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| Contents | ||||||
| Foreword | xiii | |||||
| 1. | PREHISTORY OF CRYPTOGRAPHY | 1 | ||||
| Exercises | 1 | |||||
| Exercise 1 | Mappings, etc. | 1 | ||||
| Exercise 2 | A Simple Substitution Cryptogram | 4 | ||||
| Exercise 3 | Product of Vigenère Ciphers | 5 | ||||
| Exercise 4 | *One-Time Pad | 5 | ||||
| Exercise 5 | *Latin Squares | 6 | ||||
| Exercise 6 | Enigma | 6 | ||||
| Solutions | 8 | |||||
| 2. | CONVENTIONAL CRYPTOGRAPHY | 17 | ||||
| Exercises | 17 | |||||
| Exercise 1 | Weak Keys of DES | 17 | ||||
| Exercise 2 | Semi-Weak Keys of DES | 17 | ||||
| Exercise 3 | Complementation Property of DES | 17 | ||||
| Exercise 4 | 3DES Exhaustive Search | 18 | ||||
| Exercise 5 | 2DES and Two-Key 3DES | 18 | ||||
| Exercise 6 | *Exhaustive Search on 3D ES | 19 | ||||
| Exercise 7 | An Extension of DES to 128-bit Blocks | 20 | ||||
| Exercise 8 | Attack Against the OFB Mode | 21 | ||||
| Exercise 9 | *Linear Feedback Shift Registers | 22 | ||||
| Exercise 10 | *Attacks on Cascade Ciphers | 23 | ||||
| Exercise 11 | Attacks on Encryption Modes I | 24 | ||||
| Exercise 12 | Attacks on Encryption Modes II | 28 | ||||
| Exercise 13 | *A Variant of A5/1 I | 29 | ||||
| Exercise 14 | *A Variant of A5/1 II | 31 | ||||
| Exercise 15 | *Memoryless Exhaustive Search | 32 | ||||
| Solutions | 34 | |||||
| 3. | DEDICATED CONVENTIONAL CRYPTOGRAPHIC PRIMITIVES | 57 | ||||
| Exercises | 57 | |||||
| Exercise 1 | Collisions in CBC Mode | 57 | ||||
| Exercise 2 | Collisions | 57 | ||||
| Exercise 3 | Expected Number of Collisions | 58 | ||||
| Exercise 4 | Multicollisions on Hash Functions | 58 | ||||
| Exercise 5 | Weak Hash Function Designs | 60 | ||||
| Exercise 6 | Collisions on a Modified MD5 | 62 | ||||
| Exercise 7 | First Preimage on a Modified MD5 | 62 | ||||
| Exercise 8 | *Attacks on Yi-Lam Hash Function | 62 | ||||
| Exercise 9 | MAC from Block Ciphers | 63 | ||||
| Exercise 10 | CFB-MAC | 64 | ||||
| Exercise 11 | *Universal Hashing | 64 | ||||
| Solutions | 66 | |||||
| 4. | CONVENTIONAL SECURITY ANALYSIS | 81 | ||||
| Exercises | 81 | |||||
| Exercise 1 | The SAFER Permutation | 81 | ||||
| Exercise 2 | *Linear Cryptanalysis | 81 | ||||
| Exercise 3 | *Differential and Linear Probabilities | 82 | ||||
| Exercise 4 | *Feistel Schemes | 82 | ||||
| Exercise 5 | *Impossible Differentials | 84 | ||||
| Exercise 6 | *Attacks Using Impossible Differential | 84 | ||||
| Exercise 7 | *Multipermutations | 86 | ||||
| Exercise 8 | *Orthomorphisms | 87 | ||||
| Exercise 9 | *Decorrelation | 88 | ||||
| Exercise 10 | *Decorrelation and Differential Cryptanalysis | 89 | ||||
| Exercise 11 | *Decorrelation of a Feistel Cipher | 89 | ||||
| Exercise 12 | *A Saturation Attack against IDEA | 89 | ||||
| Exercise 13 | *Fault Attack against a Block Cipher | 94 | ||||
| Solutions | 97 | |||||
| 5. | SECURITY PROTOCOLS WITH CONVENTIONAL CRYPTOGRAPHY | 125 | ||||
| Exercises | 125 | |||||
| Exercise 1 | Flipping a Coin by Email | 125 | ||||
| Exercise 2 | Woo-Lam Protocol | 126 | ||||
| Exercise 3 | Micro-Mint I | 127 | ||||
| Exercise 4 | Micro-Mint II | 127 | ||||
| Exercise 5 | Bluetooth Pairing Protocol | 128 | ||||
| Exercise 6 | UNIX Passwords | 128 | ||||
| Exercise 7 | Key Enlargement | 128 | ||||
| Solutions | 130 | |||||
| 6. | ALGORITHMIC ALGEBRA | 135 | ||||
| Exercises | 135 | |||||
| Exercise 1 | Captain's Age | 135 | ||||
| Exercise 2 | Roots in Z* 77 | 135 | ||||
| Exercise 3 | *When is Z* n Cyclic? | 135 | ||||
| Exercise 4 | Finite Fields and AES | 137 | ||||
| Exercise 5 | *A Special Discrete Logarithm | 138 | ||||
