
Cryptography and Coding
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Content
- Intro
- Title Page
- Preface
- Organization
- Table of Contents
- Invited Paper
- Can a Program Reverse-Engineer Itself?
- Introduction
- Real-Life Obfuscation
- The Construction
- oximoron: Clear Obscure Code Implementation
- Further Research
- References
- The Source Code
- A repl Session
- Homomorphic Encryption
- Improved Key Generation for Gentry's Fully Homomorphic Encryption Scheme
- Mathematical Background
- Key Generation for Gentry
- The Polynomials g(X) and h(X)
- Determining g0,g1 and h1
- General m
- The Case m = pr
- m Contains Repeated Factors
- Experiment Results
- References
- On Constructing Homomorphic Encryption Schemes from Coding Theory
- Introduction
- Preliminaries
- The Encryption Scheme
- Description
- Alternative Description in Terms of Linear Algebra
- Effort and Limitations
- Possible Applications
- Security Reduction to Coding Theory
- A Concrete Instantiation Based on Reed-Muller Codes
- References
- Coding Theory I
- Generalised Complementary Arrays
- Introduction
- New Contexts for the Complementary Pair Construction
- Polynomial Context
- Pair Recursion
- Coefficients Restricted to {1,-1}
- Type-IV: The Rayleigh Quotient Pair
- Set Recursion
- Size-2t Sets
- Size-2t Sets of 2 2 .2 Bipolar Arrays
- Generalised Boolean -Sets
- Derivation A
- Derivation B
- Type-I Boolean
- Type-II Boolean
- Type-III Boolean
- Comments on the Closed-Form Boolean Expressions
- References
- Binary Kloosterman Sums with Value 4
- Introduction
- Notation and Preliminaries
- Background on Boolean Functions
- Binary Kloosterman Sums and (Hyper, Semi)-Bentness Property
- Elliptic Curves over Finite Fields
- Divisibility of Binary Kloosterman Sums
- Classical Results
- Using Torsion of Elliptic Curves
- Finding Specific Values of Binary Kloosterman Sums
- Generic Strategy
- Zeros of Binary Kloosterman Sum
- Implementation for the Value 4
- Experimental Results for $m$ Even
- Conclusion
- References
- On the Triple-Error-Correcting Cyclic Codes with Zero Set ${1, 2^ i + 1, 2^j + 1}$
- Introduction
- Triple-Error-Correcting Cyclic Code with the Zero Set {1, 2^i + 1, 2^ j + 1}
- Triple-Error-Correcting Cyclic Code with the Zero Set{1, 2^{\ell} + 1, 2p^{p^{\ell}} + 1}
- Finding 3-Error-Correcting Cyclic Codes with the Zero Set {1, 2^i + 1, 2^j + 1} by Computatio n
- The Weight Distributions of the 3-Error-Correcting Cyclic Codes with the Zero Set {1, 2^i + 1, 2^j + 1 }
- Non-Equivalence of the 3-Error-Correcting Cyclic Codes withthe Zero Set {1, 2i + 1, 2j + 1} with the 3-Error-Correcting BCH Code
- An Algorithmic Approach to Compute a Lower Boundon the Minimum Distance of Cyclic Codes
- Schaub Algorithm Description
- An Improved Schaub Algorithm
- Schaub Algorithm and Algebraic Cryptanalysis
- Computational Results
- Conclusions
- References
- Knowledge Proof
- A Secure and Efficient Proof of Integer in an Interval Range
- Introduction
- Background
- Other Techniques Related to Range Proof
- The Range Test Technique by Peng et al.
