and Related Applications
  • A Review of Secret Key Distribution Based on Bounded Observability
  • References
  • Quantum Computing and Information Theory
  • Quantum Random Numbers Generated by a Cloud Superconducting Quantum Computer
  • 1 Introduction
  • 2 Statistical Tests for Random Number Generators
  • 3 NIST SP 800-22
  • 3.1 Frequency Test
  • 3.2 Frequency Test Within a Block
  • 3.3 Runs Test
  • 3.4 The Longest Run of Ones Within a Block Test
  • 3.5 Discrete Fourier Transform Test
  • 3.6 Approximate Entropy Test
  • 3.7 Cumulative Sums Test
  • 4 Quantum Random Number Generation on the Cloud Quantum Computer
  • 5 Conclusion
  • References
  • Quantum Factoring Algorithm: Resource Estimation and Survey of Experiments
  • 1 Introduction
  • 2 Outline of Shor's Quantum Factoring Algorithm (Shor)
  • 2.1 Quantum Computation
  • 2.2 Shor's Quantum Factoring Algorithm
  • 2.3 Circuit Construction and Resource Estimation for Shor's Quantum Factoring Algorithm
  • 2.4 Survey of Quantum Experiments for Factoring
  • 3 Quantum Circuits Without Using the Order Information
  • 3.1 Quantum Factoring Experiment Shown in IBMspsChuang
  • 3.2 Quantum Factoring Experiment Shown in joseph
  • 3.3 Quantum Factoring Experiment Shown in realization
  • 4 Quantum Circuits with Explicitly Using the Order information
  • 4.1 Quantum Factoring Experiment of N=15 Shown in photonic.
  • 4.2 Quantum Factoring Experiment of N=21 Shown in spsqubitrecycing
  • 4.3 Oversimplified Shor's Algorithm (oversimplified)
  • 5 Summary and Concluding Remarks
  • References
  • Towards Constructing Fully Homomorphic Encryption without Ciphertext Noise from Group Theory
  • 1 Introduction
  • 1.1 Our Contributions
  • 2 Preliminaries
  • 3 Our Framework for FHE
  • 3.1 Group-Theoretic Realization of Functions
  • 3.2 Lift of Realization of Functions
  • 3.3 The Proposed Framework
  • 4 Examples of Realizations of Functions in Groups
  • 4.1 Deterministic Case: Known Result
  • 4.2 Deterministic Case: Proposed Constructions
  • 4.3 Preliminaries: On Random Sampling of Group Elements
  • 4.4 Probabilistic Case: ``Commutator-Separable'' Groups
  • 4.5 Probabilistic Case: Simple Groups
  • 5 Towards Achieving Secure Lift of Realization
  • 5.1 A Remark on the Choice of Random Variables
  • 5.2 Insecurity of a Matrix-Based Naive Construction
  • 5.3 Observation for Avoiding Linear Constraints
  • 5.4 Another Trial Using Tietze Transformations
  • References
  • From the Bloch Sphere to Phase-Space Representations with the Gottesman-Kitaev-Preskill Encoding
  • 1 Introduction
  • 2 GKP Encoding of Qubit States
  • 3 Phase-Space Wigner Representation of GKP Encoded States
  • 4 Quantification of Negativity of the Wigner Function for GKP Encoded States
  • 5 Conclusions
  • References
  • Quantum Interactions
  • Number Theoretic Study in Quantum Interactions
  • References
  • A Data Concealing Technique with Random Noise Disturbance and a Restoring Technique for the Concealed Data by Stochastic Process Estimation
  • 1 Introduction
  • 2 Mathematical Setups
  • 2.1 How to Conceal Data
  • 2.2 How to Restore Data
  • 3 Example of Functionals and Simulation
  • 3.1 An Example of the Set of Functionals
  • 3.2 Simulation of Concealing and Restoring Data on Physical Layer.