| Exercise 6 | *Quadratic Residues | 138 | ||||
| Exercise 7 | *Cubic Residues | 139 | ||||
| Exercise 8 | *Generating Generators for Z* p | 139 | ||||
| Exercise 9 | *Elliptic Curves and Finite Fields I | 140 | ||||
| Exercise 10 | *Elliptic Curves and Finite Fields II | 141 | ||||
| Solutions | 142 | |||||
| 7. | ALGORITHMIC NUMBER THEORY | 159 | ||||
| Exercises | 159 | |||||
| Exercise 1 | *Rho Method and Distinguished Points | 159 | ||||
| Exercise 2 | *Factorization | 160 | ||||
| Exercise 3 | *Prime Numbers | 161 | ||||
| Exercise 4 | *Factoring n = p q | 161 | ||||
| Exercise 5 | Strong Prime Numbers | 161 | ||||
| Exercise 6 | Complexity of Eratosthenes Sieve | 161 | ||||
| Exercise 7 | *Hash Function Based on Arithmetics | 164 | ||||
| Solutions | 165 | |||||
| 8. | ELEMENTS OF COMPLEXITY THEORY | 175 | ||||
| Exercises | 175 | |||||
| Exercise 1 | *Regular Language | 175 | ||||
| Exercise 2 | *Finite State Automaton | 175 | ||||
| Exercise 3 | *Turing Machine | 175 | ||||
| Exercise 4 | *Graph Colorability I | 176 | ||||
| Exercise 5 | *Graph Colorability II | 176 | ||||
| Solutions | 177 | |||||
| 9. | PUBLIC KEY CRYPTOGRAPHY | 181 | ||||
| Exercises | 181 | |||||
| Exercise 1 | *Okamoto-Uchiyama Cryptosystem | 181 | ||||
| Exercise 2 | RSA Cryptosystem | 182 | ||||
| Exercise 3 | RSA for Paranoids | 182 | ||||
| Exercise 4 | RSA - Common Moduli | 183 | ||||
| Exercise 5 | Networked RSA | 183 | ||||
| Exercise 6 | Repeated RSA Encryption | 184 | ||||
| Exercise 7 | Modified Diffie-Hellman | 184 | ||||
| Exercise 8 | *Rabin Cryptosystem | 184 | ||||
| Exercise 9 | *Paillier Cryptosystem | 185 | ||||
| Exercise 10 | *Naccache-Stern Cryptosystem | 186 | ||||
| Solutions | 188 | |||||
| 10. | DIGITAL SIGNATURES | 199 | ||||
| Exercises | 199 | |||||
| Exercise 1 | Lazy DSS | 199 | ||||
| Exercise 2 | *DSS Security Hypothesis | 199 | ||||
| Exercise 3 | DSS with Unprotected Parameters | 200 | ||||
| Exercise 4 | Ong-Schnorr-Shamir Signature | 201 | ||||
| Exercise 5 | Batch Verification of DSS Signatures | 201 | ||||
| Exercise 6 | Ring Signatures | 203 | ||||
| Solutions | 205 | |||||
| 11. | CRYPTOGRAPHIC PROTOCOLS | 211 | ||||
| Exercises | 211 | |||||
| Exercise 1 | Breaking the RDSA Identification Scheme | 211 | ||||
| Exercise 2 | *A Blind Signature Protocol for a Variant of DSA | 213 | ||||
| Exercise 3 | *Fiat-Shamir Signature I | 215 | ||||
| Exercise 4 | *Fiat-Shamir Signature II | 216 | ||||
| Exercise 5 | *Authenticated Diffie-Hellman Key Agreement Protocol | 216 | ||||
| Exercise 6 | Conference Key Distribution System | 217 | ||||
| Solutions | 220 | |||||
| 12. | FROM CRYPTOGRAPHY TO COMMUNICATION SECURITY | 231 | ||||
| Exercises | 231 | |||||
| Exercise 1 | A Hybrid Cryptosystem Using RS A and DES | 231 | ||||
| Exercise 2 | SSL/TLS Cryptography | 233 | ||||
| Exercise 3 | Secure Shell (SSH) | 235 | ||||
| Exercise 4 | Attack against RC5-CBC-PAD | 236 | ||||
| Exercise 5 | Wired Equivalent Privacy (WEP) | 237 | ||||
| Exercise 6 | Forging X.509 Certificates | 238 | ||||
| Solutions | 240 | |||||
| References | 249 | |||||
Foreword
As a companion book of Vaudenay 's A Classical Introduction to Cryptography, this exercise book contains a carefully revised version of most of the material used in teaching by the authors or given as examinations to the undergraduate students of the Cryptography and Security lecture at EPFL from 2000 to mid-2005. It covers a majority of the subjects that make up today's cryptology, such as symmetric or public-key cryptography, cryptographic protocols, design, cryptanalysis, and implementation of cryptosystems.
