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### 应用密码学手册知识点概述 #### 一、引言《应用密码学手册》是一本关于密码学领域的经典著作，由A. Menezes、P. van Oorschot和S. Vanstone三位专家撰写，并由CRC Press出版社在1996年出版。该书虽然出版时间较早（1997年），但仍被认为是优秀的密码学入门书籍之一。书中内容全面地介绍了密码学的基础理论和技术应用，包括但不限于对称密码、公钥密码、散列函数、消息认证码（MAC）、身份验证以及密钥管理等核心主题。 #### 二、信息安全与密码学基础 - **信息安全的重要性**：密码学是信息安全领域的重要组成部分，它涉及数据的安全存储和传输。随着信息技术的发展，信息安全变得越来越重要。 - **密码学定义**：密码学是研究如何安全地传输信息的技术，主要关注信息的保密性、完整性、可用性和不可否认性。 #### 三、基本术语与概念 - **加密与解密**：加密是将明文转换为密文的过程，而解密则是相反的过程，即从密文恢复成明文。 - **密钥**：加密和解密过程中使用的密钥可以分为两种类型：对称密钥和非对称密钥。 - **对称密钥**：加密和解密使用相同的密钥。 - **非对称密钥**：使用一对密钥，其中一个用于加密，另一个用于解密。 #### 四、对称密钥加密 - **对称密钥算法**：包括DES（数据加密标准）、AES（高级加密标准）等。 - **特点**：速度快、效率高，但在密钥分发方面存在挑战。 #### 五、数字签名 - **定义**：数字签名是一种用于验证发送者身份和确保数据完整性的技术。 - **实现原理**：通常使用非对称加密技术来实现，发送者使用自己的私钥对数据进行签名，接收者则使用发送者的公钥验证签名的有效性。 #### 六、身份验证与识别 - **身份验证**：确认用户的身份是否真实的过程。 - **识别**：确定用户是谁的过程。 - **常用方法**：用户名/密码、生物特征识别等。 #### 七、公钥密码学 - **公钥基础设施（PKI）**：一种基于公钥加密技术的架构，用于管理和验证数字证书。 - **RSA算法**：最著名的公钥加密算法之一，广泛应用于安全通信和数字签名场景。 #### 八、散列函数 - **定义**：散列函数是一种将任意长度的消息转换为固定长度的摘要的方法。 - **应用场景**：数据完整性检查、密码存储等。 - **常见算法**：MD5、SHA-1、SHA-256等。 #### 九、协议与机制 - **安全协议**：如TLS/SSL、SSH等，用于保护网络通信的安全。 - **认证机制**：如OAuth、OpenID等，用于身份验证和授权。 #### 十、密钥建立、管理和认证 - **密钥交换协议**：如Diffie-Hellman协议，用于在不安全的信道上安全地建立共享密钥。 - **密钥管理**：包括密钥的生成、分配、存储、撤销等过程。 #### 十一、伪随机数与序列 - **伪随机数生成器（PRNG）**：用于生成看似随机但实际是由确定性算法产生的数字序列。 - **应用场景**：密码系统中的随机性来源，如密钥生成。 #### 十二、攻击类型与安全模型 - **攻击类型**：包括被动攻击（如窃听）和主动攻击（如篡改数据）。 - **安全模型**：如可证明安全性模型，用于评估密码系统的安全性。 #### 十三、结语与参考资料 - **结语**：本书提供了密码学领域的全面介绍，适合初学者和有一定基础的研究人员参考。 - **参考资料**：书中提供了丰富的参考文献，便于读者进一步深入学习。尽管《应用密码学手册》出版时间较早，但它仍然是一本非常有价值的参考书，尤其对于那些希望深入了解密码学基础知识的人来说。然而，由于技术的快速发展，读者还需要结合最新的研究成果和技术进展来补充学习。

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This is a Chapter from the Handbook of Applied Cryptography, by A. Menezes, P. van

Oorschot, and S. Vanstone, CR C Press, 1996.

