chapter 2_1cryptography_traditional
网络信息安全内容整理
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对称密码体制和非对称密码体制
对称密码体制(Symmetric System, One-key System, Secret-key System)
明文和密文之间统计关系尽量复杂；
confusion –混淆，使密文和加密密钥之间的关系尽量复杂。
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(A1-A5), 单位元是0，a的逆是 -a. (M1), 乘法封闭性, 如果a和b属于R, 则ab也属于R (M2), 乘法结合律,对于R中任意a, b, c有a(bc)=(ab)c. (M3), 乘法分配律, a(b+c)=ab+ac or (a+b)c=ac+bc (M4), 乘法交换律, ab=ba，交换环 (M5), 乘法单位元, R中存在元素1使得所有a有 a1=1a. (M6), 无零因子, 如果R中有a, b且ab=0, 则 a=0 or
6.1.1 双重DES
多次加密的最简单形式是进行两次加密，每次使用 不同的密钥
C = EK2(EK1(P)) P = DK1(DK2(C)) 这种方法的密钥长度是56x2=112位
虽然双重DES对应的映射与单DES对应的映射不同， 但是有中途相遇攻击 “meet-in-the-middle”
现代密码学中英文翻译(部分)
Table of ContentsModern Cryptography: Theory and PracticeBy Wenbo Mao Hewlett-Packard CompanyPublisher: Prentice Hall PTRPub Date: July 25, 2003ISBN: 0-13-066943-1Pages: 648Many cryptographic schemes and protocols, especially those based onpublic-keycryptography,have basic or so-called "textbook crypto" versions, as these versionsare usually the subjects formany textbooks on cryptography. This book takes adifferent approach to introducingcryptography: it pays much more attention tofit-for-application aspects of cryptography. Itexplains why "textbook crypto" isonly good in an ideal world where data are random and badguys behave nicely.It reveals the general unfitness of "textbook crypto" for the real world bydemonstratingnumerous attacks on such schemes, protocols and systems under variousrealworldapplication scenarios. This book chooses to introduce a set of practicalcryptographic schemes, protocols and systems, many of them standards or de factoones, studies them closely,explains their working principles, discusses their practicalusages, and examines their strong(i.e., fit-for-application) security properties, oftenwith security evidence formally established.The book also includes self-containedtheoretical background material that is the foundation formodern cryptography.Table of ContentsModern Cryptography: Theory and PracticeBy Wenbo Mao Hewlett-Packard CompanyPublisher: Prentice Hall PTRPub Date: July 25, 2003ISBN: 0-13-066943-1Pages: 648CopyrightHewlett-Packard® Professional BooksA Short Description of the BookPrefaceScopeAcknowledgementsList of FiguresList of Algorithms, Protocols and AttacksPart I: IntroductionChapter 1. Beginning with a Simple Communication GameSection 1.1. A Communication GameSection 1.2. Criteria for Desirable Cryptographic Systems and Protocols Section 1.3. Chapter SummaryExercisesChapter 2. Wrestling Between Safeguard and AttackSection 2.1. IntroductionSection 2.2. EncryptionSection 2.3. Vulnerable Environment (the Dolev-Yao Threat Model)Section 2.4. Authentication ServersSection 2.5. Security Properties for Authenticated Key Establishment Section 2.6. Protocols for Authenticated Key Establishment Using Encryption Section 2.7. Chapter SummaryExercisesPart II: Mathematical Foundations: Standard NotationChapter 3. Probability and Information TheorySection 3.1. IntroductionSection 3.2. Basic Concept of ProbabilitySection 3.3. PropertiesSection 3.4. Basic CalculationSection 3.5. Random Variables and their Probability DistributionsSection 3.6. Birthday ParadoxSection 3.7. Information TheorySection 3.8. Redundancy in Natural LanguagesSection 3.9. Chapter SummaryExercisesChapter 4. Computational ComplexitySection 4.1. IntroductionSection 4.2. Turing MachinesSection 4.3. Deterministic Polynomial TimeSection 4.4. Probabilistic Polynomial TimeSection 4.5. Non-deterministic Polynomial TimeSection 4.6. Non-Polynomial BoundsSection 4.7. Polynomial-time IndistinguishabilitySection 4.8. Theory of Computational Complexity and Modern Cryptography Section 4.9. Chapter SummaryExercisesChapter 5. Algebraic FoundationsSection 5.1. IntroductionSection 5.2. GroupsSection 5.3. Rings and FieldsSection 5.4. The Structure of Finite FieldsSection 5.5. Group Constructed Using Points on an Elliptic CurveSection 5.6. Chapter SummaryExercisesChapter 6. Number TheorySection 6.1. IntroductionSection 6.2. Congruences and Residue ClassesSection 6.3. Euler's Phi FunctionSection 6.4. The Theorems of Fermat, Euler and LagrangeSection 6.5. Quadratic ResiduesSection 6.6. Square Roots Modulo IntegerSection 6.7. Blum IntegersSection 6.8. Chapter SummaryExercisesPart III: Basic Cryptographic TechniquesChapter 7. Encryption — Symmetric TechniquesSection 7.1. IntroductionSection 7.2. DefinitionSection 7.3. Substitution CiphersSection 7.4. Transposition CiphersSection 7.5. Classical Ciphers: Usefulness and SecuritySection 7.6. The Data Encryption Standard (DES)Section 7.7. The Advanced Encryption Standard (AES)Section 7.8. Confidentiality Modes of OperationSection 7.9. Key Channel Establishment for Symmetric Cryptosystems Section 7.10. Chapter SummaryExercisesChapter 8. Encryption — Asymmetric TechniquesSection 8.1. IntroductionSection 8.2. Insecurity of "Textbook Encryption Algorithms"Section 8.3. The Diffie-Hellman Key Exchange ProtocolSection 8.4. The Diffie-Hellman Problem and the Discrete Logarithm Problem Section 8.5. The RSA Cryptosystem (Textbook Version)Section 8.6. Cryptanalysis Against Public-key CryptosystemsSection 8.7. The RSA ProblemSection 8.8. The Integer Factorization ProblemSection 8.9. Insecurity of the Textbook RSA EncryptionSection 8.10. The Rabin Cryptosystem (Textbook Version)Section 8.11. Insecurity of the Textbook Rabin EncryptionSection 8.12. The ElGamal Cryptosystem (Textbook Version)Section 8.13. Insecurity of the Textbook ElGamal EncryptionSection 8.14. Need for Stronger Security Notions for Public-key CryptosystemsSection 8.15. Combination of Asymmetric and Symmetric CryptographySection 8.16. Key Channel Establishment for Public-key CryptosystemsSection 8.17. Chapter SummaryExercisesChapter 9. In An Ideal World: Bit Security of The Basic Public-Key Cryptographic Functions Section 9.1. IntroductionSection 9.2. The RSA BitSection 9.3. The Rabin BitSection 9.4. The ElGamal BitSection 9.5. The Discrete Logarithm BitSection 9.6. Chapter SummaryExercisesChapter 10. Data Integrity TechniquesSection 10.1. IntroductionSection 10.2. DefinitionSection 10.3. Symmetric TechniquesSection 10.4. Asymmetric Techniques I: Digital SignaturesSection 10.5. Asymmetric Techniques II: Data Integrity Without Source Identification Section 10.6. Chapter SummaryExercisesPart IV: AuthenticationChapter 11. Authentication Protocols — PrinciplesSection 11.1. IntroductionSection 11.2. Authentication and Refined NotionsSection 11.3. ConventionSection 11.4. Basic Authentication TechniquesSection 11.5. Password-based AuthenticationSection 11.6. Authenticated Key Exchange Based on Asymmetric CryptographySection 11.7. Typical Attacks on Authentication ProtocolsSection 11.8. A Brief Literature NoteSection 11.9. Chapter SummaryExercisesChapter 12. Authentication Protocols — The Real WorldSection 12.1. IntroductionSection 12.2. Authentication Protocols for Internet SecuritySection 12.3. The Secure Shell (SSH) Remote Login ProtocolSection 12.4. The Kerberos Protocol and its Realization in Windows 2000Section 12.5. SSL and TLSSection 12.6. Chapter SummaryExercisesChapter 13. Authentication Framework for Public-Key CryptographySection 13.1. IntroductionSection 13.2. Directory-Based Authentication FrameworkSection 13.3. Non-Directory Based Public-key Authentication FrameworkSection 13.4. Chapter SummaryExercisesPart V: Formal Approaches to Security EstablishmentChapter 14. Formal and Strong Security Definitions for Public-Key Cryptosystems Section 14.1. IntroductionSection 14.2. A Formal Treatment for SecuritySection 14.3. Semantic Security — the Debut of Provable SecuritySection 14.4. Inadequacy of Semantic SecuritySection 14.5. Beyond Semantic SecuritySection 14.6. Chapter SummaryExercisesChapter 15. Provably Secure and Efficient Public-Key CryptosystemsSection 15.1. IntroductionSection 15.2. The Optimal Asymmetric Encryption PaddingSection 15.3. The Cramer-Shoup Public-key CryptosystemSection 15.4. An Overview of Provably Secure Hybrid CryptosystemsSection 15.5. Literature Notes on Practical and Provably Secure Public-key Cryptosystems Section 15.6. Chapter SummarySection 15.7. ExercisesChapter 16. Strong and Provable Security for Digital SignaturesSection 16.1. IntroductionSection 16.2. Strong Security Notion for Digital SignaturesSection 16.3. Strong and Provable Security for ElGamal-family SignaturesSection 16.4. Fit-for-application Ways for Signing in RSA and RabinSection 16.5. SigncryptionSection 16.6. Chapter SummarySection 16.7. ExercisesChapter 17. Formal Methods for Authentication Protocols AnalysisSection 17.1. IntroductionSection 17.2. Toward Formal Specification of Authentication ProtocolsSection 17.3. A Computational View of Correct Protocols — the Bellare-Rogaway Model Section 17.4. A Symbolic Manipulation View of Correct ProtocolsSection 17.5. Formal Analysis Techniques: State System ExplorationSection 17.6. Reconciling Two Views of Formal Techniques for SecuritySection 17.7. Chapter SummaryExercisesPart VI: Cryptographic ProtocolsChapter 18. Zero-Knowledge ProtocolsSection 18.1. IntroductionSection 18.2. Basic DefinitionsSection 18.3. Zero-knowledge PropertiesSection 18.4. Proof or Argument?Section 18.5. Protocols with Two-sided-errorSection 18.6. Round EfficiencySection 18.7. Non-interactive Zero-knowledgeSection 18.8. Chapter SummaryExercisesChapter 19. Returning to "Coin Flipping Over Telephone"Section 19.1. Blum's "Coin-Flipping-By-Telephone" ProtocolSection 19.2. Security AnalysisSection 19.3. EfficiencySection 19.4. Chapter SummaryChapter 20. AfterremarkBibliographyCopyrightLibrary of Congress Cataloging-in-Publication DataA CIP catalog record for this book can be obtained from the Library of Congress. Editorial/production supervision: Mary SudulCover design director: Jerry VottaCover design: Talar BoorujyManufacturing manager: Maura ZaldivarAcquisitions editor: Jill HarryMarketing manager: Dan DePasqualePublisher, Hewlett-Packard Books: Walter BruceA Short Description of the BookMany cryptographic schemes and protocols, especially those based on public-key cryptography,have basic or so-called "textbook crypto" versions, as these versions are usually the subjects formany textbooks on cryptography. This book takes a different approach to introducingcryptography: it pays much more attention to fit-for-application aspects of cryptography. Itexplains why "textbook crypto" is only good in an ideal world where data are random and badguys behave nicely. It reveals the general unfitness of "textbook crypto" for the real world bydemonstrating numerous attacks on such schemes, protocols and systems under various realworldapplication scenarios. This book chooses to introduce a set of practical cryptographicschemes, protocols and systems, many of them standards or de facto ones, studies them closely,explains their working principles, discusses their practical usages, and examines their strong(i.e., fit-for-application) security properties, often with security evidence formally established.The book also includes self-contained theoretical background material that is the foundation formodern cryptography.PrefaceOur society has entered an era where commerce activities, business transactions andgovernment services have been, and more and more of them will be, conducted and offered overopen computer and communications networks such as the Internet, in particular, viaWorldWideWeb-based tools. Doing things online has a great advantage of an always-onavailability to people in any corner of the world. Here are a few examples of things that havebeen, can or will be done online:Banking, bill payment, home shopping, stock trading, auctions, taxation, gambling, micropayment(e.g., pay-per-downloading), electronic identity, online access to medical records, virtual private networking, secure data archival and retrieval, certified delivery of documents, fair exchange of sensitive documents, fair signing of