© 2016

Cryptography Made Simple


  • Author is a leading researcher and practitioner in cryptography

  • Textbook emphasizes security definitions

  • Suitable for undergraduate courses in computer science, mathematics and engineering


Part of the Information Security and Cryptography book series (ISC)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Mathematical Background

    1. Front Matter
      Pages 1-1
    2. Nigel P. Smart
      Pages 27-50
    3. Nigel P. Smart
      Pages 51-66
    4. Nigel P. Smart
      Pages 67-78
    5. Nigel P. Smart
      Pages 79-93
    6. Nigel P. Smart
      Pages 95-115
  3. Historical Ciphers

    1. Front Matter
      Pages 117-117
    2. Nigel P. Smart
      Pages 119-132
    3. Nigel P. Smart
      Pages 133-161
    4. Nigel P. Smart
      Pages 163-177
    5. Nigel P. Smart
      Pages 179-194
  4. Modern Cryptography Basics

    1. Front Matter
      Pages 195-195
    2. Nigel P. Smart
      Pages 197-223
    3. Nigel P. Smart
      Pages 225-240
    4. Nigel P. Smart
      Pages 241-269
    5. Nigel P. Smart
      Pages 295-311
    6. Nigel P. Smart
      Pages 313-347

About this book


In this introductory textbook the author explains the key topics in cryptography. He takes a modern approach, where defining what is meant by "secure" is as important as creating something that achieves that goal, and security definitions are central to the discussion throughout.

The chapters in Part 1 offer a brief introduction to the mathematical foundations: modular arithmetic, groups, finite fields, and probability; primality testing and factoring; discrete logarithms; elliptic curves; and lattices. Part 2 of the book shows how historical ciphers were broken, thus motivating the design of modern cryptosystems since the 1960s; this part also includes a chapter on information-theoretic security. Part 3 covers the core aspects of modern cryptography: the definition of security; modern stream ciphers; block ciphers and modes of operation; hash functions, message authentication codes, and key derivation functions; the "naive" RSA algorithm; public key encryption and signature algorithms; cryptography based on computational complexity; and certificates, key transport and key agreement. Finally, Part 4 addresses advanced prot ocols, where the parties may have different or even conflicting security goals: secret sharing schemes; commitments and oblivious transfer; zero-knowledge proofs; and secure multi-party computation.

The author balances a largely non-rigorous style — many proofs are sketched only — with appropriate formality and depth. For example, he uses the terminology of groups and finite fields so that the reader can understand both the latest academic research and "real-world" documents such as application programming interface descriptions and cryptographic standards. The text employs colour to distinguish between public and private information, and all chapters include summaries and suggestions for further reading.
This is a suitable textbook for advanced undergraduate and graduate students in computer science, mathematics and engineering, and for self-study by professionals in information security. While the appendix summarizes most of the basic algebra and notation required, it is assumed that the reader has a basic knowledge of discrete mathematics, probability, and elementary calculus.


Block Ciphers Digital Signatures Discrete Logarithms Elliptic Curves Finite Fields Hash Functions Historical Ciphers Information-Theoretic Security Key Exchange Message Authentication Codes Primality Testing Provable Security Public-Key Cryptography Secure Multiparty Computation Stream Ciphers Symmetric-Key Cryptography The Enigma Machine

Authors and affiliations

  1. 1.Computer Science DeptUniversity of BristolBristolUnited Kingdom

About the authors

Nigel P. Smart is a professor of computer science in the University of Bristol. He is a leading cryptographer, with particular expertise in elliptic curve cryptography, pairing-based cryptography, and multi-party computation. Among his achievements and recognition, he received a Royal Society Wolfson Research Merit Award, he is currently the Vice President of the International Association for Cryptologic Research (IACR), and he has chaired the most important academic conferences in this discipline. Beyond his academic experience he also worked in industry (HP Laboratories), and he has cofounded a number of startups, most recently Dyadic Security, a company that deploys distributed cryptographic solutions based on multi-party computations. Prof. Smart was made a Fellow of the IACR in 2016 for essential contributions to the theory and practice of real-world cryptography and outstanding service to the association.

Bibliographic information

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“The goal of cryptography is to obfuscate data for unintended recipients. … The book is divided into four parts. … The book is very comprehensive, and very accessible for dedicated students.” (Klaus Galensa, Computing Reviews,, October, 2016)

“Cryptography made simple is a textbook that provides a broad coverage of topics that form an essential working knowledge for the contemporary cryptographer. It is particularly suited to introducing graduate and advanced undergraduate students in computer science to the concepts necessary for understanding academic cryptography and its impact on real-world practice, though it will also be useful for mathematicians or engineers wishing to gain a similar perspective on this material.” (Maura Beth Paterson, Mathematical Reviews, July, 2016)

“This is a very thorough introduction to cryptography, aimed at lower-division undergraduates. It is an engineering textbook that uses modern mathematical terminology (such as groups and finite fields). … Bottom line: really for engineers, and a useful book if used carefully; the organization makes is easy to get overwhelmed by the background material before you get to the 'good stuff', and even the good stuff has an overwhelming amount of detail.” (Allen Stenger, MAA Reviews,, June, 2016)

“This very thorough book by Smart (Univ. of Bristol, UK) is aimed at graduate students and advanced undergraduates in mathematics and computer science and intended to serve as a bridge to research papers in the field. … Summing Up: Recommended. Upper-division undergraduates through professionals/practitioners.” (C. Bauer, Choice, Vol. 53 (10), June, 2016)