What's Cryptology all about?

In the old days people would meet in person to exchange a secret key which they then could use to exchange secured messages. Today our lives  are very different and there is a demand for quick and easy responses. We exchange secret keys every day when we are working on our laptops and smartphones. We encrypt and authenticate messages without noticing it. "What’s Cryptology all about?” explains the basic principles of modern cryptology, how to exchange a common, secret key and how to encrypt a message such that only the  intended receiver can read it. 

It is explained how digital signatures are made today and why cryptographic hash functions are so important in that context. 

A recent and important application of these hash functions is Bitcoin, Blockchains and cryptocurrencies. It is shown how modern hash functions are constructed.

A new chapter is about to be written in the history of cryptology, namely  when large quantum computers are built. Such computers will be able to break most of the  so-called public-key cryptosystems that are in use today. Luckily there are systems that are  (believed to be) safe even in the presences of quantum computers.

This book is intended to give the reader a good understanding of what cryptology is all about without giving too many mathematical details.  

Contents

1. Introduction 

2. Diffie-Hellman key exchange 

2.1 Modular arithmetic

2.1.1 Modular exponentiation 

3. RSA (Rivest, Shamir, Adleman)

3.1 Prime number generation 

4. AES: Advanced Encryption Standard

4.1 Aftermath 

5. Hash functions 

5.1 The history of cryptographic hash functions 

5.2 Iterated hash functions 

5.3 SHA-256 

5.4 SHA-3 

6. Blockchain and crypto currencies 

6.1 Payment using cash 

6.2 Payment using plastic cards 

6.3 Payment with third party

6.3.1 SET 

6.4 Chaum’s electronic money 

6.5 Blockchain and Bitcoin 

6.5.1 Crypto puzzles

6.5.2 Hash chains 

6.5.3 Blockchain 

6.6 Bitcoin

7. Postquantum cryptology

7.1 Quantum computations

7.2 Quantum resistant systems 

7.3 Signatures based on hash functions 

7.4 Cryptosystems based on linear codes 

7.5 McEliece - public-key encryption 

8. Elliptic curves

8.1 Elliptic curve cryptosystems 

8.2 Elliptic curve signatures (ECDSA) 

8.3 Comparison of discrete logarithms

9. Secret sharing 

10. Digital signatures 

10.1 Hash functions and digital signatures 

10.2 RSA digital signatures 

10.3 El-Gamal’s digital signatures 

11. MAC 

11.1 The security of MAC algorithms

11.2 Iterated MACs 

11.3 Practical MAC algorithms 

11.3.1 Based on block ciphers 

11.3.2 Based on cryptographic hash functions

11.4 Combining authentication and encryption 

12. The rest is history

12.1 The AES competition 

12.2 The SHA-3 competition