This book explains compactly, without theoretical superstructure and with as little mathematical formalism as possible, the essential concepts in the encryption of messages and data worthy of protection. The focus is on the description of the historically and practically important cipher, signature and authentication methods. Both symmetric encryption and public-key ciphers are discussed. In each case, the strategies used to attack and attempt to "crack" encryption are also discussed. Special emphasis is placed on the practical use of ciphers, especially in the everyday environment. The book is suitable for working groups at STEM schools and STEM teacher training, for introductory courses at universities as well as for interested students and adults.
Author(s): Olaf Manz
Series: Mathematics Study Resources, 4
Publisher: Springer
Year: 2022
Language: English
Pages: 139
City: Berkeley
Preface
Contents
1: Basics and History
1.1 What It Is About: The Scenario
1.1.1 An Initial Overview
1.1.2 Sending and Storing Information
1.1.3 Receiving and Reading Information
1.2 Alphabets and Digitisation
1.2.1 Alphabets and Modulo Calculation
1.2.2 Digitisation and Bytes
1.3 Caesar Cipher
1.3.1 Shift Cipher
1.3.2 Affine Cipher
1.4 Secret Writing of the Illuminati
1.4.1 Illuminati Alphabet and Secret Writing
1.4.2 Monoalphabetic Ciphers
1.5 Vigenère Cipher
1.5.1 Polyalphabetic Ciphers
1.5.2 Vigenère Tableau
1.5.3 Smoothing of Statistical Frequencies
1.6 Kasiski and Friedman Attack
1.6.1 Kasiski Attack
1.6.2 Friedman Coincidence Index
1.6.3 Friedman Attack
1.7 Enigma Machine
1.7.1 Structure of the Enigma Machine
1.7.2 Configuration of the Enigma Machine
1.7.3 Deciphering and Security with Enigma
2: Symmetric Ciphers
2.1 Keys and Attack Strategies
2.1.1 Algorithm and Key
2.1.2 Symmetric and Asymmetric Ciphers
2.1.3 Kerckhoff’s Principle
2.1.4 Military Secrets
2.1.5 Attack Strategies
2.2 Vernam Cipher and Pseudo-Randomness
2.2.1 Vernam Cipher
2.2.2 Shift Registers
2.2.3 Pseudo-Randomness and Cryptanalysis
2.3 GSM Mobile Communications
2.3.1 The GSM Mobile Communications Standard
2.3.2 GSM Data Encryption
2.3.3 A5 Cipher of Version A5/1
2.4 Feistel Cipher
2.4.1 Stream Ciphers and Block Ciphers
2.4.2 Confusion and Diffusion
2.4.3 Construction Principle of a Feistel Cipher
2.5 Data Encryption Standard DES
2.5.1 From LUCIFER to DES
2.5.2 DES as Feistel Cipher
2.5.3 DES Expansion
2.5.4 DES Key Addition
2.5.5 DES S-Boxes
2.5.6 DES Permutation
2.5.7 DES Key Selection
2.5.8 Security of the DES
2.5.9 Differential Cryptanalysis Using the Example of DES
2.5.10 Linear Cryptanalysis Using the Example of DES
2.5.11 Brute-Force Attack and Triple-DES
2.6 Operating Modes of Block Ciphers
2.6.1 Electronic Codebook Mode
2.6.2 Cipher Block Chaining Mode
2.6.3 Cipher Feedback Mode
2.6.4 Output Feedback Mode
2.6.5 Counter Mode
2.7 UMTS/LTE Mobile Communications and Digital Television
2.7.1 The UMTS/LTE Mobile Communications Standard
2.7.2 A5 Cipher of Versions A5/3 and A5/4
2.7.3 DVB and MPEG2
2.7.4 CSA Encryption
2.8 Advanced Encryption Standard AES
2.8.1 Rijndael Procedure and AES
2.8.2 Addition and Multiplication of Bytes
2.8.3 AES State Matrix
2.8.4 AES Subbyte
2.8.5 AES ShiftRow
2.8.6 AES MixColumn
2.8.7 AES AddRoundKey
2.8.8 AES Decryption
2.8.9 Security of the AES
2.9 Hard Disk and ZIP Archive
2.9.1 Hard Disk
2.9.2 CBC-AES Hard Disk Encryption
2.9.3 XTS-AES Hard Disk Encryption
2.9.4 ZIP Archive
3: Public-Key Ciphers
3.1 Factorization and RSA Cipher
3.1.1 Prime Numbers and Factorization
3.1.2 Fermat’s Little Theorem
3.1.3 Euclidean Algorithm
3.1.4 RSA Cipher
3.1.5 Example: RSA Cipher
3.1.6 Repeated Squaring
3.1.7 Security of the RSA Cipher
3.1.8 RSA Cipher and Key Exchange
3.2 Internet and WLAN
3.2.1 Network Protocols and the Internet
3.2.2 Confidential Work on the Internet with HTTPS, SMTPS and FTPS
3.2.3 Wireless WLAN
3.3 Monte Carlo Prime Numbers
3.3.1 Prime Numbers for Public Key Ciphers
3.3.2 Carmichael Numbers
3.3.3 Fermat’s Theorem and 3. Binomial Formula
3.3.4 Miller-Rabin Primality Test
