Introduction to Cryptography
Electronic communication and financial transactions have assumed massive proportions today. But they come with high risks. Achieving cyber security has become a top priority, and has become one of the most crucial areas of study and research in IT. This book introduces readers to perhaps the most ef...
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| Médium: | E-kniha |
| Jazyk: | angličtina |
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Milton
CRC Press
2018
Taylor & Francis Group |
| Vydání: | 1 |
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| ISBN: | 1138071536, 9781138071537, 9780367781019, 0367781018 |
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- Cover -- Title Page -- Copyright Page -- Dedication -- Foreword -- Preface -- Table of Contents -- 1: Overview of Cryptography -- 1.1 Introduction -- 1.2 Goals of Cryptography -- 1.3 Classification of Cryptosystem -- 1.4 Practically Useful Cryptosystem -- 1.4.1 Confusion and Diffusion -- 1.5 Cryptanalysis -- 1.5.1 Types of Attackers -- 1.5.2 Types of Attacks -- 1.5.3 Security Notions -- 2: Basic Algebra -- 2.1 Group -- 2.2 Ring -- 2.3 Field -- 2.3.1 Finite Field -- 2.3.2 Field Construction -- 2.3.3 Field Construction using Irreducible Polynomial -- 2.3.4 Galois Field GF (2n) -- 2.3.4.1 Integer Representation of Finite Field Elements -- 2.3.5 Field Construction using Generator -- 2.4 Exercises -- 3: Number Theory -- 3.1 Prime Numbers -- 3.2 Cardinality of Primes -- 3.3 Extended Euclidean Algorithm -- 3.4 Congruences -- 3.4.1 Solving Linear Congruence in Zn -- 3.4.2 Chinese Remainder Theorem (CRT) -- 3.5 Integer Factorization Problem -- 3.5.1 Trial Division Method -- 3.5.2 Fermat's Method -- 3.5.3 Pollard's p - 1 Method -- 3.5.4 Pollard's Rho Method -- 3.5.5 Quadratic Sieve -- 3.5.6 Number Field Sieve -- 3.6 Primality Testing -- 3.6.1 Sieve of Eratosthenes -- 3.6.2 Divisibility Algorithm -- 3.6.3 AKS Algorithm -- 3.6.4 Fermat Test -- 3.6.5 Miller-Rabin Algorithm -- 3.7 Quadratic Congruence -- 3.7.1 Quadratic Residue or Non-Residue -- 3.7.2 Legendre Symbol and Jacobi Symbol -- 3.8 Exponentiation and Logarithm -- 3.8.1 Square and Multiply Method -- 3.9 Discrete Logarithm Problem -- 3.9.1 Shank's Baby-Step Giant-Step Algorithm -- 3.9.2 Pollard's Rho Algorithm -- 3.9.3 Pohlig-Hellman Algorithm -- 3.9.4 Index Calculus Algorithm -- 3.10 Exercises -- 4: Probability and Perfect Secrecy -- 4.1 Basic Concept of Probability -- 4.2 Birthday Paradox -- 4.3 Perfect Secrecy -- 4.4 Vernam One-Time Pad -- 4.5 Random Number Generation
