现代密码学入门：第二版概述

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"Introduction to Modern Cryptography, Second Edition" 是一本由Jonathan Katz和Yehuda Lindell合著的关于现代密码学的专业书籍，该书由Chapman&Hall/CRC出版社在网络安全系列中发行。现代密码学是信息技术领域的一个关键分支，它主要关注数据的安全传输、隐私保护以及数字认证等方面。本书的第二版深入介绍了这一领域的核心概念和技术，旨在为读者提供全面且深入的密码学理论基础和实际应用知识。书中涵盖了以下主要知识点： 1. 密码学基础：讨论了密码学的基本原理，包括对称密钥加密（如DES和AES）和非对称密钥加密（如RSA和椭圆曲线加密）的原理和操作。 2. 密码分析：讲解了如何评估和破解密码系统，包括统计分析、线性密码分析和差分密码分析等技术。 3. 密钥管理：讨论了密钥生成、分配、存储和更新的重要性，以及相关的安全策略。 4. 数字签名：介绍了数字签名的概念，它是确保数据完整性和发送者身份验证的关键技术，如RSA签名和ElGamal签名。 5. 密码哈希函数：讨论了哈希函数的特性，如不可逆性、抗碰撞性和确定性，并介绍了MD5和SHA家族的哈希函数。 6. 密码协议设计：探讨了如何设计安全的通信协议，如SSL/TLS协议和IPSec协议，以及安全电子邮件和文件传输协议。 7. 公钥基础设施（PKI）：详细解释了证书权威机构（CA）的角色，以及X.509证书的使用。 8. 随机数生成：讲述了在密码学中生成随机数的重要性，以及如何实现安全的伪随机数生成器。 9. 安全多方计算：介绍了允许多个参与者在不泄露各自输入的情况下进行计算的技术，如Garbled Circuits和Zero-Knowledge Proofs。 10. 密码学与安全服务：探讨了密码学如何提供机密性、完整性、认证和不可否认性等安全服务。此外，本书还可能包含实际案例研究、习题和解决方案，帮助读者将理论知识应用到实际问题中。对于希望深入理解现代密码学的学者、研究人员和从业人员来说，这是一本不可多得的参考书籍。通过学习这本书，读者可以掌握构建和评估安全系统的必备技能，以应对不断演变的网络安全威胁。

Preface

e goal of our book remains the same as in the ﬁrst editio n: to present the

basic paradigms and principles of modern cryptography to a general audience

with a basic mathematics background. We have designed this book to serve as

a textbook for undergraduate- or g raduate-level co urses in cryptography (in

computer science, electrical engineering, or mathematics departments), as a

general introduction suitable for self-study (espe cially for beginning graduate

students ), and a s a reference fo r students, researchers, and practitioners.

There are numerous other c ryptography textbooks available today, and the

reader may rightly ask whether another book on the subject is needed. We

would not have written this book—nor worked on revising it for the second

edition—if the answer to that question were anything other than an unequiv-

ocal yes. What, in our opinion, distinguishes our book from other available

books is that it provides a rigorous treatment o f modern cryptography in an

accessible manner appropriate for an introduction to the topic.

Our focus is on modern (post-1980s) crypto graphy, which is distinguished

from classical cryptography by its empha sis on deﬁnitions, precise assump-

tions, and rig orous proofs of security. We brieﬂy discuss each o f these in tur n

(these principles are explored in greater detail in Chapter 1):

• The central role of deﬁni tions: A key intellectual contribution of

modern cry ptography has been the recognition that formal deﬁnitions

of secu r ity are an essential ﬁrst step in the design of any cryptographic

primitive or protocol. The reason, in retro spect, is simple: if you don’t

know what it is you are trying to achieve , how can you hope to know

when you have achieved it? As we will see in this book, cryptographic

deﬁnitions of security are quite strong and—at ﬁrst glance—may appear

impossible to achieve. One of the most amazing aspects of cryptography

is that eﬃcient constructions satisfying such strong deﬁnitions can be

proven to exist (under rather mild assumptions).

• The importance of precise assumptions: As will be explained in

Chapters 2 and 3, many cryptographic constructions cannot currently

be proven secure in an unconditional sense. Security often relies, in-

stead, on some widely believed (though unproven) assumption(s). The

modern cryptographic approach dictates that any such assumption must

be clearly stated and unambiguously deﬁned. This not only allows for

objective evaluation of the assumption but, more impo rtantly, enables

rigorous proofs of security as described next.

xvi

• The

possibi lity of proofs of security: The previous two principles

serve as the basis for the idea that cryptographic constr uctions can be

proven secure with respect to clearly stated deﬁnitions of security and

relative to well-deﬁned cryptographic a ssumptions. This concept is the

essence of modern cryptography, and is what has transformed the ﬁeld

from an art to a science.