- The New Range Proof Protocol
- Analysis
- Conclusion and Extension
- References
- Bit Commitment in the Bounded Storage Model: Tight Bound and Simple Optimal Construction
- Introduction
- Bit Commitment and Oblivious Transfer
- Bit Commitment
- Oblivious Transfer (OT)
- The Model and Security Definitions
- The Model
- Security Definitions
- Tight Lower Bound on Storage Space
- Simple Construction
- The Protocol
- Black-Box Construction: Reducing Bit Commitment to Interactive Hashing
- Discussion
- References
- Appendix
- Cryptographic Functions
- Self-correctors for Cryptographic Modules
- Introduction
- Preliminaries
- Characterization of Correctable Functions
- Randomizable Samplers
- Spread-Probability of -Groups
- Fcorrect is Characterized by F,sample
- Revisiting the Diffie-Hellman Correctors
- Self-correcting Cryptographic Modules
- Self-correcting the ElGamal Decryption
- Self-correcting the Pailler Decryption
- Self-correcting the GHV Decryption
- Self-correcting the Hidden Pairings
- Concluding Remarks
- References
- The Symbiosis between Collision and Preimage Resistance
- Introduction
- Preliminaries
- Defining Preimage Resistance
- Implications between Preimage Notions
- Separations
- Salvaging Everywhere Preimage Resistance for Practical Applications
- Preimage Resistance of Hash Function Constructions
- References
- Enhanced Count of Balanced Symmetric Functions and Balanced Alternating Functions
- Introduction
- Properties of Symmetric and Alternating Functions
- Definitions
- The Number of Symmetric Functions
- The Number of Alternating Functions
- The ``Classes' Range
- Existence and Counts Theorems
- Counts
- Non-existence Conditions
- Numerical Results
- Search Principles
- Results on Balanced Symmetric Functions
- Results on Balanced Alternating Functions
- Conclusion
- References
- Appendix: Some General Results
- Tables on Number of Balanced Functions
- Comparison of Actual Number of Balanced Alternating Functions with Known Bound
- Comparison of Actual Number of Balanced Symmetric Functions with Known Bounds
- Public Key Cryptosystem
- Ciphertext-Policy Delegatable Hidden Vector Encryption and Its Application to Searchable Encryption in Multi-user Setting
- Introduction
- Our Contribution
- Our Techniques
- Related Work
- Organization of the Paper
- Preliminaries
- Notations
- Bilinear Map
- Complexity Assumptions
- Ciphertext-Policy Delegatable Hidden Vector Encryption
- General Organization
- Security Definition
- Our Construction
- Security
- Comparison to Other Schemes
- Public-Key Encryption with Conjunctive Keyword Search in Multi-user Setting
- General Organization
- Security Definition
- Our Construction
- Security
- Comparison to the Other Scheme
- Conclusion
- References
- Proof Outline of Theorem 1
- Constructing Secure Hybrid Encryption from Key Encapsulation Mechanism with Authenticity
- Introduction
- Preliminaries
- Public Key Encryption
- Key Encapsulation Mechanism
- Key Encapsulation Mechanism with Tags (tag-KEM)
- Data Encapsulation Mechanism
- A New Framework of Hybrid Encryption: AKEM/DEM
- The Model of AKEM
- Security Definitions of AKEM
- Composition of AKEM and DEM
- Relation between AKEM and tag-KEM
- Fujisaki-Okamoto Conversion and REACT in AKEM
- Fujisaki-Okamoto Conversion
- REACT
- Construction of AKEM
- Based on PKE and CR
- Based on Weak KEM and MAC
- Based on ID-Based PKE and One-Time Signatures
- Concluding Remarks
- References
- Appendix
- Coding Theory II
- A Note on the Dual Codes of Module Skew Codes
- Introduction
- Some Remarks about Module -Codes
- Duals of Module -Codes over IFq
- Parity Check Matrix of Module (,)-Codes over a Field
- Duals of Module -Codes Defined over Rings
- Self-dual Euclidean Module Skew Codes of Length 2s over IF4
- References
- Ensuring Message Embedding in Wet Paper Steganography
- Introduction
- Steganography and Coding Theory
- Steganographic Schemes
- From Coding Theory to Steganography
- Randomized (wet paper) Syndrome Coding
- Case of Perfect Linear Codes
- General Statement
- Golay Codes
- Hamming Codes
- Using ZZW Construction to Embed Dynamic Parameters
- The Scheme
- Analysis
- Conclusion
- References
- On the Stability of m-Sequences
- Introduction
- Preliminaries
- k-Error Complexity and Period for Various Classes of m-Sequence
- Prime Period
- Reducing the Period of an m-Sequence by an Arbitrary Factor
- Reducing the Period by a Mersenne Number
- Reducing the Period by a Prime p with ordp(2)=p-1
- The Minimum Number of Errors Needed for Reducing the Period of an m-Sequence
- Application to Grain and Other Stream Ciphers
- Conclusions
- References
- Pairing and ECC Implementation
- Parallelizing the Weil and Tate Pairings
- Introduction
- Background on Pairings
- Parallelizing the Optimal Ate Pairing
- Optimal Weil Pairings
- Hess's Weil Pairing Construction
- The Weil Pairing
- The Weil Pairing
