New Directions of Modern Cryptography

New Directions of Modern Cryptography

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  • Introduces the latest modern cryptographies: proxy re-cryptography, attribute-based cryptography, batch cryptography, and noncommutative cryptography
  • Emphasizes the core idea that cryptography is born and developed for the application requirements
  • Presents the applications of the latest modern cryptographies to show its practical value in everyday life
  • Explores challenges in the future of cryptography


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.

Table of Contents

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
Proxy Re-Cryptography
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
Security Models
Basic BCPABE Scheme BCP1
Security Proof of BCP1
Extended BCPABE Scheme BCP2
Security Proof of BCP2
Multi-Authority Encryption Schemes
Security Models
Security Analysis
Security Proofs
Interval Encryption Schemes
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
Security Models
Security Proofs
Applications to Biometric Authentication

Batch Cryptography
Aggregate Signature and Batch Verification
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
On Proxy Re-Cryptography
On Attribute-Based Cryptography
On Batch Cryptography
On Noncommutative Cryptography
Appendix A
Appendix B
Appendix C

Author Bio(s)

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

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