3.3.5 Example: Miller-Rabin Primality Test
3.3.6 Euler Criterion
3.3.7 Solovay-Strassen Primality Test
3.3.8 AKS Primality Test
3.4 Attack by Factorization
3.4.1 Fermat Factorization
3.4.2 Example: Fermat Factorization
3.4.3 Example and Basic Idea: Quadratic Sieve
3.4.4 Pollard’s ρ- Factorization
3.4.5 Example: Pollard’s ρ-Factorization
3.4.6 Pollard’s p – 1- Factorisation
3.4.7 Example: Pollard’s p − 1 Factorization
3.5 Discrete Logarithm and Diffie-Hellman
3.5.1 Existence of Generating Elements
3.5.2 Determination of Generating Elements
3.5.3 Discrete Logarithm
3.5.4 Diffie-Hellman Key Exchange
3.5.5 Example: Diffie-Hellman Key Exchange
3.5.6 Security of Diffie-Hellman Key Exchange
3.5.7 Diffie-Hellman in Colour
3.5.8 Semi-Static Diffie-Hellman
3.6 Attack with Baby and Giant Steps
3.6.1 Baby-Step-Giant-Step Method
3.6.2 Example: Baby-Step-Giant-Step Method
3.6.3 Pohlig-Hellman Method
3.6.4 Example: Pohlig-Hellman Method
3.6.5 Pollard’s ρ-Method for Discrete Logarithms
3.6.6 Example: Pollard’s ρ-Method for Discrete Logarithms
3.7 Bluetooth and ECDH
3.7.1 Bluetooth Radio Interface
3.7.2 Bluetooth Data Encryption
3.7.3 Elliptic Curves Modulo a Prime Number
3.7.4 Addition of Points on Elliptic Curves
3.7.5 Base Points on Elliptic Curves
3.7.6 ECDH
3.7.7 EC-Standard P-256
3.7.8 Diffie-Hellman on the Internet
3.7.9 ECDH Security and Performance
3.8 ElGamal Cipher
3.8.1 ElGamal Cipher
3.8.2 Example: ElGamal Cipher
3.8.3 ElGamal Cipher and Key Exchange
3.8.4 ElGamal Cipher for Elliptic Curves
3.8.5 Other Public-Key Ciphers
3.9 Knapsack and Merkle-Hellman Cipher
3.9.1 Packed Knapsack
3.9.2 The Super-Knapsack
3.9.3 Merkle-Hellman Cipher
3.9.4 Example: Merkle-Hellman Cipher
3.9.5 Security of the Merkle-Hellman Cipher
4: Digital Signature
4.1 Man-in-the-Middle Attack and Authentication
4.1.1 Passive and Active Attack
4.1.2 Authentication of Messages
4.1.3 MAC Authentication and CBC-MAC
4.1.4 Authentication of Users
4.1.5 Attack on Diffie-Hellman Key Exchange
4.2 RSA and ElGamal Signature
4.2.1 Authentication by Digital Signature
4.2.2 RSA Signature
4.2.3 Example: RSA Signature
4.2.4 ElGamal Signature
4.2.5 Example: ElGamal Signature
4.2.6 Cryptographic Envelope and Digital Fingerprint
4.3 Hash Value and Secure Hash Algorithm SHA
4.3.1 Cryptographic Hash Function and Hash Value
4.3.2 MAC Authentication and HMAC
4.3.3 Merkle-Damgård Construction
4.3.4 Davies-Meyer and Matyas-Meyer-Oseas Compression Function
4.3.5 Cryptographic Hash Functions SHA
4.3.6 Cryptographic Hash Functions MD
4.3.7 Cryptographic Hash Function SHA-2-256
4.4 Email with PGP and WhatsApp
4.4.1 Sending and Receiving Cryptographic Envelopes
4.4.2 PGP Pretty Good Privacy
4.4.3 OpenPGP and GPG
4.4.4 Implemented Procedures for PGP/openPGP/GPG
4.4.5 WhatsApp
4.5 DSA and ECDSA Signature
4.5.1 Discrete Logarithm with Non-Generating Element
4.5.2 DSA Signature
4.5.3 Example: DSA Signature
4.5.4 Diffie-Hellman with Non-Generating Element
4.5.5 ECDSA Signature
4.5.6 Security of the DSA and ECDSA Signature
4.5.7 EC Standards sepc256kl and brainpoolP256r1
4.5.8 EC Standard Curve25519
4.6 Online Banking
4.6.1 HBCI and FinTS
4.6.2 2-Factor Authentication with TAN
4.6.3 FinTS with Digital Signature
4.6.4 Encryption and Signature Procedures for FinTS
4.7 Blind Signature and Cryptocurrencies
4.7.1 Anonymity and Blind Signature
4.7.2 Cryptocurrency eCash
4.7.3 Cryptocurrency Bitcoin
4.7.4 Bitcoin Transactions
4.7.5 The Bitcoin Blockchain
4.8 Password Security and Challenge Response
4.8.1 Password as Hash Value
4.8.2 Attacks on Passwords
4.8.3 Salted Hash Values
4.8.4 RADIUS Server for WLAN and DSL
4.8.5 Challenge-Response Authentication
4.8.6 Challenge-Response with Digital Signature
4.9 Mobile Phone, Credit Card and Passport
4.9.1 Authentication in GSM Mobile Communications
4.9.2 Authentication in UMTS/LTE Mobile Communications
4.9.3 Credit Card and Secure Data Transmission
4.9.4 Authentication When Purchasing with a Credit Card
4.9.5 Electronic Passport ePassport
4.9.6 Authentication on Entry or Exit with ePassport
Bibliography
Index
