Resources

There are many good free sources of cryptography online. Most of the Wikipedia articles on basic concepts of cryptography are helpful, but there are also lecture notes prepared by well-known researchers in the field as well as full books or drafts of books.

Online Books

• Handbook of Applied Cryptography. Full online version of a printed book on applied cryptography, generously made freely available by its authors Alfred J. Menezes, Paul C. van Oorschot and Scott A. Vanstone, and the publishers CRC Press.
• Lecture Notes on Cryptography. Lecture notes from courses given by Bellare and Goldwasser.
• A Computational Introduction to Number Theory and Algebra. Full online version of a printed book on computational number theory, generously made freely available by its author Victor Shoup and the publisher Cambridge University Press.
• Codes, Ciphers and Codebreaking. Historical account of cryptography by Greg Goebel. He is not a professional cryptographer, but in particular the historical account in his book is interesting.
• The Not So Short Introduction to Latex2ε. Short introduction to Latex by Tobias Oetiker, Hubert Partl, Irene Hyna and Elisabeth Schlegl. This is the best guide to LaTex ever written.

Books

We use the first book below of Stinson as the course book, and I recommend one of the other books to students who wish to buy more than one book.

• Cryptography: Theory and Practice, Third Edition by Douglas R. Stinson (main source for this course).
• Introduction to Modern Cryptography: Principles and Protocols by Jonathan Katz and Yehuda Lindell. Students who buy two books, should buy this one. It is a more comprehensive and rigorous, but it still covers much of the same topics as Stinson's book.
• Foundations of Cryptography -- Volume 1 and Volume 2 by Oded Goldreich. These books are more theoreticaly oriented and contains interesting discussions and historical remarks along with definitions and results. Drafts of these books are still available online (see the links), but please buy the books if you want to use this book.
• Applied Cryptography, Second Edition by Bruce Schneier. This book is more practice oriented than the other books. It is not so relevant to the course, but you should know about this book if you hope work in computer security.
• Elliptic Curves in Cryptography by Ian F. Blake, Gadiel Seroussi, and Nigel P. Smart. This is one of the standard books on elliptic curves in cryptography.

Links

Most Important Facts

• Alice and Bob, and Eve.

Classic Ciphers

• Cipher
• Shift Cipher
• Substitution Cipher
• Affine Cipher
• Vigenère Cipher
• Hill Cipher
• Permutation Cipher

Classic Cryptanalysis

• Frequency Analysis
• Letter Frequencies
• Bigram, Trigram, . . ., N-gram
• Dot Product and Inner Product
• Kasisiski Test
• Index of Coincidence

Perfect Secrecy and Information Theory

• Bayes' Theorem
• Entropy
• Concavity
• Jensen's Inequality
• Kraft's Inequality
• Shannon's Source Coding Theorem
• Huffman Coding
• Unicity Distance
• A Mathematical Theory of Communication, Shannon, 1948. One of the most influential papers ever written.
• Communication Theory of Secrecy Systems, Shannon, 1949.
• Rényi Entropy
• Min Entropy
• Leftover Hash Lemma

Modern Ciphers

• Kerckhoffs' Principle
• Substitution-Permutation Network
• A Tutorial on Linear and Differential Cryptanalysis, Heys. The treatment in Stinson's book is based on this paper.
• DES
• Standing the Test of Time: The Data Encryption Standard
• Triple-DES
• Linear Cryptanalysis of DES, Junod. Describes findings of an actual implementation of linear cryptanalysis of DES.
• Modes of Operations
• NIST Recommendation for Block Cipher Modes of Operation, 2001.

Probability Theory

• Birthday Paradox

Elementary Number Theory

• Extended Euclidean Algorithm
• Bezout's Lemma
• Chinese Remainder Theorem
• Coset
• Lagrange Theorem
• Euler's Phi Function
• Fermat's Little Theorem
• Euler's Theorem
• Modular Multiplicative Group of Integers
• Finite Field
• Quadratic Residue
• Jacobi Symbol
• Prime Number Theorem
• Solovay-Strassen Primality Test
• Integer Factorization
• Discrete Logarithm

Public Key Cryptosystems

• Public-Key Cryptography
• Merkle's Puzzles
• The RSA Problem, Rivest and Kaliski. A paper giving an overview of the history of the RSA problem.
• Rabin's Cryptosystem
• Key Exchange
• Diffie-Hellman Key Exchange.

Random Oracle Model

• How To Prove Yourself: Practical Solutions to Identification and Signature Problems, Fiat and Shamir, 1987. Paper that, among other important contributions, suggest the heuristic of considering a hash function as if it was random.
• Random oracles are practical: A paradigm for designing efficient protocols, Bellare and Rogaway, 1993. Proposing the random oracle model as a general practical tool to construct efficient cryptographic schemes.
• The Random Oracle Methodology, Revisited, Canetti, Goldreich, and Halevi, 1998. First paper proving that the random oracle methodology is unsound.
• Indifferentiability, Impossibility Results on Reductions, and Applications to the Random Oracle Methodology, Maurer, Renner, and Holenstein. Especially the first part of this paper gives a simple explaination of the key issue with random oracles.

Hashfunctions

• Hashfunction
• Merkle-Damgård
• Sponge function
• Universal Hashing
• CBC-MAC

Pseudo-Random Generators

• Hardware Random Number Generator
• Pseudo-Random Generator
• /dev/random
• Analysis of the Linux Random Number Generator, Zvi Gutterman, Benny Pinkas, and Tzachy Reinman.
• The Linux Pseudorandom Number Generator Revisited, Lacharme, Röck, Strubel, Videau.
• Yarrow
• Fortuna
• Attacks Against Weak PRGs