contracts,time-stamping,notarization, voting, advertising, licensing, ticket booking, interactive games, digitallibraries, digital rights management, pirate tracing, …And more can be imagined.Many cryptographic schemes and protocols, especially those based onpublic-keycryptography,have basic or so-called "textbook crypto" versions, as these versionsare usually the subjects formany textbooks on cryptography. This book takes adifferent approach to introducingcryptography: it pays much more attention tofit-for-application aspects of cryptography. Itexplains why "textbook crypto" isonly good in an ideal world where data are random and badguys behave nicely.It reveals the general unfitness of "textbook crypto" for the real world bydemonstratingnumerous attacks on such schemes, protocols and systems under variousrealworldapplication scenarios. This book chooses to introduce a set of practicalcryptographic schemes, protocols and systems, many of them standards or de factoones, studies them closely,explains their working principles, discusses their practicalusages, and examines their strong(i.e., fit-for-application) security properties, oftenwith security evidence formally established.The book also includes self-containedtheoretical background material that is the foundation formodern cryptography.PrefaceOur society has entered an era where commerce activities, business transactions andgovernment services have been, and more and more of them will be, conducted and offered overopen computer and communications networks such as the Internet, in particular, viaWorldWideWeb-based tools. Doing things online has a great advantage of an always-onavailability to people in any corner of the world. Here are a few examples of things that havebeen, can or will be done online:Banking, bill payment, home shopping, stock trading, auctions, taxation, gambling, micropayment(e.g., pay-per-downloading), electronic identity, online access to medical records, virtual private networking, secure data archival and retrieval, certified delivery of documents, fair exchange of sensitive documents, fair signing of contracts,time-stamping,notarization, voting, advertising, licensing, ticket booking, interactive games, digitallibraries, digital rights management, pirate tracing, …And more can be imagined.Fascinating commerce activities, transactions and services like these are only possible ifcommunications over open networks can be conducted in a secure manner. An effective solutionto securing communications over open networks is to apply cryptography. Encryption, digitalsignatures, password-based user authentication, are some of the most basic cryptographictechniques for securing communications. However, as we shall witness many times in this book,there are surprising subtleties and serious security consequences in the applicationsof even themost basic cryptographic techniques. Moreover, for many "fancier" applications, such as manylisted in the preceding paragraph, the basic cryptographic techniques are no longer adequate.With an increasingly large demand for safeguarding communications over open networks formore and more sophisticated forms of electronic commerce, business and services[a], anincreasingly large number of information security professionals will be needed for designing,developing, analyzing and maintaining information security systems and cryptographicprotocols. These professionals may range from IT systems administrators, information securityengineers and software/hardware systems developers whose products have securityrequirements, to cryptographers.[a] Gartner Group forecasts that total electronic business revenues for business to business (B2B) andbusiness to consumer (B2C) in the European Union will reach a projected US $2.6 trillion in 2004 (withprobability 0.7) which is a 28-fold increase from the level of 2000 [5]. Also, eMarketer [104] (page 41) reportsthat the cost to financial institutions (in USA) due to electronic identity theft was US $1.4 billion in 2002, andforecasts to grow by a compound annual growth rate of 29%.In the past few years, the author, a technical consultant on information security and cryptographic systems at Hewlett-Packard Laboratories in Bristol, has witnessed the phenomenon of a progressively increased demand for information security professionalsunmatched by an evident shortage of them. As a result, many engineers, who are oriented toapplication problems and may have little proper training in cryptography and informationsecurity have become "roll-up-sleeves" designers and developers for information securitysystems or cryptographic protocols. This is in spite of the fact that designing cryptographicsystems and protocols is a difficult job even for an expert cryptographer.The author's job has granted him privileged opportunities to review many information securitysystems and cryptographic protocols, some of them proposed and designed by "roll-up-sleeves"engineers and are for uses in serious applications. In several occasions, the author observed socalled"textbook crypto" features in such systems, which are the result of applications of cryptographic algorithms and schemes in ways they are usually introduced in many cryptographic textbooks. Direct encryption of a password (a secret number of a smallmagnitude) under a basic public-key encryption algorithm (e.g., "RSA") is a typical example oftextbook crypto. The appearances of textbook crypto in serious applications with a "nonnegligibleprobability" have caused a concern for the author to realize that the general danger oftextbook crypto is not widely known to many people who design and develop informationsecurity systems for serious real-world applications.Motivated by an increasing demand for information security professionals and a belief that theirknowledge in cryptography should not be limited to textbook crypto, the author has written thisbook as a textbook on non-textbook cryptography. This book endeavors to: Introduce a wide range of cryptographic algorithms, schemes and protocols with a particular emphasis on their non-textbook versions.Reveal general insecurity of textbook crypto by demonstrating a large number of attacks onand summarizing typical attacking techniques for such systems.Provide principles and guidelines for the design, analysis and implementation of cryptographic systems and protocols with a focus on standards.Study formalism techniques and methodologies for a rigorous establishment of strong andfit-for-application security notions for cryptographic systems and protocols. Include self-contained and elaborated material as theoretical foundations of modern cryptography for readers who desire a systematic understanding of the subject.ScopeModern cryptography is a vast area of study as a result of fast advances made in the past thirtyyears. This book focuses on one aspect: introducing fit-for-application cryptographic schemesand protocols with their strong security properties evidently established.The book is organized into the following six parts:Part I This part contains two chapters (1—2) and serves an elementary-level introductionfor the book and the areas of cryptography and information security. Chapter 1 begins witha demonstration on the effectiveness of cryptography in solving a subtle communicationproblem. A simple cryptographic protocol (first protocol of the book) for achieving "fair cointossing over telephone" will be presented and discussed. This chapter then carries on toconduct a cultural and "trade" introduction to the areas of study. Chapter 2 uses a series ofsimple authentication protocols to manifest an unfortunate fact in the areas: pitfalls areeverywhere.As an elementary-level introduction, this part is intended for newcomers to the areas.Part II This part contains four chapters (3—6) as a set of mathematical background knowledge, facts and basis to serve as a self-contained mathematical reference guide forthe book. Readers who only intend to "knowhow," i.e., know how to use thefit-forapplicationcrypto schemes and protocols, may skip this part yet still be able to follow most contents of the rest of the book. Readers who also want to "know-why," i.e., know whythese schemes and protocols have strong security properties, may find that this selfcontainedmathematical part is a sufficient reference material. When we present working principles of cryptographic schemes and protocols, reveal insecurity for some of them andreason about security for the rest, it will always be possible for us to refer to a precise pointin this part of the book for supporting mathematical foundations.This part can also be used to conduct a systematic background study of the theoreticalfoundations for modern cryptography.Part III This part contains four chapters (7—10) introducing the most basic cryptographicalgorithms and techniques for providing privacy and data integrity protections. Chapter 7 isfor symmetric encryption schemes, Chapter 8, asymmetric techniques. Chapter 9 considersan important security quality possessed by the basic and popular asymmetric cryptographicfunctions when they are used in an ideal world in which data are random. Finally, Chapter10 covers data integrity techniques.Since the schemes and techniques introduced here are the most basic ones, manyof themare in fact in the textbook crypto category and are consequently insecure. While the schemes are introduced, abundant attacks on many schemes will be demonstrated withwarning remarks explicitly stated. For practitioners who do not plan to proceed with an indepthstudy of fit-for-application crypto and their strong security notions, this textbook crypto part will still provide these readers with explicit early warning signals on the generalinsecurity of textbook crypto.Part IV This part contains three chapters (11—13) introducing an important notion inapplied cryptography and information security: authentication. These chapters provide awide coverage of the topic. Chapter 11 includes technical background, principles, a series ofbasic protocols and standards, common attacking tricks and prevention measures. Chapter12 is a case study for four well-known authentication protocol systems for real world applications. Chapter 13 introduces techniques which are particularly suitable for openfor-application) security properties, oftenwith security evidence formally established.The book also includes self-containedtheoretical background material that is the foundation formodern cryptography.systems which cover up-to-date and novel techniques.Practitioners, such as information security systems administration staff in an enterprise andsoftware/hardware developers whose products have security consequences may find thispart helpful.Part V This part contains four chapters (14—17) which provide formalism and rigoroustreatments for strong (i.e., fit-for-application) security notions for public-key cryptographictechniques (encryption, signature and signcryption) and formal methodologies for theanalysis of authentication protocols. Chapter 14 introduces formal definitions of strongsecurity notions. The next two chapters are fit-for-application counterparts to textbookcrypto schemes introduced in Part III, with strong security properties formally established(i.e., evidently reasoned). Finally, Chapter 17 introduces formal analysismethodologiesand techniques for the analysis of authentication protocols, which we have not been able todeal with in Part IV.Part VI This is the final part of the book. It contains two technical chapters (18—19) and ashort final remark (Chapter 20). The main technical content of this part, Chapter 18, introduces a class of cryptographic protocols called zero-knowledge protocols. Theseprotocols provide an important security service which is needed in various "fancy" electronic commerce and business applications: verification of a claimed property of secretdata (e.g., in conforming with a business requirement) while preserving