The importance of this idea cannot be overemphasized. Historic ally,

cryptographic schemes were designed in a largely ad hoc fashion, and

were deemed to be secure if the designers themselves could not ﬁnd

any attacks. In contr ast, modern cryptography advocates the design

of schemes with formal, mathematical proofs of security in well-deﬁned

models. Such schemes are guaranteed to be secure unless the underly-

ing assumption is false (or the security deﬁnition did not appropria tely

model the real-wo rld security concerns). By re lying on long-standing

assumptions (e.g., the assumption that “factoring is hard”), it is thus

possible to o btain s chemes that are extremely unlikely to be broken.

A uniﬁed approach. The above principles of mo de rn cryptography are rel-

evant not only to the “theory of cryptography” co mmunity. The imp ortance

of precise deﬁnitions is, by now, widely understood and appreciated by de-

velopers and security engineers who use cryptographic tools to build secure

systems, and rigorous pr oo fs of security have become one of the requirements

for cryptographic schemes to be standardized.

Changes in the Seco nd Edition

In preparing the second edition, we have made a conscious eﬀort to integrate

a more practical perspective (without sacriﬁcing a rigorous appro ach). This

is re ﬂe cted in a number of changes and additions we have made:

• We have increas ed our coverag e of stream ciphers, introducing them

as a variant of pseudorandom g enerators in Section 3.3.1, discussing

stream-cipher modes of operation in Section 3.6.1, and describing mod-

ern stream-cipher design principles and ex amples in Section 6.1.

• We have e mphasized the importa nc e of authenticated encryption (see

Section 4 .5) and have added a section on secure communication sessions.

• We have moved our treatment of hash functions into its own chapter

(Chapter 5 ), have included some s tandard applications of cryptographic

hash functions (Section 5.6), and have added a section on hash-function

design principles and widely used constructions (Section 6.3). We have

also improved our treatment of birthday attacks (covering small-space

birthday attacks in Section 5.4.2) and have added a discussion of rainbow

tables and time/space tradeoﬀs (Section 5.4.3).

xvii

• We

have included several important attacks on implementations of cryp-

tography that arise in practice, including chosen-plaintext attacks on

chained-CBC encryption (Section 3.6.2), padding-oracle attacks on CBC-

mode encryption (Section 3.7.2 ), and timing attacks on MAC ve riﬁca-

tion (Section 4 .2).

• After much deliberation, we have decided to introduce the random-

oracle model much earlier in the book (Section 5.5). This allows us to

give a proper, integrated treatment of standardized, widely used public-

key encryption and signature schemes in later chapters, instead of rele-

gating them to second-class status in a chapter at the end of the book.

• We have stre ngthened our coverage of elliptic- curve cryptography (Sec-

tion 8.3.4) and have added a disc ussion of its impact on recommended

key lengths (Section 9.3).

• In the chapter on public-key enc ryption, we introduce the KE M/DEM

paradigm as a form of hybrid encryption (see Section 11.3). We also

cover DHIES/EC IES in addition to the RSA PKCS #1 standards.

• In the chapter on digital signatures, we now describe the construction of

signatures fr om identiﬁcation schemes using the Fiat–Shamir trans form,

with the Schnorr signature scheme as a prototypic al example. We have

also improved our coverage of DSA/ECDSA. We include brief discus-

sions of SSL/TLS and signcr yption, both of which serve as culminations

of everything covered up to that point.

• In the “advanced topics” chapter, we have ampliﬁed our treatment of

homomorphic encryption, and have included sections on secret sharing

and threshold encryption.

Beyond the above, we have also edited the entire book to make extensive

corrections as well as smaller adjustments, including more worked examples ,

to impr ove the e xposition. Several additional exercise s have also been added.

Guide t o Using This Book

This section is intended primarily for instructors seeking to adopt this book

for their cours e, though the student picking up this book on his or her own

may also ﬁnd it a useful overview.

Required background. We have structured the book so that the only formal

prerequisite is a course on discrete mathematics. Even here we rely on very

little material: we assume familiarity with basic (discrete) probability and

modular arithmetic. Students reading this book are also expected to have had

some exposure to algorithms, mainly to be comfortable reading pseudocode

and to be familiar w ith big-O notation. Many of these concepts are revie wed

in Appendix A and/or when ﬁrst used in the book.

xviii

twithstanding the above, the book doe s use deﬁnitions, pro ofs, and ab-

stract mathema tical concepts, and therefore requires some mathematical ma-

turity. In particular, the reader is assumed to have had some exposure to

proofs at the college level, whether in an upper-level mathematics course or a

course o n discrete mathematics, algorithms, or computability theory.

