New Directions of Modern Cryptography: 1st Edition (Hardback) book cover

New Directions of Modern Cryptography

1st Edition

By Zhenfu Cao

CRC Press

400 pages | 43 B/W Illus.

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pub: 2012-12-06
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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

About the Author

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

Subject Categories

BISAC Subject Codes/Headings:
COMPUTERS / Information Technology
COMPUTERS / Security / General
COMPUTERS / Security / Cryptography
MATHEMATICS / Combinatorics