a strict privacyquality for the claimant. Zero-knowledge protocols to be introduced in this part exemplifythe diversity of special security needs in various real world applications, which are beyondconfidentiality, integrity, authentication and non-repudiation. In the final technical chapterof the book (Chapter 19) we will complete our job which has been left over from the firstprotocol of the book: to realize "fair coin tossing over telephone." That final realization willachieve a protocol which has evidently-established strong security properties yet with anefficiency suitable for practical applications.Needless to say, a description for each fit-for-application crypto scheme or protocol has to beginwith a reason why the textbook crypto counterpart is unfit for application. Invariably, thesereasons are demonstrated by attacks on these schemes or protocols, which, by the nature ofattacks, often contain a certain degree of subtleties. In addition, a description of a fit-forapplicationscheme or protocol must also end at an analysis that the strong (i.e.,fit-forapplication)security properties do hold as claimed. Consequently, some parts of this book inevitably contain mathematical and logical reasonings, deductions and transformations in orderto manifest attacks and fixes.While admittedly fit-for-application cryptography is not a topic for quick mastery or that can bemastered via light reading, this book, nonetheless, is not one for in-depth researchtopics whichwill only be of interest to specialist cryptographers. The things reported and explained in it arewell-known and quite elementary to cryptographers. The author believes that they can also becomprehended by non-specialists if the introduction to the subject is provided with plenty ofexplanations and examples and is supported by self-contained mathematical background andreference material.The book is aimed at the following readers.Students who have completed, or are near to completion of, first degree courses in computer, information science or applied mathematics, and plan to pursue a career ininformation security. For them, this book may serve as an advanced course in appliedcryptography.Security engineers in high-tech companies who are responsible for the design and development of information security systems. If we say that the consequence of textbookcrypto appearing in an academic research proposal may not be too harmful since the worstcase of the consequence would be an embarrassment, then the use of textbook crypto in aninformation security product may lead to a serious loss. Therefore, knowing the unfitness oftextbook crypto for real world applications is necessary for these readers. Moreover, thesereaders should have a good understanding of the security principles behind thefit-forapplicationschemes and protocols and so they can apply the schemes and the principles correctly. The self-contained mathematical foundations material in Part II makes the book asuitable self-teaching text for these readers.Information security systems administration staff in an enterprise andsoftware/hardwaresystems developers whose products have security consequences. For these readers, Part Iis a simple and essential course for cultural and "trade" training; Parts III and IV form asuitable cut-down set of knowledge in cryptography and information security. These threeparts contain many basic crypto schemes and protocols accompanied with plenty of attacking tricks and prevention measures which should be known to and can be grasped by。
cryptography
cryptography Cryptography: An Introduction to Secure CommunicationIntroductionIn today's digital age, the security of sensitive information has become a major concern for individuals, organizations, and governments alike. The practice of cryptography plays a crucial role in safeguarding this information from unauthorized access, manipulation, and theft. In this document, we will explore the fundamentals of cryptography, its history, different types of cryptographic algorithms, and its applications in various fields.1. History of CryptographyCryptography can be traced back to ancient times when it was used to send secret messages during wars and conflicts. The early methods of cryptography involved simple substitution ciphers, where each letter in a message was replaced by another letter following a fixed pattern. Over the years, cryptography evolved, and more complex algorithms were developed to ensure stronger security.2. Symmetric CryptographySymmetric cryptography, also known as secret-key cryptography, is a fundamental technique in which the same key is used for both encryption and decryption of messages. The sender and receiver share this secret key, which should be kept confidential to ensure secure communication. The Advanced Encryption Standard (AES) and Data Encryption Standard (DES) are examples of symmetric cryptographic algorithms widely used today.3. Asymmetric CryptographyAsymmetric cryptography, also known as public-key cryptography, uses two keys - a private key and a public key. The private key is kept secret by the owner, while the public key is shared with others. Messages encrypted with the public key can only be decrypted using the corresponding private key, providing a higher level of security. The most popular algorithm used in asymmetric cryptography is the Rivest-Shamir-Adleman (RSA) algorithm.4. Hash FunctionsHash functions are an essential component of cryptography. They are algorithms that convert data of any size into a fixed-size hash value. A hash function always produces the same hash value for the same input data and is designed to be computationally irreversible, ensuring that it is nearly impossible to obtain the original data from the hash value. Hash functions are extensively used in data integrity checks and digital signatures.5. Cryptographic ApplicationsCryptography finds applications in various fields, ensuring the security of sensitive information and enabling secure communication. Some of the common applications include:a. Internet Security: Cryptography is used in Secure Socket Layer (SSL) and Transport Layer Security (TLS) protocols to secure data transmitted over the internet, thereby protecting online transactions and sensitive information.b. Digital Signatures: Cryptography enables the creation of digital signatures, which provide authentication, integrity, and non-repudiation to electronic documents and messages.c. Password Protection: Cryptographic techniques are used in password hashing algorithms to protect user passwords. This ensures that even if the stored passwords are compromised, they cannot be easily deciphered.d. Virtual Private Networks (VPNs): Cryptography plays a critical role in securing VPNs, providing a secure tunnel for remote users to access corporate networks over the internet.e. Blockchain Technology: Cryptography forms the backbone of blockchain technology, securing transactions and ensuring the immutability of data stored in a decentralized network.6. Challenges and Future TrendsWhile cryptography has significantly advanced over the years, it still faces challenges and opportunities for growth. With the rise of quantum computing and the potential threat it poses to traditional encryption algorithms, researchers are exploring post-quantum cryptography techniques. Additionally, advancements in homomorphic encryption and secure multi-party computation hold the potential for securecomputation on encrypted data without revealing the underlying information.ConclusionCryptography is a fundamental tool in securing communication and protecting sensitive information in today's digital world. With its rich history and continuous advancements, cryptography continues to play a vital role in ensuring privacy, integrity, and authenticity. Understanding the different types of cryptographic algorithms and their applications will empower individuals and organizations to make informed decisions when it comes to secure communication.。
IGCSE数学词汇
General Vocabulary Chapter 1 Sets of Numbersset M nfinite set 有湿集 infinite set 无溟美 subset 于集 single-element set 单元素集合 union S6t 芥輿 intersection set 交集 complement set 补集 empty set 空集 belong to 属于 not belong to 不 属于 contain 包,含 Lie in 包含亍 true table 真偵表 original proposition 原命题 inverse proposition 逆会题 inverse and negative proposition 题 」‘、statement 浴句 sufficient condition 充分条件 necessary condition 必要条件 sufficient and necessary condition 条件 if and only if 当且仅当 operation 运算 correspondence 对应 • one-to-one correspondence 1-1 对应 converse operation 逆运算 add (addition)加multiply (multiplication)乘 subtract (difference)减 divide (division)除'number 数 natural number/ counting number 数 rational number 有理数 irrational number 无理数 real number 实数 complex number 复数 integer 整数逆否命 充要 自然positive integer 正整数 negative integer 员整数 whole number / nonnegative integer 员整数 traction 分数proper fraction 真分数 improper fraction 假分数 mixed fraction 带分数 compound fraction 繁分数 simple fraction 简分数 numerator 分子denominator 分母 reciprocal 倒数 consecutive integer 连续整数 decimal number system 十进制数系 decimal point 小数点 prime number 素数，质数 composite number 合数 random number 随机数 recurring decimal 循环小数 non-repeating decimal/irrecurringdecimal 不循环小数 infinite recurring decimal 无限循环小数 infinite irrecurring decimal 无限不循环 小数 terminating decimal 有限小数 approximation 近似值number line 数轴 real number line 实数轴 unit length 单位长度 highest common factor最大公纟勺数 least common multiple. 最小公倍数 commutative law 交換律 associative law 结合律 distributive law 分配律 binary operation 二元运算 reflexive property 自 反性 symmetric property对称性 transitive property 传递性 c substitutionprop^rty 育代性Chapter 2 Expression---------------- 1base （对数、幕运算的）底数 Linear Function —次函数 expanded form 扩展式 quadratic function 二次函数 condensed form 紧缩式 cubic function 三次函数index 指数vertical asymptote 竖萱渐近线 zero index 琴指数 horizontal asymptote 水平渐近线 negative index 负指数 slant asymptote 倾斜渐近统rational index 有理数指数 exponential increasing 指数型増蛇 fractional index 分数指数 bound 边界 parentheses 小括号() orbit 轨迹brace 大括号{ } dash line 虚线 bracket 中括号[] solid line 实线anti-logarithm 真数parameter equation 参数方程 common logarithm 常用对数 jc-intercept x 截距 natural logarithm 自然对数 y-intercept y 截强 laws of logarithm 对数运算律parallel line 平行线 change of base formula 对数换底公式 perpendicular 垂亶的 surd expression 根式表达式 nth root n 次方根 ， scientific form 科学记数法radical 根式three significant figures 三位有效数字 radical exponent 根指数 polynomial function 多项式函数 radicand 被开方数descending order 递减顺序 common factor 公因式 ascending order 递増顺序 cancel 消去，相消 leading coefficient 首项系数 inequality 不等式 synthetic division 综合除法 interval 区间quotient 商continuous 连续的dividend 被除数 discontinuous 不连续的 remainder 余数 y-axis y 轴 divisor 除数 x-axis x 轴consequence 结论 oblique 斜的 corollary 推论 subscript 下标function 函数Chapter 3 Equation and Inequalitystandard deviation 标准差 standard form 标准形式 solution set 解集Imear programming 线性规划 feasible region 可行区域 constraint condition 约束条件domain 定义域 range 值域 nonnegative number 非负数 constant 常数 composite function 复合函数 dependent variable 因变量independent variable 自变量objective function 目标函故argument自变量optimal solution 最优發distinguish 区别maximum 极大值relation 关糸minimum 极小值mapping 茨射inequality with absolute value 含绝对值function 函数的不等式.element 元素one variable quadratic inequality _兀一symmetric 对称次不等式even number 溪数image 像odd number 奇数inverse image 原像reflection 反射one-one mapping, one-to-one mapping dilation 伸缩--- 映射stretching 伟长two-point form 两点式slir inking 压缩slope-intercept form 斜載式cross multiply 交叉相美point-slope form 点斜式cubic centimeter 立方厘米intercept form 截距式shift left 4 units 向左移4个单位system of inequalities 不等式组symbol 记号origin 原点Chapter 4 Functionabsolute value 縫双值scalar quantity 数量absolute value function 绝对值函数vector quantity 向量reciprocal function 倒数函数bounded 有界的opposite number 相反数unbounded 无界的.. piecewise function 分段函数convex polygon 凸多边形step function 阶跃函数concave polygon 凹多边形greatest integer function 取整函数open half-plane开的半平面open interval 开区间closed half-plane封闭的半平面closed interval 闭区间basic function 