For further information, see www.cacr.math.uwaterloo.ca/hac

CRC Press has granted the following speciﬁc permissions for the electronic vers ion of this

book:

Permission is granted to retrieve, print and store a single copy of this chapter for

personal use. This permission does not extend to binding multiple chapters of

the book, photocopying or producing copies for other than personal use of the

person creating the copy, or making electronic copies available for retrieval by

others without prior permissi on in writing from CRC Press.

Except where over-ridden by the speciﬁc permission abo ve, the standard copyright notice

from CRC Press applies to this electronic v ersion:

Neither this book nor any part may be reproduced or transmitted in any form or

by any means, electronic or mechanical, including photocopying, microﬁlming,

and recording, or by any information storage or retrieval system, without prior

permission in writing from the publisher.

The consent of CR C Press does not extend to copying for general distribution,

for promotion, for creating new works, or for resale. Speciﬁc permission must be

obtained in writing from CRC Press for such copying.

1997 by CRC Press, Inc.

Chapter

Overview of Cryptography

Contents in Brief

1.1 Introduction ............................. 1

1.2 Information security and cryptography .............. 2

1.3 Background on functions ...................... 6

1.4 Basic terminology and concepts ................... 11

1.5 Symmetric-key encryption ..................... 15

1.6 Digital signatures .......................... 22

1.7 Authentication and identiﬁcation .................. 24

1.8 Public-key cryptography ...................... 25

1.9 Hash functions ........................... 33

1.10 Protocols and mechanisms ..................... 33

1.11 Key establishment, management, and certiﬁcation ......... 35

1.12 Pseudorandom numbers and sequences .............. 39

1.13 Classes of attacks and security models ............... 41

1.14 Notes and further references .................... 45

1.1 Introduction

Cryptographyhas a long and fascinating history. The most complete non-technical account

of the subject is Kahn’s The Codebreakers. This book traces cryptography from its initial

and limited use by the Egyptians some 4000 years ago, to the twentieth century where it

played a crucial role in the outcome of both world wars. Completed in 1963, Kahn’s book

coversthoseaspects of thehistory which were most signiﬁcant (up to thattime) to thedevel-

opment of the subject. The predominant practitioners of the art were those associated with

the military, the diplomatic service and government in general. Cryptography was used as

a tool to protect national secrets and strategies.

The proliferationof computersand communications systems in the 1960s brought with

it a demand from the private sector for means to protect information in digital form and to

provide security services. Beginning with the work of Feistel at IBM in the early 1970sand

culminating in 1977 with the adoption as a U.S. Federal Information Processing Standard

for encrypting unclassiﬁed information, DES, the Data Encryption Standard, is the most

well-known cryptographic mechanism in history. It remains the standard means for secur-

ing electronic commerce for many ﬁnancial institutions around the world.

Themoststrikingdevelopmentinthe historyofcryptographycamein1976whenDifﬁe

and Hellman published New Directions in Cryptography. This paper introduced the revolu-

tionary concept of public-key cryptographyand also provided a new and ingeniousmethod

2 Ch. 1 Overview of Cryptography

for key exchange, the security of which is based on the intractability of the discrete loga-

rithm problem. Although the authors had no practical realization of a public-key encryp-

tion scheme at the time, the idea was clear and it generated extensive interest and activity

in the cryptographic community. In 1978 Rivest, Shamir, and Adleman discovered the ﬁrst

practical public-key encryption and signature scheme, now referred to as RSA. The RSA

scheme is based on another hard mathematical problem, the intractability of factoring large

integers. This application of a hard mathematical problem to cryptography revitalized ef-

forts to ﬁnd more efﬁcient methods to factor. The 1980s saw major advances in this area

but none which rendered the RSA system insecure. Another class of powerful and practical

public-key schemes was found by ElGamal in 1985. These are also based on the discrete

logarithm problem.