Exercises do not require a large background in mathematics, since the most important notions are introduced and discussed in many of the exercises. We expect the readers to be comfortable with basic facts of discrete probability theory, discrete mathematics, calculus, algebra, as well as computer science. Following A Classical Introduction to Cryptography, exercises related to the more advanced parts of the textbook are marked with a star.
The difficulty of the exercises covers a broad spectrum. In some the student is expected to simply apply basic facts, while in others more intuition and reflexion will be necessary to find the solution. Nevertheless, the solutions accompanying the exercises have been written as clearly as possible. Some exercises are clearly research-oriented, like for instance the ones dedicated to decorrelation theory or to very recent results in the field of hash functions. The idea was to give to our readers a taste of this exciting research world.
Chapter 1 is dedicated to the prehistory of cryptology, exposing the design and the cryptanalysis of very simple and/or historical ciphers. Chapter 2 investigates basic facts of modern symmetric cryptography, focusing on the Data Encryption Standard, modes of operations, and stream ciphers. Chapter 3 handles the hash functions topic, while Chapter 4 describes some more involved notions of cryptanalysis of block ciphers. Chapter 5 considers protocols based on symmetric cryptography. Chapter 6 is based on some basic facts of algebra and on the algorithms used to compute within the usual algebraic structures used in cryptology, while Chapter 7 is devoted to number theory with a strong emphasis put on its algorithmic aspects. Chapter 8 is built around some elements of complexity theory. Chapter 9 treats the important subject of public-key encryption schemes and Chapter 10 contains exercises centered around the notion of digital signatures. Chapter 11 exposes some protocols using public-key cryptography, and Chapter 12 handles the case of hybrid protocols, combining both symmetric and public-key schemes.
A website (http://www.intro-to-crypto.info) has been set up as a companion of this book. It will contain inevitable errata as well as other material related to this book, like challenging tests and more exercises.
Finally, the authors would like to thank Gildas Avoine, Matthieu Finiasz, and all the EPFL students who attended at least one of our lectures, as well as the Springer-Verlag staff for having provided us so many useful comments on these exercises, their solutions, and on the textbook.
We wish the reader a wonderful trip in the exciting world of cryptology!
A Classical Introduction to Cryptography Exercise Book
By Thomas Baignères, Pascal Junod, Yi Lu Jean Monnerat and Serge Vaudenay
This companion exercise and solution book to A Classical Introduction to Cryptography: Applications for Communications Security contains a carefully revised version of teaching material. It was used by the authors or given as examinations to undergraduate and graduate-level students of the Cryptography and Security Lecture at EPFL from 2000 to mid-2005.
A Classical Introduction to Cryptography Exercise Book for A Classical Introduction to Cryptography: Applications for Communications Security covers a majority of the subjects that make up today's cryptology, such as symmetric or public-key cryptography, cryptographic protocols, design, cryptanalysis, and implementation of cryptosystems. Exercises do not require a large background in mathematics, since the most important notions are introduced and discussed in many of the exercises.
The authors expect the readers to be comfortable with basic facts of discrete probability theory, discrete mathematics, calculus, algebra, as well as computer science. Following the model of A Classical Introduction to Cryptography: Applications for Communications Security, exercises related to the more advanced parts of the textbook are marked with a star.
Springer
springeronline.com
ISBN 0-387-27934-2
From the reviews: "This companion exercise and solution book to A Classical Introduction to Cryptography ... contains a carefully revised version of teaching material used by the authors and given as examinations to advanced level students of the Cryptography and Security Lecture at EPFL from 2000 to mid-2005. This book covers a majority of the subjects that make up today's cryptography ... . Exercises do not require an extensive background in mathematics, since the most important notions are introduced and discussed ... ." (Cryptologia, Vol. 30, 2006)