基本函数half-open interval半开半闭区间squaring function 平方函数unit circle 单位圆cubing function 立方函数objective function 目标函数square root function 平方根函数optimization 最优化.constant function 常值函数multiple-solution 多解.increasing function 增函数mathematical model 数学模型decreasing function 减函数solve graphically 图解法cryptography 密码术linear system线性系统，线性方程组decipher 解密码parity奇偶性even root偶次方根even function 偶函数radicand被开方数odd function 奇函数ordered pairs有序数对solid line 实线. .inverse function 反函数dashed line 虚线comp osite function 复合函数dotted line 点线vector 向量reverse operation 运算Chapter 5 Graph of Functionslope斜率gradient 斜率angle of inclination 傾斜角quadratic equation 二次方程horizontal distance 水平距离vertical distance 垂直距离point-slope form 点斜式slope-intercept form 斜截式hvo-point form 两点式general form —般式endpoint 現点axis of symmetry 对称軸midpoint formula 中点公式transformation 转移，变换translation 平移upper bound 上界lower bound ' 界symmetric with respect to the y-axis 宇y轴对称reflection 反射intersection 相交congruent triangle 全等三角形similar triangle 相似三角形capacity 容积surface area 表面积perimeter 周长accuracy 精度bar chart*条形图flow chart流程图graphical methods 图解法ordered pair number 有序数对rate of change 受化率vertex顶点downward 向下upward 向上real solution 实数解关imaginary solution 虚数解Chapter 6 Trigonometryangle of depression 俯角angle of elevation 仰角solving triangle 解三角形law of sine 正弦定理law of cosine余弦定理obtuse triangle钝角三角形right triangle 直角三角形acute triangle 锐角三角形oblique triangle 斜三角形Pythagorean theorem 勾股定理hypdtenuse 斜边adjacent 邻边opposite 对边counterexample 反例reduce to lowest terms 化成既约形式sine 正弦cosecant 余割~ cosine 余弦seceint 正割tangent 正切cotangent 余切reference triangle 辅助三角形quadrantal angle 象限角terminal side 终边initial side 始边area S3 积circumference 周长the (first, second, third, fourth) quadranttrigonomtJtrkal ratios 三甬比第一，二，三，四象限Ml 尽trigonometric identity 三角恒等式protractor 量用器region区域amplitude 振险Heron,s formula 海伦公式phase shift周期变换included angle 夹角scale factor比例因于included side 夹边counterclockwise 逆时针opposite the angle 对甫clockwise顺时针correlation 相关性frequency 频率major arc 优抓completing square 配平万minor arc 劣弧periodic function 周期函数sector 扇形vertical shift 竖直平移Chapter 7 Geometryplane 平蘆congruent triangle 全等三角形line线 > 行similar triangle 相似三角形segment 线段skew lines异面直线ray射线hypotenuse 斜边point 点legs of right triangle 直角边midpoint 中点base 底边angle 角base angle 底角right angle 直角parallelogram 平行四边形acute angle 锐角rhombus 菱形obtuse angle 钝角trapezoid 梯形adjacent angle 邻角ratio比，比率complementary angle 余角angle of depression 俯角supplementary angle 补角angle of elevation 仰角congruent angle 等角circle 圆hypothesis 假设semicircle 半圆conclusion 结论diameter 直径theorem 定理radius半径corollary 推论chord 弦converse theorem 逆定理arc 弧.contra-positive theorem 逆否定理.minor arc 劣弧parallel line 平行线major arc 优弧corresponding angles 同位角inscribed angle 圆周角alternate interior angles 内错角secant 割线same-side interior angles 同旁内角tangent 切线interior angle 内角arc length 弧长exterior angle 外角circumference of a circle 圆周长polygon多边形sector of circle 扇形concave polygon 凹多边形segment of a circle 弓形regular polygon 正多边形SBafiftedby CamScannertriangle 二魚形central angle 中心角equiangular triangle 等角三角形auxiliary line 辅助线equilateral triangle 等边三角形diagonal line 对角线regular triangle正三角形（=等边三角形）centroid重心isosceles triangle 等腰三角形scalene triangle不规则三角形，不等边二角形一quadrilateral 四边形rectangle 矩形square 正方形pentagon 五泣形hexagon 六边形heptagon 七边形octagon 八边形nonagon 九边形decagon 十边形undecagon '-[—边形dodecagon 十二边形median 中线included angle 夹角included side 夹边adjacent side 邻边opposite side 对边opposite angle 对角interior angle 内角exterior angle 外角Chapter 8 Analytical Geometryparabola抛物线hyperbola双曲线rectangular hyperbola 等轴双曲线ellipse 椭圆transverse axis 实轴imaginary axis 虚轴polarcoordinate 极坐标polar axis 极轴polar angle 极角polar distance 极径polar equation极坐标方程parameter equation 参数方程complex number 复数perpendicular bisector 中垂线，垂直平分线circumcenter 夕卜心circumscribed circle 外接圆angle bisector 角平分线incenter 内心incircle 内接圆altitude 高orthocenter 垂心cone圆锥cylinder 圆柱Vface 面edge 校lateral face 侧面lateral area 侧面积surface area 表面积base area 底面积pyramid 棱锥prism棱柱right circular cylinder 直圆柱right circular cone 直圆锥coordinate system 坐标系origin 原点jt-axis x轴y-axis y轴ordered pair 有序对quadrant 象限vertical line 垂直线horizontal line 水平线conic sections 圆锥曲线directrix 准线eccentricity 离心率focus 焦点vertex 顶点quadratic equation 二次方程Chapter 9 Sequence and Seriesarithme tic means 算术中项arithmetic sequence 等差数列arithmetic series 等差级数binomial coefficient 二项式系数binoniial theorem 二项式定理common difference 公差common ratio 公比converge，收敛diverge 发散explicit formula 显式公式factorial notation 阶乘记号finite sequence 有限数列geometric means 等比中项the formula of general term 通项公式sequence 数列series 级数geometric sequence 等比数列geometric series 等比级数infinite sequence 无穷数列limit of a sequence 数列极限mathematical induction 数学归纳法nth term 第n项通项partial sum 部分和Pascal's triangle伯斯卡三角形power series 幕级数recursive formula 递推公式sum of an infinite series 无穷级数和terms of a sequence 数列的项major axis 长轴minor axis 短轴focal length 焦瑁fractal geometry 分形几何polar form复数极坐标形式rectangular form复数代数形式pole极点argument 幅角。
CISSP培训笔记
CISSP 最新学习笔记此文是我班2014年高分考生袁同学在准备CISSP考试过程中的边看书边整理的一个学习笔记,整理的非常细致到位，特借此供各位备考学员参考。
第1章节到第10章节主要是学习all in one第六版资料时笔记；第11章到18章节主要是在学习完all in one后做cccure网站上面练习题后,补充的知识点;第19章到25章节为学习officeial guide教材后补充的知识点；最后第26章是总复习时作actual练习题时补充的知识点。
在看书3遍all in one后,主要补充学习了pre guide的学习笔记，cccure练习题和official guide进行知识点的补充,最后总复习阶段（1周左右）以本复习笔记为基础,配合actual练习题进行。
目录一. Chapter 3：Security management practices (5)1。
1 安全管理 (5)1。
2 风险管理 (6)1。
3 Policies、standards、baselines、guidelines、procedures (7)1。
4 Classification (8)1。
5 employee (9)二。
chapter 4：Access Control (10)2.1 Identification，Authentication（= Validating），and Authorization（标识、认证、授权） (10)2.2 Access Control Models(访问控制模型） (12)2.3 Access Control Techniques and Technologies（方法和技术) (13)2.4 Access Control Administration（访问控制管理） (13)2.5 Access Control Methods（访问控制方法） (14)2.6 Access Control Type (15)2.7 access control practices (15)2。
Full_Solution_Chap_02
q
r1
r2
r
s1
s2
s
t1
t2
t
0474101010
1 7 4 3 0 1 −1 1 0 1
1 4 3 1 1 −1 2 0 1 −1
8. The set Zn is the set of all positive integer between 0 and n − 1. The set Zn∗ is the set of all integers between 0 and n − 1 that are relatively prime to n. Each element in Zn has an additive inverse; each element in Zn∗ has a multiplicative inverse. The extended Euclidean algorithm is used to find the multiplicative inverses in Zn∗.
f. It is false because 8 is greater than 5.
12.
3
a. gcd (88, 220) = 44, as shown in the following table:
q
r1
r2
r
0
88
220
88
2
220
88
44
2
88
44
0
44
0
b. gcd (300, 42) = 6, as shown in the following table:
q
review problem_solving_through_problems
Review of the book“Problem Solving Through Problems”Loren C. LarsonProblem Book in MathematicsSpringer, 1983ISBN: 0-387-96171-2Dr Kian B TayCenter for Strategic Infocomm Technologies1 What the book is aboutWhat do Don Coppersmith, Berlekamp, Jeff Lagarias, Peter Shor, Paul Vojta, Peter Montgomery, Neal Koblitz and Richard Feynman have in common? Well, they are all Putnam Fellows. These are undergraduate students who have been ranked top 5 participants in the famous annual Putnam math competition in USA/Canada. All of them in this list are great problem solvers, and many of them have made significant contributions to cryptography (eg. Don Coppersmith's work on RSA via lattices-he was Putnam Fellow for 4 consecutive years). Math problem solving skills are obviously important to cryptographers and this book covers many ways of solving math problems. It is highly recommended by many, including Stanford math professor Ravi Vakil, himself a 4-time Putnam fellow, UC-Irvine math professor Karl Rubin, also a Putnam fellow.The purpose of this book is to draw attention to the most important problem solving techniques encountered in undergraduate math and to illustrate their use by interesting examples and problems. Each section features a single idea and versatility of which is demonstrated in the examples and reinforced in the problems.This 332-page book is both an anthology of problems and a manual of instruction. It contains overs 700 problems, over 33% of which are worked out in detail. The book's aim throughout is to show how a basic set of simple techniques can be applied in diverse ways to solve an enormous variety of math problems.2 What the book is likeThere are 8chapters in this book:Chapter 1: Heuristics (basic problem solving techniques such as searching for patterns, drawing relevant figures, modifying or formulating an equivalent simpler problem, exploiting symmetry, dividing into simpler cases, working backwards, argue by contradiction, pursuing parity, considering extreme cases and sometimes generalising the problem).Chapter 2: Induction and Pigeonhole, which is a simple but powerful principle to prove existence results)Chapter 3: Arithmetic (elementary number theory)Chapter 4: AlgebraChapter 5: Summation of SeriesChapter 6: Intermediate Real AnalysisChapter 7: InequalitiesChapter 8: GeometryMany examples are given to illustrate these concepts. The writing style is casual and detailed and is thus easy to follow the arguments. Sometimes multiple solutions are given to illustrate the different angles in attacking a problem (e.g. in page 281, 5 solutions are given).3 What I like about this bookThe book considers interesting problems (with full solutions) likeP1. Prove there exists a,b,c integers not all zero, with absolute value <106 such that|a + b√2 + c√3| < 10-11 (pp 81).P2. Given 9 lattice points in R3, show that there is a lattice point on the interior of one of the line segments joining two of these lattice points. (pp 47)P3. Find positive integers n and a1,…, a n such that a1+… + a n = 1000 and the product of the a1 's is as large as possible. (pp 7)P4. If 3n +1 is a perfect square, show that n+1 is the sum of 3 perfect squares. (pp 26)P5. symetryEvaluate the integral ∫ 1/[ 1 + (tan x)√2]d x from 0 to π/2. (pp 32)P6. pGiven any set of 10 integers between 1 and 99 inclusive, prove that there are 2 disjoint nonempty subsets of the set with equal sum of their elements. (pp 81)P7. Are there 1million consecutive integers each of which contains a repeated prime factor? (pp 97). P8. Does [x] + [2x] +[4x]+…+ [16x] + [32x] = 12345 have a real number solution? (pp 107)P9. Prove that there are no prime numbers in the infinite sequence of integers10001, 100010001, 1000100010001,….(pp 123)P10. The n- polygon of greatest area that can be inscribed in a circle must be the regular n-polygon (pp 70).Hints: P1, P2, P6 (pigeonhole principle), P3 (observation), P4,P9 (algebra), P8 (positional notation), P10 (induction & trigonometry), P5 (symmetry), P7 (Chinese Remainder Theorem). Many of the problems in the book are from math olympiads, Putnam exams and math journals (index to problems given at the end of book). Many important topics are covered and they are done in detail. Plenty of interesting examples and exercises (with solutions to about 33% of them). The authors also covered many formulations of important problems.The font size is quite large and the arguments are neatly displayed.4 Possible ImprovementsI feel that the author should add 2 very important topics: counting and probability. Counting theory is extremely beautiful and many faceted. Probability is fundamental in math.Brief answers or hints to every problem in the book will be helpful to those who want to check if they have done the problem correctly.5 Would you recommend this book?The book's intended audience: upper undergraduates or even a mature sophomores who has some exposure to elementary number theory, algebra analysis and geometry. However the problems chosen are deeper than typical undergraduat problems, though the tools needed are basic. This book is especially suited to prepare students for math competitons. It can also be used byscientific/technical professionals who are interested to develop their mental agility and creativity. By now the reader should know that I strongly endorse this book.The reviewer is a researcher in infocomm security with specialty in math and cryptography. He was formerly a professor in math.。
大学数学专业英语教材