One of the most signiﬁcant contributions provided by public-key cryptography is the

digital signature. In 1991 the ﬁrst international standard for digital signatures (ISO/IEC

9796) was adopted. It is based on the RSA public-key scheme. In 1994 the U.S. Govern-

ment adopted the Digital Signature Standard, a mechanism based on the ElGamal public-

key scheme.

The search for new public-keyschemes, improvementsto existing cryptographicmec-

hanisms, and proofs of security continues at a rapid pace. Various standards and infrastruc-

tures involving cryptographyare being put in place. Security products are being developed

to address the security needs of an information intensive society.

The purpose of this book is to give an up-to-date treatise of the principles, techniques,

and algorithms of interest in cryptographic practice. Emphasis has been placed on those

aspects which are most practical and applied. The reader will be made aware of the basic

issues and pointed to speciﬁc related research in the literature where more indepth discus-

sions can be found. Due to the volume of material which is covered, most results will be

stated without proofs. This also serves the purpose of not obscuring the very applied nature

of the subject. This book is intended for both implementers and researchers. It describes

algorithms, systems, and their interactions.

Chapter 1 is a tutorial on the many and various aspects of cryptography. It does not

attempt to convey all of the details and subtleties inherent to the subject. Its purpose is to

introducethe basicissuesandprinciplesand topointthe reader toappropriatechaptersin the

book for more comprehensive treatments. Speciﬁc techniques are avoided in this chapter.

1.2 Information security and cryptography

The concept of information will be taken to be an understood quantity. To introduce cryp-

tography, an understandingof issues related to information security in general is necessary.

Information security manifests itself in many ways according to the situation and require-

ment. Regardless of who is involved, to one degree or another, all parties to a transaction

must have conﬁdencethat certain objectivesassociated with informationsecurity have been

met. Some of these objectives are listed in Table 1.1.

Over the centuries, an elaborate set of protocols and mechanisms has been created to

deal with information security issues when the information is conveyed by physical doc-

uments. Often the objectives of information security cannot solely be achieved through

mathematical algorithms and protocols alone, but require procedural techniques and abid-

ance of laws to achieve the desired result. For example, privacy of letters is provided by

sealed envelopes delivered by an accepted mail service. The physical security of the en-

velope is, for practical necessity, limited and so laws are enacted which make it a criminal

1997 by CRC Press, Inc. — See accompanying notice at front of chapter.

1.2 Information security and cryptography 3

privacy

or conﬁdentiality

keeping information secret from all but those who are autho-

rized to see it.

data integrity ensuring information has not been altered by unauthorized or

unknown means.

entity authentication

or identiﬁcation

corroboration of the identity of an entity (e.g., a person, a

computer terminal, a credit card, etc.).

message

authentication

corroborating the source of information; also known as data

origin authentication.

signature a means to bind information to an entity.

authorization conveyance, to another entity, of ofﬁcial sanction to do or be

something.

validation a means to provide timeliness of authorization to use or ma-

nipulate information or resources.

access control restricting access to resources to privileged entities.

certiﬁcation endorsement of information by a trusted entity.

timestamping recording the time of creation or existence of information.

witnessing verifying the creationor existence of information by an entity

other than the creator.

receipt acknowledgement that information has been received.

conﬁrmation acknowledgement that services have been provided.

ownership a means to provide an entity with the legal right to use or

transfer a resource to others.

anonymity concealing the identity of an entity involved in some process.

non-repudiation preventing the denial of previous commitments or actions.

revocation retraction of certiﬁcation or authorization.

Table 1.1:

Some information security objectives.

offense to open mail for which one is not authorized. It is sometimes the case that security

is achieved not through the information itself but through the physical document recording

it. For example, papercurrencyrequires special inks and material to prevent counterfeiting.

Conceptually, the way informationis recorded has not changed dramaticallyover time.

