Self-study Lecture: Introduction to cryptography

Reading

Anderson (2nd edition) Chapter 5 on cryptography, especially Sections 5.2, 5.3, 5.6, and 5.7, Gollmann Chapter 14.

Additional resources

Interesting stuff: 

• A Stick Figure Guide to the Advanced Encryption Standard (AES)
• short article about the book Svenska krypto bedrifter - Hur Arne Beurling knäckte den tyska chiffertrafien by Bengt Beckman (both in Swedish only)
• Swedish film about the Geheimschreiber cracking Links to an external site.

 

Videos

 

• Secure hash functions (5 min)
• Cryptosystems and symmetric crypto (7 min)  (updated link)
• Public-key cryptography

Khan academy has some nice visual explanations for some cryptographic algorithms and the mathematics behind them, so I post those instead of re-inventing the wheel.

The whole modern cryptography subsection Links to an external site. is relevant for this:

The fundamental theorem of arithmetic Links to an external site. (3.5 min) talks about prime numbers and factorization.

Public key cryptography: What is it? Links to an external site. (4.5 min) The first minutes are a bit U.S.-centric, but there is a nice visualization of one-way functions and and intuition for the Diffie-Hellman key exchange Links to an external site. (2.5 min).

The discrete logarithm problem Links to an external site. (2 min) introduces modular arithmetic in an intuitive way. For more background on that check modular arithmetic Links to an external site. and modular addition and subtraction. Links to an external site.

The RSA encryption steps (1 Links to an external site. (4 min), 2 Links to an external site. (2.5 min), 3 Links to an external site. (3 min), 4 Links to an external site. (5 min) and the explanation of phi Links to an external site. (2.5 min)) are helpful to understand the basic idea behind public-key cryptography and concretely one of its main algorithms used for, e.g., encrypting and signing e-mail as in the GPG lab. Again, there are some intuitive analogies with colors.