大学数学专业英语教材IntroductionMathematics plays a crucial role in various fields and industries, and studying mathematics at the university level requires a solid foundation in both the subject itself and the English language. A well-designed mathematics textbook for university students in the field of mathematics can effectively integrate mathematical concepts with English language learning. In this article, we will explore the essential features and requirements of a comprehensive English textbook for mathematics students at the university level.Chapter 1: Fundamental ConceptsThe first chapter of the textbook should cover the fundamental concepts of mathematics, introducing students to the basic principles that underpin the subject. It should provide concise explanations and definitions, supplemented with examples and illustrations to aid comprehension. Additionally, this chapter should include exercises to reinforce learning and promote critical thinking.Chapter 2: AlgebraAlgebra is a cornerstone of mathematics, and this chapter should delve into its key theories and principles. It should cover topics such as equations, inequalities, functions, and matrices. The textbook should present clear explanations of concepts, accompanied by real-life applications to demonstrate the practical relevance of algebra.Chapter 3: CalculusCalculus is essential for advanced mathematics and the study of other disciplines such as physics and engineering. The textbook should guide students through both differential and integral calculus, ensuring a thorough understanding of concepts like limits, derivatives, and integrals. Practical examples and exercises should be incorporated to enhance students' problem-solving skills.Chapter 4: Probability and StatisticsIn this chapter, the textbook should introduce students to probability theory and statistical analysis. The content should cover topics such as probability distributions, hypothesis testing, and regression analysis. The inclusion of real-world data sets and case studies can foster students' ability to apply statistical methods effectively.Chapter 5: Discrete MathematicsDiscrete mathematics is vital in areas like computer science and cryptography. This chapter should explore concepts such as set theory, logic, graph theory, and combinatorics. The textbook should present clear explanations of these topics, accompanied by relevant examples and exercises to consolidate understanding.Chapter 6: Linear AlgebraLinear algebra is widely applicable in various fields, including computer science and physics. This chapter should cover vector spaces, linear transformations, and eigenvalues. Emphasis should be placed on theconnections between linear algebra and other mathematical disciplines, demonstrating its practical significance.Chapter 7: Number TheoryNumber theory explores the properties and relationships of numbers, and it forms the basis for cryptographic algorithms and computer security systems. This chapter should introduce students to prime numbers, modular arithmetic, and cryptographic algorithms. Examples and exercises should be given to develop students' problem-solving skills in the realm of number theory.Chapter 8: Numerical AnalysisNumerical analysis involves using algorithms to solve mathematical problems on computers. This chapter should cover topics such as interpolation, numerical integration, and numerical solutions of equations. The textbook should provide step-by-step guidance on implementing numerical algorithms, allowing students to develop practical coding skills.ConclusionA comprehensive English textbook for university-level mathematics students should provide a solid foundation in mathematical concepts while simultaneously enhancing students' English language proficiency. By incorporating clear explanations, practical examples, and engaging exercises, this textbook can foster a deep understanding of mathematics within an English language learning context. Such a resource will empower students to pursue further studies in mathematics and apply their skills in various professional domains.。
流程密码第一章心得
流程密码第一章心得英文回答：In the intriguing realm of cryptography, the seminal work "Flow Cryptography" unveils a novel approach to data protection, captivating the minds of cryptographers worldwide. Central to this concept is the notion of flow, a continuous stream of data parcels transmitted across a secure channel. By harnessing the fundamental properties of flow, flow cryptography offers an innovative framework for thwarting cryptographic adversaries.One of the remarkable characteristics of flow cryptography lies in its ability to facilitate secure distributed computations. Unlike traditional cryptographic protocols that rely on centralized servers, flow cryptography leverages the inherent parallelism of data streams to enable computation distribution. Thisdistributed approach not only enhances performance and scalability but also mitigates the risks associated with asingle point of failure.Furthermore, flow cryptography introduces a paradigm shift in the way encryption and decryption are performed. Conventional encryption algorithms operate on static blocks of data, whereas flow cryptography treats data as an uninterrupted stream. This continuous flow of data parcels enables a continuous encryption process, offering real-time protection against unauthorized access.Another significant aspect of flow cryptography is its inherent resistance to side-channel attacks. Traditional cryptographic implementations are susceptible to various side-channel attacks, such as timing analysis and power analysis. However, by incorporating the notion of flow, flow cryptography effectively eliminates these vulnerabilities, rendering it immune to such attacks.Moreover, flow cryptography opens up avenues for exploring novel cryptographic primitives. The continuous nature of data flow enables the development of cryptographic protocols that exploit the temporal andspatial properties of data streams. This opens up a vast landscape of possibilities for designing innovative cryptographic algorithms with enhanced security and performance characteristics.In conclusion, the advent of flow cryptography has revolutionized the field of data protection, offering a transformative approach to safeguarding data in a world increasingly reliant on digital communication. Its unique characteristics of distributed computation, continuous encryption, side-channel resistance, and novel cryptographic primitives make it a promising solution for securing data in the digital age.中文回答：流程密码第一章节心得。
密码学总结——精选推荐
密码学总结CTF中那些脑洞⼤开的编码和加密0x00 前⾔正⽂开始之前先闲扯⼏句吧，玩CTF的⼩伙伴也许会遇到类似这样的问题:表哥，你知道这是什么加密吗？其实CTF中脑洞密码题(⾮现代加密⽅式)⼀般都是各种古典密码的变形，⼀般出题者会对密⽂进⾏⼀些处理，但是会给留⼀些线索，所以写此⽂的⽬的是想给⼩伙伴做题时给⼀些参考，当然常在CTF⾥出现的编码也可以了解⼀下。
本来是想尽快写出参考的⽂章，⽆奈期间被各种事情耽搁导致⽂章断断续续写了2个⽉，⽂章肯定有许多没有提及到，欢迎⼩伙伴补充，总之，希望对⼩伙伴们有帮助吧！最后欢迎⼩伙伴来玩耍:P0x01 ⽬录1. 常见编码:1. ASCII编码2. Base64/32/16编码3. shellcode编码4. Quoted-printable编码5. XXencode编码6. UUencode编码7. URL编码8. Unicode编码9. Escape/Unescape编码10. HTML实体编码11. 敲击码(Tap code)12. 莫尔斯电码(Morse Code)13. 编码的故事2. 各种⽂本加密3. 换位加密:1. 栅栏密码(Rail-fence Cipher)2. 曲路密码(Curve Cipher)3. 列移位密码(Columnar Transposition Cipher)4. 替换加密:1. 埃特巴什码(Atbash Cipher)2. 凯撒密码(Caesar Cipher)3. ROT5/13/18/474. 简单换位密码(Simple Substitution Cipher)5. 希尔密码(Hill Cipher)6. 猪圈密码(Pigpen Cipher)7. 波利⽐奥斯⽅阵密码（Polybius Square Cipher)8. 夏多密码(曲折加密)9. 普莱菲尔密码(Playfair Cipher)10. 维吉尼亚密码(Vigenère Cipher)11. ⾃动密钥密码(Autokey Cipher)12. 博福特密码(Beaufort Cipher)13. 滚动密钥密码(Running Key Cipher)14. Porta密码(Porta Cipher)15. 同⾳替换密码(Homophonic Substitution Cipher)16. 仿射密码(Affine Cipher)17. 培根密码(Baconian Cipher)18. ADFGX和ADFGVX密码(ADFG/VX Cipher)19. 双密码(Bifid Cipher)20. 三分密码(Trifid Cipher)21. 四⽅密码(Four-Square Cipher)22. 棋盘密码（Checkerboard Cipher)23. 跨棋盘密码(Straddle Checkerboard Cipher)24. 分组摩尔斯替换密码(Fractionated Morse Cipher)25. Bazeries密码(Bazeries Cipher)26. Digrafid密码(Digrafid Cipher)27. 格朗普雷密码(Grandpré Cipher)28. ⽐尔密码(Beale ciphers)29. 键盘密码(Keyboard Cipher)5. 其他有趣的机械密码:1. 恩尼格玛密码6. 代码混淆加密:1. asp混淆加密2. php混淆加密3. css/js混淆加密4. VBScript.Encode混淆加密5. ppencode6. rrencode7. jjencode/aaencode8. JSfuck9. jother10. brainfuck编程语⾔7. 相关⼯具8. 参考⽹站0x02 正⽂常见编码1.ASCII编码ASCII编码⼤致可以分作三部分组成：第⼀部分是：ASCII⾮打印控制字符（参详ASCII码表中0-31）;第⼆部分是：ASCII打印字符，也就是CTF中常⽤到的转换;第三部分是：扩展ASCII打印字符(第⼀第三部分详见解释)。
cryptography 使用手册
cryptography 使用手册摘要：1.引言：介绍密码学的概念和应用场景2.密码学基础知识：加密和解密原理，常见加密算法3.密码学工具：介绍常用的密码学工具和软件4.安全实践：如何在日常生活中使用密码学保障信息安全5.密码学发展趋势：探讨密码学在未来信息安全领域的应用和发展6.结论：总结全文，呼吁加强密码学知识学习正文：【引言】密码学（cryptography）是一种研究加密和解密技术的技术领域，它在信息安全、通信保密等方面具有重要的应用价值。
随着互联网的普及，信息安全问题日益凸显，学习密码学成为保障个人和机构信息安全的重要手段。
本文将为您介绍密码学的基本知识、常用工具和实践方法，帮助您更好地应对日益严峻的信息安全挑战。
【密码学基础知识】密码学的基本原理是基于数学难题，将明文转换为密文，实现通信保密。
加密过程包括key 生成、加密算法和密文输出。
解密过程则需要相同的密钥和解密算法，将密文还原为明文。
常见的加密算法有对称加密算法（如AES、DES）、非对称加密算法（如RSA、ECC）和哈希算法（如SHA-256）等。
【密码学工具】在实际应用中，有许多密码学工具和软件可以帮助我们实现加密和解密。
例如，Windows 操作系统自带的BitLocker 可以对硬盘进行加密；浏览器中的HTTPS 协议使用SSL/TLS 加密通信；移动设备上的指纹识别和面部识别也是一种加密手段。
此外，还有许多开源的加密软件，如GnuPG、TrueCrypt 等，可以为用户提供多种加密方案和便捷的加密工具。
【安全实践】在日常生活中，我们可以通过以下方法运用密码学保障信息安全：1.使用复杂且唯一的密码：为每个账户设置难以猜测的密码，并定期更换。
2.启用双重身份验证：在支持双重身份验证的网站和应用上启用该功能，以减少密码泄露的风险。
3.加密重要数据：对敏感文件进行加密，防止数据泄露。
4.学习并使用数字签名：数字签名可以确保文档的完整性和真实性，防止篡改和伪造。
美的历程英译本
美的历程英译本**The Journey of Beauty**Beauty, an abstract concept that has intrigued humanity since ancient times, has taken various forms across cultures and epochs. The journey of beauty is not merely a chronological progression but a narrative woven through the fabric of human experience, reflecting the ideals, values, and aspirations of each era. From the majestic artworks of the Renaissance to the minimalist designs of the modern age, beauty evolves, transcending boundaries and resonating with the human soul.**Ancient Origins**The roots of our fascination with beauty can be traced back to the dawn of civilization. In the ancient world, beauty was intertwined with divinity, as seen in theexquisite sculptures of Greek gods and goddesses. Beauty was not just an aesthetic quality but a manifestation of harmony, balance, and proportion – principles that echoed throughout Greek philosophy and art.**Classical Influences**The classical ideals of beauty laid the groundwork for subsequent civilizations. In the splendor of Roman architecture and the refinement of Chinese calligraphy, we see the enduring legacy of classical aesthetics. Beauty became synonymous with order and elegance, inspiring generations to seek perfection in art, literature, and everyday life.**The Renaissance Rebirth**The Renaissance marked a pivotal moment in the journey of beauty, as artists and scholars rediscovered the classical heritage and redefined artistic expression. From the breathtaking frescoes of Michelangelo to the serene portraits of Leonardo da Vinci, the Renaissance witnessed an explosion of creativity and innovation. Beauty became a means of celebrating human potential and exploring the depths of the human experience.**Baroque Extravagance**The Baroque era brought a dramatic shift in artistic sensibilities, as beauty took on a more dynamic andtheatrical quality. In the opulent palaces of Versailles and the grand cathedrals of Europe, beauty became synonymous with grandeur and excess. Yet beneath the ornate façade lay a profound sense of emotional intensity and spiritual fervor, as artists sought to evoke awe and wonder in their audiences.**Enlightenment Rationalism**The Enlightenment ushered in an era of reason and rationality, challenging traditional notions of beauty and aesthetics. Beauty was no longer solely the domain of the elite but a universal ideal accessible to all. From the elegant simplicity of neoclassical architecture to the naturalistic landscapes of the Romantic painters, beauty became intertwined with notions of truth, freedom, and human dignity.**Modernist Experimentation**The modernist movement of the 20th century shattered conventions and pushed the boundaries of artistic expression. From the bold abstractions of Picasso to the avant-garde designs of Le Corbusier, beauty became a subject of debateand controversy. Yet amid the chaos and upheaval, beauty endured, evolving to reflect the tumultuous realities of the modern world.**Postmodern Pluralism**In the postmodern era, beauty has fragmented into a kaleidoscope of diverse perspectives and voices. From the playful pastiche of pop art to the provocative installationsof contemporary artists, beauty defies easy categorization.It is no longer confined to traditional mediums orconventional standards but thrives in the interplay of ideas, cultures, and identities.**The Global Age**Today, in our increasingly interconnected world, beauty transcends borders and embraces diversity. From the soaring skyscrapers of Dubai to the intricate textiles of West Africa, beauty manifests in myriad forms, reflecting the richness and complexity of human experience. As we navigate the challenges of the 21st century, beauty remains a source of inspiration, solace, and hope, reminding us of our shared humanity and the enduring power of creativity.**Conclusion**The journey of beauty is a testament to the resilienceand creativity of the human spirit. Across time and space, beauty has captivated our imagination, inspired ouraspirations, and enriched our lives. From the sublime to the ordinary, beauty surrounds us, inviting us to contemplate the mysteries of existence and celebrate the wonders of creation. As we continue on this journey, may we always strive to cultivate beauty in ourselves and in the world around us, for in beauty lies the promise of a more harmonious and meaningful existence.。