Whereas information was typically stored and transmitted on paper, much of it now re-

sides on magnetic media and is transmitted via telecommunications systems, some wire-

less. What has changed dramatically is the ability to copy and alter information. One can

make thousands of identical copies of a piece of information stored electronically and each

is indistinguishable from the original. With information on paper, this is much more difﬁ-

cult. What is needed then for a society where information is mostly stored and transmitted

in electronic form is a means to ensure information security which is independent of the

physical medium recording or conveying it and such that the objectives of information se-

curity rely solely on digital information itself.

One of the fundamental tools used in information security is the signature. It is a build-

ing block for manyother services such as non-repudiation, data origin authentication, iden-

tiﬁcation, and witnessing, to mention a few. Having learned the basics in writing, an indi-

vidual is taught how to produce a handwritten signature for the purpose of identiﬁcation.

At contract age the signature evolves to take on a very integral part of the person’s identity.

This signature is intended to be unique to the individual and serve as a means to identify,

authorize, and validate. With electronic information the concept of a signature needs to be

Handbook of Applied Cryptography by A. Menezes, P. van Oorschot and S. Vanstone.

4 Ch. 1 Overview of Cryptography

redressed; it cannot simply be something unique to the signer and independent of the in-

formation signed. Electronic replication of it is so simple that appending a signature to a

document not signed by the originator of the signature is almost a triviality.

Analogues of the “paper protocols” currently in use are required. Hopefully these new

electronic based protocols are at least as good as those they replace. There is a unique op-

portunity for society to introduce new and more efﬁcient ways of ensuring information se-

curity. Much can be learned from the evolutionof the paper based system, mimicking those

aspects which have served us well and removing the inefﬁciencies.

Achieving information security in an electronic society requires a vast array of techni-

cal and legal skills. There is, however, no guarantee that all of the information security ob-

jectives deemed necessary can be adequatelymet. The technical means is providedthrough

cryptography.

1.1 Deﬁnition Cryptography is the study of mathematical techniques related to aspects of in-

formation security such as conﬁdentiality, data integrity, entity authentication, and data ori-

gin authentication.

Cryptography is not the only means of providing information security, but rather one set of

techniques.

Cryptographic goals

Of all the information security objectives listed in Table 1.1, the following four form a

frameworkuponwhichtheotherswill be derived: (1)privacyor conﬁdentiality (§1.5, §1.8);

(2) data integrity (§1.9); (3) authentication (§1.7); and (4) non-repudiation (§1.6).

1. Conﬁdentiality is a service used to keep the content of information from all but those

authorized to have it. Secrecy is a term synonymouswith conﬁdentiality and privacy.

There are numerous approaches to providing conﬁdentiality, ranging from physical

protection to mathematical algorithms which render data unintelligible.

2. Data integrity is a service which addresses the unauthorized alteration of data. To

assure data integrity, one must have the ability to detect data manipulation by unau-

thorized parties. Data manipulation includes such things as insertion, deletion, and

substitution.

3. Authenticationis a service relatedto identiﬁcation. This function applies to bothenti-

ties andinformationitself. Twopartiesenteringinto acommunicationshouldidentify

each other. Informationdeliveredover a channel shouldbe authenticatedas to origin,

date of origin, data content, time sent, etc. For these reasons this aspect of cryptog-

raphy is usually subdivided into two major classes: entity authentication and data

origin authentication. Data origin authentication implicitly provides data integrity

(for if a message is modiﬁed, the source has changed).

4. Non-repudiationis a servicewhich preventsanentity from denyingpreviouscommit-

ments or actions. When disputes arise due to an entity denying that certain actions

were taken, a means to resolve the situation is necessary. For example, one entity

may authorize the purchase of property by another entity and later deny such autho-

rization was granted. A procedure involving a trusted third party is needed to resolve

the dispute.

A fundamental goal of cryptography is to adequately address these four areas in both

theory and practice. Cryptography is about the prevention and detection of cheating and

other malicious activities.

This book describes a number of basic cryptographictools (primitives) used to provide

information security. Examples of primitives include encryption schemes (§1.5 and §1.8),

1997 by CRC Press, Inc. — See accompanying notice at front of chapter.

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