- 9.3.4.1 Recommended Size of Modulus -- 9.3.4.2 Selecting Primes -- 9.3.4.3 Choice of e and d -- 9.3.5 Efficiency of RSA -- 9.3.5.1 RSA with CRT -- 9.3.6 Semantic Security of RSA -- 9.3.6.1 Secure RSA (RSA-OAEP) -- 9.4 Rabin Cryptosystem -- 9.4.1 Efficiency of Rabin Cryptosystem -- 9.4.2 Cryptanalysis of Rabin Cryptosystem -- 9.4.2.1 Security against Ciphertext Only Attack -- 9.4.2.2 Security of Rabin against CCA -- 9.5 ElGamal Cryptosystem -- 9.5.1 Correctness of Decryption -- 9.5.2 Efficiency -- 9.5.3 ElGamal and Diffie-Hellman -- 9.5.4 Semantic Security of ElGamal -- 9.5.5 Malleablity of ElGamal Cryptosystem -- 9.6 Elliptic Curve Cryptosystem -- 9.6.0.1 Elliptic Curve over a Field Fp -- 9.6.1 Addition Operation of Elliptic Curve E(a,b) over Fp (Chord and Tangent Method) -- 9.6.1.1 Geometrical Explanation of the Addition Operation -- 9.6.2 Elliptic Curves over GF(2n) -- 9.6.2.1 Addition Law of Elliptic Curve E (a,b) over F2n -- 9.6.3 Elliptic Curve Cryptosystem -- 9.6.3.1 Elliptic Curve DH Protocol (ECDHP) -- 9.6.3.2 Elliptic Curve based ElGamal Cryptosystem -- 9.6.3.3 Advantages and Disadvantages of ECC over RSA -- 9.7 Exercises -- 10: Digital Signature -- 10.1 Formal Definitions -- 10.1.1 Basic Elements of Digital Signature -- 10.1.2 Formal Structure -- 10.1.3 Digital Signature Scheme -- 10.2 Attack Goals of an Adversary of a Digital Signature -- 10.3 Digital Signature in Practice -- 10.3.1 RSA Signature -- 10.3.1.1 Security of RSA Signature -- 10.3.1.2 Performance -- 10.3.2 ElGamal Signature -- 10.3.2.1 Security of ElGamal Signature -- 10.3.2.2 RSA vs ElGamal Signature -- 10.3.3 Digital Signature Algorithm (DSA) -- 10.3.3.1 Security of DSA -- 10.3.3.2 ElGamal vs DSA -- 10.3.4 Elliptic Curve Digital Signature Algorithm (ECDSA) -- 10.3.4.1 Security of ECDSA -- 10.3.4.2 Why ECDSA over other Signatures? -- 10.3.4.3 Application of ECDSA
- 7.5.5 DESX -- 7.5.6 TDES -- 7.6 Advanced Encryption Standard (AES) -- 7.6.1 Role of GF (28) in AES -- 7.6.2 Basic Steps -- 7.6.3 Basic Structure -- 7.6.4 AES-Key Schedule -- 7.6.5 AES-Decryption -- 7.7 Exercises -- 8: Hash Function -- 8.1 Compression and Hash Functions -- 8.1.1 Compression Function -- 8.1.2 Computable Map -- 8.1.3 Hash Function -- 8.1.4 Additional Properties -- 8.2 Hash Function for Cryptography -- 8.2.1 Security Aspects of Communication -- 8.2.2 Modification Detection Code (MDC) -- 8.2.3 Message Authentication Codes (MAC) -- 8.2.3.1 MAC Algorithm -- 8.2.3.2 Security of MAC -- 8.2.3.3 HMAC -- 8.2.3.4 HMAC Algorithm -- 8.2.3.5 Limitations of MAC -- 8.2.4 Digital Signature -- 8.3 Random Oracle Model -- 8.4 Cryptographic Hash Functions -- 8.4.1 Iterated Hash Function -- 8.4.2 Merkle-Damgård Hash Function -- 8.4.3 MD5 -- 8.4.3.1 Working Principle of MD5 -- 8.4.3.2 Attacks on MD5 -- 8.4.4 SHA-1 -- 8.4.4.1 Working Principle of SHA-1 -- 8.4.4.2 Example -- 8.4.4.3 Attacks on SHA-1 -- 8.5 Exercises -- 9: Public Key Cryptosystem -- 9.1 Introduction -- 9.1.1 Symmetric Key Cryptosystem vs Public Key Cryptosystem -- 9.2 Diffie-Hellman Key Exchange Protocol -- 9.2.1 The Man-in-the-Middle Attack -- 9.2.2 CDH Assumption & -- DL Assumption -- 9.2.2.1 Relation between CDH Assumption & -- DL