20.Chinese Characters
01
Chapter 1: The History of Chinese Characters
Chapter 1: The History of Chinese Characters
• Chinese characters, also known as Hanzi, are logograms developed for the writing of the Chinese language. The history of Chinese characters can be traced back over 3,000 years to the Shang dynasty. The development of Chinese characters has been a reflection of the cultural and technological advancements of ancient China.
• Origin and Evolution • Cultural Significance • Influence Beyond Language
Origin and Evolution
• The origins of Chinese characters can be found in ancient inscriptions on oracle bones and bronze ware. These early forms of writing consisted of simple pictograms and ideograms representing objects and ideas. Over time, the characters evolved into more intricate forms, incorporating phonetic elements and semantic radicals.
密码学外文文献及译文
外文文献：1.IntroductionCryptography is the science of keeping secrets secret.Assume a sender referred to here and in what follows as Alice(as is commonly used)wants tosend a message m to a receiver referred to as Bob. She uses an insecure communication channel.For example,the channel could be a computer network or a telephone line.There is a problem if the message contains confidential information. The message could be intercepted and read by an eavesdropper.Or,even worse,the adversary,as usual referred to here as Eve,might be able to modify the message during transmission in such a way that the legitimate recipient Bob does not detect the manipulation.One objective of cryptography is to provide methods for preventing such attacks.Other objectives are discussed in Section 1.2.1.1 Encryption and SecrecyThe fundamental and classical task of cryptography is to provide confidentiality by encryption methods.The message to be transmitted–it can be some text,numerical data,an executable program or any other kind of information–is called the plaintext.Alice encrypts the plaintext m and obtains the ciphertext c.The ciphertext c is transmitted to Bob.Bob turns the ciphertext back into the plaintext by decryption.To decrypt,Bob needs some secret information,a secret decryption key. Adversary Eve still may intercept the ciphertext.However,the encryption should guarantee secrecy and prevent her from deriving any information about the plaintext from the observed ciphertext.Encryption is very old.For example,Caesar’s shift cipher was introduced more than 2000 years ago.Every encryption method provides an encryption algorithm E and a decryption algorithm D.In classical encryption schemes,both algorithms depend on the same secret key k.This key k is used for both encryption and decryption.These encryption methods are therefore called symmetric.For example,in Caesar’s cipher the secret key is the offset of the shift.We haveSymmetric encryption and the important examples DES(data encryption standard)and AES (advanced encryption standard)are discussed in Chapter 2.In 1976,W.Diffie and M.E.Hellman published their famous paper,New Directions in Cryptography ([DifHel76]).There they introduced the revolutionary concept of public-key cryptography. They provided a solution to the long standing problem of key exchange and pointed the way to digital signatures.The public-key encryption methods(comprehensively studied in Chapter 3)are asymmetric.Each recipient of messages has his personal key pkk ,consisting of two parts:pk is the encryption key and is made public,sk is the (sk,)decryption key and is kept secret. If Alice wants to send a message m to Bob,she encrypts m by use of Bob’s publicly known encryption key pk.Bob decrypts the ciphertext by use of his decryption key sk,which is known only to him.We haveMathematically speaking,public-key encryption is a so-called one-way function with a trapdoor. Everyone can easily encrypt a plaintext using the public key pk,but the other direction is difficult.It is practically impossible to deduce the plaintext from the ciphertext,without knowing the secret key sk(which is called the trapdoor information).Public-key encryption methods require more complex computations and are less efficient than classical symmetric methods.Thus symmetric methods are used for the encryption of large amounts of data.Before applying symmetric encryption,Alice and Bob have to agree on a key.To keep this key secret,they need a secure communication channel.It is common practice to use public-key encryption for this purpose.1.2 The Objectives of CryptographyProviding confidentiality is not the only objective of cryptography.Cryptography is also used to provide solutions for other problems:1.Data integrity.The receiver of a message should be able to check whether the message was modified during transmission,either accidentally or deliberately.No one should be able to substitute a false message for the original message,or for parts of it.2.Authentication.The receiver of a message should be able to verify its origin.No one should be able to send a message to Bob and pretend to be Alice(data origin authentication).When initiating a communication,Alice and Bob should be able to identify each other(entity authentication).3.Non-repudiation.The sender should not be able to later deny that she sent a message.If messages are written on paper,the medium-paper-provides a certain security against manipulation. Handwritten personal signatures are intended to guarantee authentication and non-repudiation.If electronic media are used,the medium itself provides no security at all,since it is easy to replace some bytes in a message during its transmission over a computer network,and it is particularly easy if the network is publicly accessible,like the Internet.So,while encryption has a long history,the need for techniques providing data integrity and authentication resulted from the rapidly increasing significance of electronic communication.There are symmetric as well as public-key methods to ensure the integrity of messages.Classical symmetric methods require a secret key k that is shared by sender and receiver.The message m is augmented by a message authentication code(MAC).The code is generated by an algorithm and depends on the secret key.The augmented message))km is protected against modifications.The receiver may test the integrity of (mMAC,(,an incoming message(m,m)by checking whetherMessage authentication codes may be implemented by keyed hash functions (see Chapter 3).Digital signatures require public-key methods(see Chapter 3 for examples and details).As with classical handwritten signatures,they are intended to provide authentication and non-repudiation.Note that non-repudiation is an indispensable feature if digital signatures are used to sign contracts.Digital signatures depend on the secret key of the signer-they can be generated only by him.On the other hand,anyone can check whether a signature is valid,by applying a publicly known verification algorithm Verify,which depends on the public key of the signer.If Alice wants to sign the message m,she applies the algorithm Sign with her secret key sk and gets the signature Sign)sk.Bob receives a signature s for message m,and may then(m,check the signature by testing whetherwith Alice’s public key pk.It is common not to sign the message itself,but to apply a cryptographic hash function(seeSection 3.4)first and then sign the hash value.In schemes like the famous RSA(named after its inventors:Rivest,Shamir and Adleman),the decryption algorithm is used to generate signatures and the encryption algorithm is used to verify them.This approach to digital signatures is therefore often referred to as the“hash-then-decrypt”paradigm(see Section3.4.5 for details).More sophisticated signature schemes,like the probabilistic signature scheme(PSS),require more steps.Modifying the hash value by pseudorandom sequences turns signing into a probabilistic procedure(seeSection 3.4.5).Digital signatures depend on the message.Distinct messages yield different signatures.Thus,like classical message authentication codes,digital signatures can also be used to guarantee the integrity of messages.1.3 AttacksThe primary goal of cryptography is to keep the plaintext secret from eavesdroppers trying to get some information about the plaintext.As discussed before,adversaries may also be active and try to modify the message.Then,cryptography is expected to guarantee the integrity of the messages.Adversaries are assumed to have complete access to the communication channel.Cryptanalysis is the science of studying attacks against cryptographic schemes.Successful attacks may,for example,recover the plaintext(or parts of the plaintext)from the ciphertext,substitute parts of the original message,or forge digital signatures.Cryptography and cryptanalysis are often subsumed by the more general term cryptology.A fundamental assumption in cryptanalysis was first stated by A.Kerkhoff in the nineteenth century.It is usually referred to as Kerkhoff’s Principle.It states that the adversary knows all the details of the cryptosystem,including algorithms and their implementations.According to this principle,the security of a cryptosystem must be entirely based on the secret keys.Attacks on the secrecy of an encryption scheme try to recover plaintexts from ciphertexts,or even more drastically,to recover the secret key.The following survey is restricted to passive attacks.The adversary,as usual we call her Eve,does not try to modify the messages.She monitors the communication channel and the end points of the channel.So she may not only intercept the ciphertext,but(at least from time to time)she may be able to observe the encryption and decryption of messages.She has no information about the key.For example,Eve might be the operator of a bank computer.She sees incoming ciphertexts and sometimes also the correspondingplaintexts.Or she observes the outgoing plaintexts and the generated ciphertexts.Perhaps she manages to let encrypt plaintexts or decrypt ciphertexts of her own choice.The possible attacks depend on the actual resources of the adversary Eve. They are usually classified as follows:1.Ciphertext-only attack.Eve has the ability to obtain ciphertexts.This is likely to be the case in any encryption situation.Even if Eve cannot perform the more sophisticated attacks described below,one must assume that she can get access to encrypted messages.An encryption method that cannot resist