1st Edition

New Directions of Modern Cryptography

By Zhenfu Cao Copyright 2012
    400 Pages 43 B/W Illustrations
    by CRC Press

    Modern cryptography has evolved dramatically since the 1970s. With the rise of new network architectures and services, the field encompasses much more than traditional communication where each side is of a single user. It also covers emerging communication where at least one side is of multiple users. New Directions of Modern Cryptography presents general principles and application paradigms critical to the future of this field.

    The study of cryptography is motivated by and driven forward by security requirements. All the new directions of modern cryptography, including proxy re-cryptography, attribute-based cryptography, batch cryptography, and noncommutative cryptography have arisen from these requirements. Focusing on these four kinds of cryptography, this volume presents the fundamental definitions, precise assumptions, and rigorous security proofs of cryptographic primitives and related protocols. It also describes how they originated from security requirements and how they are applied.

    The book provides vivid demonstrations of how modern cryptographic techniques can be used to solve security problems. The applications cover wired and wireless communication networks, satellite communication networks, multicast/broadcast and TV networks, and newly emerging networks. It also describes some open problems that challenge the new directions of modern cryptography.

    This volume is an essential resource for cryptographers and practitioners of network security, security researchers and engineers, and those responsible for designing and developing secure network systems.

    Introduction
    Trust Problem
    Trusted Domains Transfer Problem
    Trusted Server Problem
    Ciphertext Access Control Problem
    Efficiency Problems in Multi-Message Cryptology
    The Challenges from Quantum and Biological Computing
    Organization
    Proxy Re-Cryptography
    Introduction
    Proxy Re-Signature
    Properties and Definition
    Related Work
    Security Model: the AH Model
    Multiuse, Private Proxy and Bidirectional Scheme
    Incompleteness of the AH Model
    AH+ Model
    Proxy Re-Encryption
    Properties and Definition
    Related Work
    Security Models
    Single-use, Unidirectional Scheme
    Attribute-Based Cryptography
    Universal Definitions
    Bounded Ciphertext-Policy Encryption Schemes
    Definitions
    Security Models
    Basic BCPABE Scheme BCP1
    Security Proof of BCP1
    Extended BCPABE Scheme BCP2
    Security Proof of BCP2
    Comparisons
    Multi-Authority Encryption Schemes
    Security Models
    Construction
    Security Analysis
    Security Proofs
    Interval Encryption Schemes
    Definitions
    Security Models
    Binary Tree Encryption and Forward Secure Encryption
    A Generic Transformation from BTE to Interval Encryption
    Basic Construction: A Concrete Instantiation Based on HIBE
    Discussion on Efficiency and Security
    Extension Work
    Fuzzy Identity-Based Signature Schemes
    Definitions
    Security Models
    Construction
    Security Proofs
    Applications to Biometric Authentication

    Batch Cryptography
    Aggregate Signature and Batch Verification
    Definitions
    Aggregate Signature
    Identity-Based Aggregate Signature
    Batch Decryption and Batch Key Agreement
    Review of RSA
    Batch RSA
    Batch Key Agreement
    Batch RSA’s Implementation Based on Diophantine Equations
    Implementation Based on Plus-Type Equations
    A Concrete Example Based on Plus-Type Equations
    Implementation Based on Minus-Type Equations
    A Concrete Example Based on Minus-Type Equations
    Solving the Diophantine Equations
    Plus-Type Equations
    Minus-Type Equations
    Noncommutative Cryptography
    Braid-Based Cryptography
    Basic Definitions
    Conjugacy and Related Problems
    Key Exchange, Encryption and Authentication
    Braid-Based Signatures
    One-More Like Assumptions and Provable Security
    New Cryptographic Problems in Braid Groups
    Z-Modular Method
    Z-Modular Method over Noncommutative Rings
    New Problems over Noncommutative Rings
    Diffie-Hellman-Like Key Agreement Protocol
    ElGamal-Like Encryption Scheme
    Instantiation and Illustration (I)
    Z-Modular Method over Noncommutative Groups/Semigroups
    Instantiation and Illustration (II)
    Using Monomials in Z-Modular Method
    Conjugate Left Self-Distributed System (Conj-LD)
    New Assumptions in Conj-LD Systems
    Cryptosystems from Conj-LD Systems
    Security and Efficiency Issues on Fat (b)
    Improved Key Exchange over Thompson’s Group
    Thompson’s Group and Decomposition Problem
    Analysis of SU05 Protocol
    Analysis of RST07 Attack
    Tests and Improvements
    Perspectives
    On Proxy Re-Cryptography
    On Attribute-Based Cryptography
    On Batch Cryptography
    On Noncommutative Cryptography
    Appendices
    Appendix A
    Appendix B
    Appendix C

    Biography

    Zhenfu Cao is with Shanghai Jiao Tong University, P.R. of China