Suggestions for course organization. The core material of this book,

which we r ecommend should be covered in any introductory course on cryp-

tography, consists of the following (in all cases, starred sections are excluded;

more on this be low):

• Introduction and Classical Cryptography: Chapters 1 and 2 dis cuss clas-

sical crypto graphy and set the stage for modern cryptography.

• Private-Key ( Symmetric) Cryptography: Chapter 3 on private-key en-

cryption, Chapter 4 on message authentication, and Chapter 5 on hash

functions provide a thorough treatment of these topics.

We also highly recommend covering Section 6.2, which deals with block-

cipher design; in our experience students re ally enjoy this material, and

it makes the abstract ideas they have lear ne d in previous chapters more

concrete. Although we do consider this c ore material, it is not used in

the rest of the book and so c an be safely skipped if desired.

• Public-Key (Asymmetric) Cryptography: Chapter 8 gives a se lf-conta ine d

introductio n to all the number theory needed for the remainder of the

book. The material in Chapter 9 is not used subsequently; however,

we do recommend at le ast c overing Section 9.3 on recommended key

lengths. The public-key revolution is described in Chapter 10. Ideally,

all of Chapters 11 and 12 should be covere d; those presse d for time can

pick and choose appropriately.

We are typically able to cover mos t of the ab ove in a one-semes ter (35-hour)

undergraduate course (omitting some proofs and skipping some topics, as

needed) or, with some changes to add more material on theoretical founda-

tions, in the ﬁrst three-quarters of a one-semester graduate course. Instructors

with more time available can proceed at a more leisurely pace or incorporate

additional topics, as discussed below.

Those wishing to cover additional material, in either a longer course or a

faster-paced gr aduate course, will ﬁnd that the book is structured to allow

ﬂexible incorporation of other topics as time permits (and depending on the

interests of the instructor). Speciﬁcally, the starred (*) sections and chapters

may be covered in any order, or skipped entirely, without aﬀecting the overall

ﬂow of the book. We have taken care to ensure that none of the core ma terial

depe nds on any of the starred material and, for the most part, the starred

sections do not depend on ea ch other. (When they do, this dependence is

explicitly noted.)

xix

suggest the following from among the starred topic s for those wishing

to give their cours e a particular ﬂavor:

• Theory: A more theoretically inclined course could include material

from Section 3.2.2 (semantic security); Chapter 7 (one-way functions

and hard-core predicates, and constructing pseudorandom generators,

functions, and permutations from one-way permutations); Section 8.4

(one-way functions and collision-resistant has h functions from number-

theoretic assumptions); Sec tion 11.5.3 (RSA encryption without random

oracles); and Section 12.6 (signature s without random oracles).

• Mathematics: A c ourse directed at students with a str ong mathemat-

ics background—or being taught by someone who enjoys this aspect

of cryptography—could incor porate Section 4.6 (information-theoretic

MACs in ﬁnite ﬁelds); some of the more advanc ed number theory from

Chapter 8 (e.g., the Chinese remainder theorem and the Miller–Rabin

primality test); and all of Chapter 9.

In either case, a selection of advanced topics from Chapter 13 could also be

included.

Feedback and Errata

Our goa l in writing this book was to make modern cryptography accessible

to a wide audience beyond the “theoretical computer s cience” community. We

hope you will let us know if we have succeeded. The many enthusiastic emails

we have received in res ponse to our ﬁrst edition have made the whole process

of writing this book worthwhile.

We are always happy to receive feedback. We hope there are no errors

or typos in the book; if you do ﬁnd any, however, we would greatly appre-

ciate it if you let us know. (A list of known errata will be maintained at

http://www.cs.umd.edu/~jkatz/imc.html.) You can email your comments

and errata to jkatz@cs.umd.edu and lindell@biu.ac.il; please put “In-

troduction to Modern Cryptography” in the subject line.

Acknowledgments

For the second edition: We are grateful to the many readers o f the ﬁrst edi-

tion who have sent us comments, suggestions, and co rrections that helped to

greatly improve the book. Discussions with Claude Cr´epeau, Bill Gasarch,

Gene Itkis, Leonid Reyzin, Tom Shrimpton, and Salil Vadhan regar ding the

content and overall “philosophy” of the book were especially fruitful. We also

thank Bar Alon, Gilad Asharov, Giuseppe Ateniese, Amir Azodi, O mer Berk-

man, Sergio de Biasi, Aurora B ristor, Richard Chang, Qingfeng Cheng, Kwan

Tae Cho, Kyliah Clarkson, Ran Cohen, Nikolas Coukouma, Dana Dachman-

Soled, Michael Fang, Michael Farcasin, Pooya Fars him, Marc Fischlin, Lance

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