a ciphertext-only attack is completely insecure.2.Known-plaintext attack.Eve has the ability to obtain plaintext-ciphertext ing the information from these pairs,she attempts to decrypt a ciphertext for which she does not have the plaintext.At first glance,it might appear that such information would not ordinarily be available to an attacker.However,it very often is available.Messages may be sent in standard formats which Eve knows.3.Chosen-plaintext attack.Eve has the ability to obtain ciphertexts for plaintexts of her choosing.Then she attempts to decrypt a ciphertext for which she does not have the plaintext.While again this may seem unlikely,there are many cases in which Eve can do just this.For example,she sends some interesting information to her intended victim which she is confident he will encrypt and send out.This type of attack assumes that Eve must first obtain whatever plaintext-ciphertext pairs she wants and then do her analysis, without any further interaction.This means that she only needs access to the encrypting device once.4.Adaptively-chosen-plaintext attack.This is the same as the previous attack,except now Eve may do some analysis on the plaintext-ciphertextpairs,and subsequently get more pairs.She may switch between gathering pairs and performing the analysis as often as she likes.This means that she has either lengthy access to the encrypting device or can somehow make repeated use of it.5.Chosen-and adaptively-chosen-ciphertext attack.These two attacks are similar to the above plaintext attacks. Eve can choose ciphertexts and gets the corresponding plaintexts.She has access to the decryption device.1.4 Cryptographic ProtocolsEncryption and decryption algorithms,cryptographic hash functions or pseudorandom generators(see Section 2.1,Chapter 8)are the basic building blocks(also called cryptographicprimitives)for solving problems involving secrecy,authentication or data integrity.In many cases a single building block is not sufficient to solve the given problem:different primitives must be combined.A series of steps must be executed to accomplish a given task.Such a well-defined series of steps is called a cryptographic protocol.As is also common,we add another condition:we require that two or more parties are involved.We only use the term protocol if at least two people are required to complete the task.As a counter example,take a look at digital signature schemes.A typical scheme for generating a digital signature first applies a cryptographic hash function h to the message m and then,in a second step,computes the signature by applying a public-key decryption algorithm to the hash value h(m).Both steps are done by one person.Thus,we do not call it a protocol.Typical examples of protocols are protocols for user identification.There are many situations where the identity of a user Alice has to be verified. Alice wants to log in to a remote computer,for example,or to get access to an account for electronic banking.Passwords or PIN numbers are used for this purpose.This method is not always secure.For example,anyone who observes Alice’s password or PIN when transmitted might be able to impersonate her.We sketch a simple challenge-and-response protocol which prevents this attack(however,it is not perfect;see Section 4.2.1).The protocol is based on a public-key signature scheme,and we assume that Alice has a key)pkk=for this scheme.Now,Alice can prove her identity to Bob in the following way.(sk,1.Bob randomly chooses a“challenge”c and sends it to Alice.2.Alice signs c with her secret key,)Signs=,and sends the“response”s to Bob.sk:c(,3.Bob accepts Alice’s proof of identity,if Verify ok,,()cpk=sOnly Alice can return a valid signature of the challenge c,because only she knows the secret key sk. Thus, Alice proves her identity,without showing her secret.No one can observe Alice’s secret key,not even the verifier Bob.Suppose that an eavesdropper Eve observed the exchanged ter,she wants to impersonate Alice. Since Bob selects his challenge c at random(from a huge set),the probability that he uses the same challenge twice is very small.Therefore,Eve cannot gain any advantage by her observations.The parties in a protocol can be friends or adversaries.Protocols can be attacked.The attacks may be directed against the underlying cryptographic algorithms or against the implementation of the algorithms and protocols.There may also be attacks against a protocol itself.There may be passive attacks performed by an eavesdropper,where the only purpose is to obtain information.An adversary may also try to gain an advantage by actively manipulating the protocol.She might pretend to be someone else,substitute messages or replay old messages.Important protocols for key exchange,electronic elections,digital cash and interactive proofs of identity are discussed in Chapter 4.1.5 Provable SecurityIt is desirable to design cryptosystems that are provably secure.Provably secure means that mathematical proofs show that the cryptosystem resists certain types of attacks.Pioneering work in this field was done by C.E.Shannon.In his information theory,he developed measures for the amount of information associated with a message and the notion of perfect secrecy.A perfectly secret cipher perfectly resists all ciphertext-only attacks.An adversary gets no information at all about the plaintext,even if his resources in computing power and time are unlimited.Vernam’s one-time pad(see Section 2.1),which encrypts a message m by XORing it bitwise with a truly random bit string,is the most famous perfectly secret cipher.It even resists all the passive attacks mentioned.This can be mathematically proven by Shannon’s theory.Classical information-theoretic security is discussed in Section 9.1;an introduction to Shannon’s information theory may be found in Appendix B.Unfortunately,Vernam’s one-time pad and all perfectly secret ciphers are usually impractical.It is not practical in most situations to generate and handle truly random bit sequences of sufficient length as required for perfect secrecy.More recent approaches to provable security therefore abandon the ideal of perfect secrecy and the(unrealistic) assumption of unbounded computing power.The computational complexity of algorithms is taken into account.Only attacks that might be feasible in practice are considered.Feasible means that the attack can be performed by an efficient algorithm.Of course,here the question about the right notion of efficiency arises.Certainly,algorithms with non-polynomial running time are inefficient.Vice versa algorithms with polynomial running time are often considered as the efficient ones.In this book,we also adopt this notion of efficiency.The way a cryptographic scheme is attacked might be influenced by randomevents.Adversary Eve might toss a coin to decide which case she tries next.Therefore,probabilistic algorithms are used to model attackers. Breaking an encryption system,for example by a ciphertext-only attack,means that a probabilistic algorithm with polynomial running time manages to derive information about the plaintext from the ciphertext,with some non-negligible probability.Probabilistic algorithms can toss coins,and their control flow may be at least partially directed by these random events.By using random sources,they can be implemented in practice.They must not be confused with non-deterministic algorithms.The notion of probabilistic(polynomial) algorithms and the underlying probabilistic model are discussed in Chapter 5.The security of a public-key cryptosystem is based on the hardness of some computational problem(there is no efficient algorithm for solving the problem).For example,the secret keys of an RSA scheme could be easily figured out if computing the prime factors of a large integer were possible.However,it is believed that factoring large integers is infeasible.There are no mathematical proofs for the hardness of the computational problems used in public-key systems.Therefore,security proofs for public-key methods are always conditional: they depend on the validity of the underlying assumption.The assumption usually states that a certain function f is one way;i.e.,f can be computed efficiently,but it is infeasible to compute x from )(x f .The assumptions,as well as the notion of a one-way function,can be made very precise by the use of probabilistic polynomial algorithms.The probability of successfully inverting the function by a probabilistic polynomial algorithm is negligibly small,and negligibly small means that it is asymptotically less than any given polynomial bound(see Chapter 6,Definition 6.12).Important examples,like the factoring,discrete logarithm and quadratic residuosity assumptions,are included in this book(see Chapter 6).There are analogies to the classical notions of security.Shannon ’s perfect secrecy has a computational analogy:ciphertext indistinguishability(or semantic security).An encryption is perfectly secret if and only if an adversary cannot distinguish between two plaintexts,even if her computing resources are unlimited:if adversary Eve knows that a ciphertext c is the encryption of either m or 'm ,she has no better chance than 21 of choosing the right one.Ciphertextindistinguishability–also called polynomial-time indistinguishability–means that Eve’s chance of successfully applying a probabilistic polynomial algorithm is at most negligibly greater than1/2(Chapter 9,Definition 9.14).As a typical result,it is proven in Section 9.4 that public-key one-time pads are ciphertext-indistinguishable. This means,for example,that the RSA public-key one-time pad is ciphertext-indistinguishable under the sole assumption that the RSA function is one way.A public-key one-time pad is similar to Vernam’s one-time pad. The difference is that the message m is XORed with a pseudorandom bit sequence which is generated from a short truly random seed,by means of a one-way function.Thus,one-way functions are not only the essential ingredients of public-key encryption and digital signatures. They also yield computationally perfect pseudorandom bit generators(Chapter 8).If f is a one-way function,it is not only impossible to compute x from )(xf,but certain bits(called hard-core bits)of x are equally difficult to deduce.This feature is called the bit security of a one-way function.For example,the least-significant bit is a hard-core bit for the RSA function e xx mod n.Starting with a truly random seed,repeatedly applying f and taking the hard-core bit in each step,you get a pseudorandom bit sequence.These bit sequences cannot be distinguished from truly random bit sequences by an efficient algorithm,or,equivalently (Yao’s Theorem, Section 8.2),it is practically impossible to predict the next bit from the previous ones.So they are really computationally perfect.The bit security of important one-way functions is studied in detail in Chapter 7 including an in-depth analysis of the probabilities involved.Randomness and the security of cryptographic schemes are closely related.There is no security without randomness.An encryption method provides secrecy only if the ciphertexts appear random to the adversary Eve.Vernam’s one-time pad is perfectly secret,because,due to the truly random key string k,the encrypted message km is a truly random bit sequence for Eve.The public-key one-time pad is ciphertext-indistinguishable,because if Eve applies an efficient probabilistic algorithm,she cannot distinguish the pseudorandom key string and,as a consequence,the ciphertext from a truly random sequence.Public-key one-time pads are secure against passive eavesdroppers,who perform aciphertext-only attack(see Section 1.3 above for a classification of attacks).However,active adversaries,who perform adaptively-chosen-ciphertext attacks,can be a real danger in practice–as demonstrated by Bleichenbacher’s 1-Million-Chosen-Ciphertext Attack(Section 3.3.3).Therefore,security against such