Assumption -- 9.3 RSA Cryptosystem -- 9.3.1 RSA as a Block Cipher -- 9.3.2 RSA Assumption and RSA Problem -- 9.3.3 Cryptanalytic Attacks on RSA -- 9.3.3.1 Factoring Attack -- 9.3.3.2 Secrete Key and Factoring -- 9.3.3.3 Computing ø(n) -- 9.3.3.4 Common Modulus Attack -- 9.3.3.5 Low Encryption Exponent Attack -- 9.3.3.6 Small Decryption Exponent Attack -- 9.3.3.7 Meet-in-the-Middle Attack -- 9.3.3.8 Forward Search Attack -- 9.3.3.9 Cyclic Attack -- 9.3.3.10 Partial Key Exposure Attack -- 9.3.3.11 Timing Attack -- 9.3.4 RSA in Practice
- 4.6 Pseudo-random Number Generator -- 4.7 Exercises -- 5: Complexity Theory -- 5.1 Running Time and Size of Input -- 5.2 Big-O Notation -- 5.2.1 Big-O and Growth Rate -- 5.2.2 Properties of Order Notation -- 5.3 Types of Algorithm -- 5.4 Complexity Classes -- 5.5 Exercises -- 6: Classical Cryptosystems -- 6.1 Classification of Classical Cryptosystem -- 6.2 Block Cipher -- 6.2.1 Substitution Cipher -- 6.2.1.1 Shift Cipher -- 6.2.1.2 Affine Cipher -- 6.2.1.3 Substitution Cipher -- 6.2.1.4 Vigenere Cipher -- 6.2.1.5 Hill Cipher -- 6.2.2 Transposition Cipher -- 6.2.2.1 Scytale -- 6.2.2.2 The Rail Fence Cipher -- 6.3 Stream Cipher -- 6.3.1 Synchronous Stream Cipher -- 6.3.1.1 Vigenere Cipher as Synchronous Stream Cipher -- 6.3.2 Linear Feedback Shift Register (LFSR) -- 6.3.3 Non-Synchronous Stream Cipher -- 6.3.3.1 Autokey Cipher -- 6.4 Cryptanalysis of Cryptosystems -- 6.4.1 Frequency Analysis -- 6.4.2 Cryptanalysis of Affine Cipher -- 6.4.3 Cryptanalysis of Substitution Cipher -- 6.4.4 Cryptanalysis of Vigenere Cipher -- 6.4.5 Cryptanalysis of Hill Cipher -- 6.4.6 Cryptanalysis of LFSR Stream Cipher -- 6.5 Exercises -- 7: Block Ciphers -- 7.1 Introduction -- 7.1.1 Notations -- 7.2 Modes of Operation -- 7.2.1 Electronic Code Book (ECB) -- 7.2.1.1 ECB Properties -- 7.2.2 Cipher-Block Chaining (CBC) -- 7.2.2.1 CBC Properties -- 7.2.3 Cipher FeedBack (CFB) -- 7.2.3.1 CFB Properties -- 7.2.4 Output FeedBack (OFB) -- 7.2.4.1 OFB Properties -- 7.2.5 Counter (CTR) -- 7.3 Padding -- 7.3.1 Ciphertext Stealing -- 7.3.1.1 Ciphertext Stealing (ECB mode) -- 7.3.1.2 Ciphertext Stealing (CBC mode) -- 7.4 Design Considerations -- 7.4.1 Diffusion -- 7.4.2 Confusion -- 7.4.3 Avalanche Effect -- 7.4.4 Basic Design Considerations -- 7.5 Data Encryption Standard (DES) -- 7.5.1 The Mangler Function f -- 7.5.2 The S-boxes -- 7.5.3 Key Schedule -- 7.5.4 DES Variants
- 10.3.4.4 Issues with ECDSA -- 10.4 Some Popular Digital Signatures -- 10.5 Exercises -- 11: Research Directions in Cryptography -- 11.1 Pairing-based Cryptography -- 11.2 Zero-knowledge Proof System -- 11.3 Authenticated Group Key Exchange -- 11.4 Attribute-based Cryptography -- 11.5 Homomorphic Encryption -- 11.6 Secure Multi-party Computation -- 11.7 Secret Sharing -- 11.8 Post-Quantum Cryptography -- 11.9 Side-Channel Analysis -- References -- Index