- Parallel Implementation of the BN Pairings
- Parallel Implementation of the Eta Pairing
- Concluding Remarks
- References
- Relationship between G_1, G_2, 1 and 2
- On the Efficient Implementation of Pairing-Based Protocol s
- Introduction
- Pairings
- Optimizations
- Pairing Friendly Curves
- A Simple Example: Boneh-Boyen IBE
- Attribute Based Cryptography
- Inner-Product Predicate Encryption
- Discussion
- Conclusion
- References
- Efficient Pairing Computation on Ordinary Elliptic Curves of Embedding Degree 1 and 2
- Introduction
- Preliminaries
- Pairings on Elliptic Curves over Finite Fields
- Pairings on Elliptic Curves over Finite Rings
- Pairing Lattices
- Pairing Lattices over Composite-Order Groups
- Omega Pairing Lattices
- Computation of Composite-Order Pairings on Ordinary Curves over Finite Fields
- Embedding Degree 1
- Embedding Degree 2
- Computation of Prime-Order Pairings on Ordinary Curves over RSA Rings
- Curves Generation
- More Pairings over RSA Rings
- Choice of Bilinear Pairing
- Pairing Computation
- Conclusion and Further Work
- References
- Proof of the Equivalent Form of fs,h,R
- Improved Precomputation Scheme for Scalar Multiplication on Elliptic Curves
- Introduction
- Montgomery Trick
- Previous Work
- Contributions
- Elliptic Curve Cryptography
- Elliptic Curves over Finite Fields
- Scalar Multiplication
- Preliminary Observations
- Precomputation Scheme in Affine Coordinates
- Algorithm
- Performance Comparison
- Conclusion
- References
- Security Analysis
- Breaking an Identity-Based Encryption Scheme Based on DHIES
- Introduction
- The IBE Scheme
- An Attack on the Underlying Hard Problem
- Where the Proof Fails
- Gröbner Basics
- Refining the Basic Attack
- Conclusions
- References
- Analysis of the SSH Key Exchange Protocol
- Introduction
- Related Work
- Basic Security Model
- Shared Secret Exchange
- Application Keys
- Conclusions
- References
- Cryptanalysis of the Light-Weight Cipher A2U2
- Introduction
- Description of the Cipher
- A2U2 Description
- Useful Properties
- A Chosen Plaintext Attack
- Disproving the Chai/Fan/Gong Attack
- A Leak in the Output Function
- The Attack
- Guess-and-Determine Attack
- Targeting the Low Number of Initialisation Rounds
- Recovering the 5-bit Counter Key
- Recovering the Master Key Bits
- Exploiting the Noisy Keystream
- Final Remarks
- Necessary Changes and Possible Improvements
- Conclusion
- References
- Symmetric Key Cryptosystem
- Building Blockcipher from Tweakable Blockcipher: Extending FSE 2009 Proposal
- Introduction
- Preliminaries
- Notation
- Cryptographic Functions
- Building Blocks
- Blockcipher Constructions beyond Birthday Bound
- Overview
- Small-Block Cipher
- Large-Block Cipher, Method 1
- Large-Block Cipher, Method 2
- Discussions
- Blockcipher-Based Instantiations
- Security Proofs
- Overview
- Additional Notation for Proof
- Maurer's Methodology
- Proof of Theorem 1 (Small-Block Cipher)
- Proof of Theorem 2 (Large-Block Cipher Method 1)
- Proof of Theorem 3 (Large-Block Cipher Method 2)
- Conclusion
- References
- Lemmas from Maurer's Methodology
- Proof of Lemma 3
- Security of Hash-then-CBC Key Wrapping Revisited
- Introduction
- Preliminaries
- Notation
- Blockciphers
- CBC Mode
- Hash Functions
- Hash-then-CBC Key Wrapping
- Definition of Hash-then-CBC Key Wrapping
- Security Definition: DAE-Security
- Securityof $ U_{CC}$-then-CBC Scheme
- Theorem Statement
- Proof Overview
- Construction of a $ U_{CC}$-Hash Function
- Discussions
- Analysis of Hash-then-CBC Schemes
- Linear-then-CBC Scheme
- SPR-then-CBC Scheme
- Universal-then-CBC Scheme
- Conclusion
- References
- A Security Definition: AKW-Security
- Cryptographic Protocols
- Block-Wise P-Signatures and Non-interactive Anonymous Credentials with Efficient Attributes
- Introduction
- Background and Definitions
- Bilinear Maps and Complexity Assumptions
- Commitments to Vectors
- Block-Wise F-Unforgeable Signatures and P-Signatures
- Groth-Sahai Proofs
- A Construction for Inner Product Relations
- Non-interactive Anonymous Credentials with Efficient Attributes
- References
- On Forward Secrecy in One-Round Key Exchange
- Introduction
- Strong Forward Secrecy in One Round
- Defining Forward Secrecy
- Strong Forward Secrecy and Ephemeral Key Reveal
- Reconciling Strong and Weak Forward Secrecy
- Current protocols with sFS
- Remaining Secure with a More Powerful Adversary
- A Compiler for Protocols with Graceful Security Degradation
- Discussion
- References
- Designated Confirmer Signatures with Unified Verification
- Introduction
- Preliminaries
- Bilinear Pairings and the BLS Signature
- Complexity Assumptions
- Concurrent Zero Knowledge from Honest-Verifier Zero-Knowledge
- Security Model
- The Proposed Scheme
- SecurityProofs
- Conclusion and Future Work
- References
- Author Index
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