attacks is also desirable.In Section 9.5,we study two examples of public-key encryption schemes which are secure against adaptively-chosen-ciphertext attacks,and their security proofs.One of the examples,Cramer-Shoup’s public key encryption scheme,was the first practical scheme whose security proof is based solely on a standard number-theoretic assumption and a standard assumption of hash functions(collision-resistance).The ideal cryptographic hash function is a random function.It yields hash values which cannot be distinguished from randomly selected and uniformly distributed values.Such a random function is also called a random oracle.Sometimes,the security of a cryptographic scheme can be proven in the random oracle model.In addition to the assumed hardness of a computational problem,such a proof relies on the assumption that the hash functions used in the scheme are truly random functions.Examples of such schemes include the public-key encryption schemes OAEP(Section 3.3.4)and SAEP(Section9.5.1),the above mentioned signature scheme PSS and full-domain-hash RSA signatures(Section 3.4.5).We give the random-oracle proofs for SAEP and full-domain-hash signatures.Truly random functions can not be implemented,nor even perfectly approximated in practice.Therefore,a proof in the random oracle model can never be a complete security proof.The hash functions used in practice are constructed to be good approximations to the ideal of random functions.However,there were surprising errors in the past(see Section 3.4).We distinguished different types of attacks on an encryption scheme.In a similar way,the attacks on signature schemes can be classified and different levels of security can be defined.We introduce this classification in Chapter 10 and give examples of signature schemes whose security can be proven solely under standard assumptions(like the factoring or the strong RSA assumption).No assumptions on the randomness of a hash function have to be made,in contrast,for example,to schemes like PSS.A typical security proof for the highest level of security is included.For the given signature scheme,we show that not a single signature can be forged,even if the attacker Eve is able to obtain valid signatures from the legitimate signer,formessages she has chosen adaptively.The security proofs for public-key systems are always conditional and depend on(widely believed,but unproven)assumptions.On the other hand,Shannon’s notion of perfect secrecy and,in particular,the perfect secrecy of Vernam’s one-time pad are unconditional.Although perfect unconditional security is not reachable in most practical situations,there are promising attempts to design practical cryptosystems which provably come close to perfect information-theoretic security.The proofs are based on classical information-theoretic methods and do not depend on unproven assumptions.The security relies on the fact that communication channels are noisy or on the limited storage capacity of an adversary.Some results in this approach are reviewed in the chapter on provably secure encryption(Section 9.6).中文译文：密码学介绍说明密码学是一门保守秘密的科学。
英语作文-古老卜辞：解读世界文化的神秘密码
英语作文-古老卜辞：解读世界文化的神秘密码In the annals of history, the ancient practice of divination has always held a place of intrigue and mysticism. Among the various methods of divination, the oracle bones of ancient China stand out as a unique testament to the human quest for understanding the unknown. These artifacts, primarily dating back to the Shang Dynasty (1600–1046 BCE), are one of the earliest forms of written Chinese language and provide a fascinating glimpse into the worldviews and cultural practices of early Chinese civilization.Oracle bones were typically made from the scapulae of oxen or the plastrons of turtles. They were used in divination ceremonies where questions were inscribed onto the bone or shell, which was then subjected to heat until it cracked. The diviners would interpret the patterns of the cracks to predict the future or explain natural phenomena. This practice was not merely a form of fortune-telling but was deeply embedded in the governance and decision-making processes of the state. Kings and nobles would consult the oracle bones on matters ranging from weather forecasting and crop planting to warfare and royal births.The inscriptions on oracle bones are a treasure trove for historians and linguists, as they reveal a wealth of information about the social, political, and religious life of the Shang Dynasty. They contain the earliest known references to many fundamental Chinese concepts, such as the Mandate of Heaven, which justified the rule of the king, and the veneration of ancestors, which remains a significant aspect of Chinese culture to this day.Moreover, the oracle bone script is a precursor to modern Chinese characters, and studying these inscriptions has helped scholars trace the evolution of one of the world's oldest continuous writing systems. The characters found on oracle bones are often pictographic or ideographic, representing objects or ideas directly. Over time, these characters have evolved, but many can still be recognized in the simplified and traditional characters used today.The practice of divination using oracle bones declined with the fall of the Shang Dynasty, but its impact on Chinese culture and its contribution to the understanding of ancient civilizations cannot be overstated. The oracle bones serve as a bridge between the past and the present, offering insights into the human desire to seek guidance from the divine and to connect with the spiritual realm.In a broader context, the study of oracle bones is a reminder of the universal human fascination with the metaphysical. Across different cultures and epochs, people have sought to decipher the mysteries of existence and the cosmos. Whether through the runes of the Norse, the auguries of the Romans, or the geomancy of the Africans, the quest for knowledge beyond the tangible world is a common thread that weaves through the tapestry of human history.The legacy of the oracle bones extends beyond their historical and cultural significance. They challenge us to consider the ways in which we seek meaning and direction in our own lives. In a world that is increasingly driven by technology and data, the ancient oracle bones invite us to reflect on the value of intuition, tradition, and the human connection to the spiritual dimensions of life.In conclusion, the oracle bones of ancient China are not just relics of a bygone era; they are keys to unlocking the enigmatic codes of world culture. They remind us that, despite the passage of millennia, the human spirit's quest for understanding and the search for answers to life's great mysteries remain unchanged. As we continue to explore and interpret these ancient symbols, we honor the wisdom of our ancestors and enrich our collective cultural heritage. 。
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Chapter 2 – Classical Encryption Techniques
Many savages at the present day regard themselves, and therefore take great pains to conceal their real names, lest these should give to evildisposed persons a handle by which to injure their owners. —The Golden Bough, Sir James George Frazer
公开发表的加密算法、政府指定的加密算法、著名 厂家产品、专家推荐的加密算法
通信信道的加密
链路加密－点到点加密 高层连接加密－端到端加密
存储数据的加密
硬盘级加密和文件级加密
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现代密码学基本原则
by team led by Horst Feistel used 64-bit data blocks with 128-bit key
1975, Diffie-Hellman, A New Direction in Cryptography, 首次提出适应网络保密通信的公开密钥思想，揭开现代密 码学研究的序幕，具有划时代的意义 1976-1977，美国国家标准局正式公布实施DES，Data Encryption Standard
现代密码学的基本原则
chapter2.1
Fiber Optic Networks
A fiber optic ring with active repeaters(有源中继器).
2010-12-12 Computer Networks 21
Fiber Optic Networks (2)
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Fiber Optics
50,000 Gbps 10 Gbps limit: convert between electrical and optical signals
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Computer Networks
18
Fiber Cables
2010-12-12 Computer Networks 7
Bandwidth-Limited Signals (2)
(d) – (e) Successive approximations to the original signal.
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Bandwidth-Limited Signals (3)
Chapter 2
The Physical Layer
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2.1 The Theoretical Basis for Data Communication
• Fourier Analysis （傅立叶分析） • Bandwidth-Limited Signals （有限带宽信号） • Maximum Data Rate of a Channel （信道的最大数据传输率）
密码编码学与网络安全-原理与实践 课后答案
密码学与网络安全 山东大学数学院的信息安全专业师资雄厚，前景广阔，具有密码理论、密码技术与网络安全 技术三个研究方向。有一大批博士、硕士及本科生活跃于本论坛。本版块适合从事密码学或网络 安全方面学习研究的朋友访问。
Third Edition WILLIAM STALLINGS
Copyright 2002: William Stallings -1-
TABLE OF CONTENTS
Chapter 2: Chapter 3: Chapter 4: Chapter 5: Chapter 6: Chapter 7: Chapter 8: Chapter 9: Chapter 10: Chapter 11: Chapter 12: Chapter 13: Chapter 14: Chapter 15: Chapter 16: Chapter 17: Chapter 18: Chapter 19: Chapter 20:
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SOLUTIONS MANUAL
CRYPTOGRAPHY AND NETWORK SECURITY
W.ห้องสมุดไป่ตู้.
-3-
CHAPTER 2 CLASSICAL ENCRYPTION TECHNIQUES
cryptography 使用手册
cryptography 使用手册一、简介Cryptography，即加密学，是保护数据机密性、完整性和可用性的关键技术。
随着互联网的发展，信息安全逐渐成为人们关注的焦点，而加密技术作为信息安全的核心手段，其重要性不言而喻。
本手册将为您介绍加密学的基础知识、常见算法及其应用。
二、基础知识1.对称加密与非对称加密：对称加密：加密和解密使用相同的密钥。
常见的算法有AES、DES等。
非对称加密：加密和解密使用不同的密钥。
常见的算法有RSA、ECC等。
2.哈希函数：单向函数，将输入数据（通常是消息）转化为固定长度的哈希值。
常见的哈希函数如SHA-256。
三、常见算法介绍1.AES (Advanced Encryption Standard) ：类型：对称加密。
应用：适用于大量数据的加密，如文件、数据库等。
2.RSA (Rivest–Shamir–Adleman) ：类型：非对称加密。
应用：数字签名、身份验证及加密数据。
3.SHA-256 ：类型：哈希函数。
应用：确保数据完整性，常与数字签名结合使用。
四、实际应用1.数据传输加密：使用对称加密算法对传输的数据进行加密，确保数据在传输过程中的安全性。
2.数字签名：使用非对称加密算法对数据进行签名，验证数据的完整性和来源。
3.身份验证：通过非对称加密算法实现用户身份的验证，确保只有合法的用户可以访问特定的资源。
4.文件加密：使用对称加密算法对文件进行加密，保护文件内容不被未授权的用户访问。
5.安全通信：通过建立加密的通信通道，保证数据在传输过程中的安全性和机密性。
五、注意事项1.选择合适的加密算法和密钥管理策略，确保数据的安全性和完整性。
2.定期更新和更换密钥，以降低密钥泄露的风险。
3.遵循最佳实践，避免使用已知的漏洞或弱加密方法。
4.保持对最新加密技术和算法的了解，以便及时应对新的安全威胁。
六、总结Cryptography作为信息安全的核心技术，广泛应用于数据保护、身份验证和通信安全等领域。
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维吉尼亚密码
Key: deceptive P：wearediscoveredsaveyourself 查表
A B C D E F G H I J K L M N O P Q R S T UV W XY Z
A A B C D E F G H I J K L M N O P Q R ST UV W XY Z
PART ONE Cryptography
Cryptology(密码学)
Cryptography(密码编码学) Cryptanalytics(密码分析学)
Basic Vocabulary
Plaintext ciphertext['saifətekst] Encryption [in'kripʃən] encryption algorithm
secret
Decryption [di:'kripʃən decryption algorithm
key
Five elements
五元组：P、 C、 k、 E、 D
c = Ek (p) p = Dk (c)
classification
One key（对称算法）
K加=K解
P
B B C D E F G H I J K L M N O P Q R ST UV W XY Z A
C C D E F G H I J K L M N O P Q R ST UV W XY Z A B
D D E F G H I J K L M N O P Q R ST UV W XY Z A B C
Playfair cipher
“Hide the gold in the tree stump “ If both letters are the same (or only one letter is left), add an "X" after the first letter. Some variants of Playfair use "Q" instead of "X", but any uncommon monograph will do.
k
维吉尼亚密码
Key: deceptive P：wearediscoveredsaveyourself K：deceptivedeceptivedeceptive 查表 C：zicvtwqngrzgvtwavzhcqyglmgj
Vigenere cipher
维吉尼亚密码
C = (P+ k) Mod 26 – 1 ？ P= [C - k] Mod 26 + 1 ？ correct？
HI DE TH EG OL DI NT HE TR EX ES TU MP
–
Keyword: “playfair example“
The alphabet square is a five-by-five grid. The key phrase is first written without repeating any letters. The remaining letters of the alphabet are filled in in order :
K加!=K解
Two keys（公钥算法，非对称算法）
Traditional methods
Ancient: Julius Caesar
Method:
replaces each letter by 3rd letter
……
a b cd e f g h i j k lmnopqrstuv w x y z
P I B J T
L R C K U
A E D N V
Y X G O WF M H S Z三个规则
如果一对明文在同一行，那么分别用5*5矩阵中 紧接着右边的字母替代；如果右边没有字母，那 么采用循环技术，用左边第一个字母替代. 如果一对明文在同一列，那么分别用5*5矩阵中 紧接着下边的字母替代；如果下面没有字母，那 么采用循环技术，用上面第一个字母替代. 如果不属于上述情况，那么分别用对角线上的字 母替代，以行为准
…… X XY Z A B C D E F G H I J K L M N O P Q R S T UV W YY Z A B C D E F G H I J K L M N O P Q R ST UV W X Z Z A B C D E F G H I J K L M N O P Q R ST UV W XY
t u v w x y z a bc d
p q r s
example:
Plaintext: meet me after the toga party Ciphertext: fxxm fx tymxk max mhzt itkmr
Caesar密码
C = Ek (P) = (P + k) mod q P = Dk (C) = (C - k) mod q