  • 4 Application to Data on Physical Layer and Presentation Layer
  • 4.1 Binary Data of Pictorial Image
  • 4.2 Analog Data of Pictorial Image
  • 5 Conclusion and Future Work
  • References
  • Quantum Optics with Giant Atoms-the First Five Years
  • 1 Introduction
  • 2 Theory for Giant Atoms
  • 2.1 One Giant Atom
  • 2.2 One Giant Atom with Time Delay
  • 2.3 Multiple Giant Atoms
  • 3 Experiments with Giant Atoms
  • 3.1 Superconducting Qubits and Surface Acoustic Waves
  • 3.2 Superconducting Qubits and Microwave Transmission Lines
  • 3.3 Cold Atoms in Optical Lattices
  • 4 Conclusion and Outlook
  • References
  • Topics in Mathematics
  • Extended Divisibility Relations for Constraint Polynomials of the Asymmetric Quantum Rabi Model
  • 1 Introduction
  • 2 The Confluent Picture of the Asymmetric Quantum Rabi Model
  • 3 Extended Divisibility Properties for Constraint and Related Polynomials
  • 4 Open Problems
  • 4.1 Number of Exceptional Solutions of the AQRM
  • 4.2 Classification of Parameter Regimes
  • References
  • Generalized Group-Subgroup Pair Graphs
  • 1 Introduction
  • 1.1 Conventions
  • 2 Preliminaries
  • 3 Cayley Graphs and Group-Subgroup Pair Graphs
  • 3.1 Cayley Graphs
  • 3.2 Group-Subgroup Pair Graphs
  • 4 Homogeneity
  • 5 Generalized Group-Subgroup Pair Graph
  • 5.1 Definition
  • 5.2 Examples
  • 6 Spectra of G(G,H,S)
  • 6.1 Adjacency Matrix of G(G,H,S)
  • 6.2 When H is abelian
  • 6.3 Petersen Extension
  • References
  • Post-Quantum Cryptography
  • A Survey of Solving SVP Algorithms and Recent Strategies for Solving the SVP Challenge
  • 1 Introduction
  • 2 Mathematical Background
  • 2.1 Lattices and Their Bases
  • 2.2 Successive Minima, Hermite's Constants, and Gaussian Heuristic
  • 2.3 Introduction to Lattice Problems
  • 3 Solving SVP Algorithms
  • 3.1 Exact-SVP Algorithms
  • 3.2 Approximate-SVP Algorithms.
  • 4 The SVP Challenge and Recent Strategies
  • 4.1 The Random Sampling Strategy
  • 4.2 The Sub-Sieving Strategy
  • References
  • Recent Developments in Multivariate Public Key Cryptosystems
  • 1 Introduction
  • 2 UOV, Rainbow, and Variants of HFE
  • 2.1 Basic Constructions of Multivariate Public Key Cryptosystems
  • 2.2 UOV
  • 2.3 Rainbow
  • 2.4 HFE
  • 2.5 Variants of HFE
  • 3 New Encryption Schemes
  • 3.1 HFERP
  • 3.2 ZHFE
  • 3.3 EFC
  • 3.4 ABC
  • 4 Conclusion
  • References
  • Ramanujan Graphs for Post-Quantum Cryptography
  • 1 Introduction
  • 2 Ramanujan Graphs and Their Cryptographic Applications
  • 2.1 Security on Cayley Hashes and Word Problems
  • 2.2 Lifting Attacks
  • 3 The Families of LPS-Type Graphs
  • 3.1 Proof of the Ramanujan-Ness of Graphs XP,Q(p,q) when P=13
  • 4 Relationship Between LPS-Type Graphs and Pizer's Graphs
  • 4.1 Similarities and Differences
  • 5 Open Problems
  • References
  • Post-Quantum Constant-Round Group Key Exchange from Static Assumptions
  • 1 Introduction
  • 1.1 Background
  • 1.2 Our Contributions
  • 1.3 Key Techniques
  • 1.4 Organization
  • 2 Preliminaries
  • 2.1 Group Key Exchange
  • 2.2 SIDH and CSIDH Key Exchange
  • 3 New Assumptions on Supersingular Invariants
  • 3.1 New Assumptions on Supersingular j-Invariants
  • 3.2 New Assumptions on Supersingular Montgomery Coefficients
  • 4 Proposed Post-Quantum Group Key Exchange (GKE)
  • 4.1 A Generic JV-Type Compiler for GKE from Two-Party KE (ch18JusVau96)
  • 4.2 Constant-Round GKE from Static Standard Assumptions
  • 4.3 Two-Round Product-BD (PBD) GKE from d-DSJP Assumption
  • 4.4 Two-Round PBD GKE from d-DSMP Assumption
  • References
  • 19 Correction to: International Symposium on Mathematics, Quantum Theory, and Cryptography.
  • Correction to: T. Takagi et al. (eds.), International Symposium on Mathematics, Quantum Theory, and Cryptography, Mathematics for Industry 33, https://doi.org/10.1007/978-981-15-5191-8
  • Index.

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