BRICS PhD School Core Course

                Cryptography

                       1999 version, Ivan Damgård

This is the home page of the 7-week course in Cryptography for new BRICS PhD students,
(and whoever else may be interested).

We cover some basic concepts and results in theoretical and practical cryptography (see
the plan below for specific subjects), with an emphasis on a theory-based approach.

Time and Place

Documentation

Course Material

• Ivan Damgård: A quick and dirty introduction to Cryptography
- a small warm-up explaining some basic concepts.
Available here as ps file.
• Bellare and Goldwasser: Lecture Notes on Cryptography
- lecture notes from a course taught by the authors at MIT. Very good
coverage of almost any theoretical, complexity based cryptographic
construction. It's BIG, about 200 pages. We will not be able to cover
everything.
Available here as ps file (about 2Mb).
• Ivan Damgård: The hard core of the hard-core bit theorem
- a supplementary note to the proof of the hard-core bit theorem, explains the central
part in detail.
Avalable here as ps file.
• Stefan Wolf: Unconditional Security in Cryptography
- introduction to information theory and unconditional security.
Available here as ps file.
• Ivan Damgård: Note on hash functions. NOTE now new version with references added!
Available here as ps file.
• Ivan Damgård: Note on Privacy Amplification.
Available here as ps file.

Course Plan

• Introdution to some basic concepts and models
• A quick look at conventional ciphers,
• DES, IDEA etc.
• Modern cryptanalysis
• One-way functions,
• variants: one-way permutations, trapdoor functions
• examples: RSA, Discrete log, etc.
• Secure Public-Key Encryption,
• Passive security definitions
• Example systems
• The hard-core bit theorem and connections to encryption
• Chosen ciphertext security,
• definitions
• Cramer-Shoup system
• Digital Signatures
• Hash functions, the hash-and-sign paradigm
• Tree-based authentication
• Unconditional Security
• Information theory
• Shannon's perfect security results
• universal hashing and privacy amplification
• key exchange over noisy channels
• Key management
• Certificate systems
• Secret Sharing, threshold crypto

Links

• The home page of IACR, the International Association for Cryptologic Research. Info on conferences, journals etc. IACR is behind most worthwhile activities of this sort in the area.
• DigiCrime, where you can have almost any digitial crime committed that your heart desires: you can ask them to break into other peoples systems, counterfeit electronic money, etc. Of course it's all a joke, and hilariously funny too, but with a serious purpose: you can find a seemingly endless list of real-life security problems and break-in's that really happened. Of course, DigiCrime were not responsible for those - or so they say...
• The Theory of Cryptography Library, nice source of the very latest papers in the area.
• The theory group at MIT, houses one of the best cryptography research groups in complexity based cryptography. They also have several nice literature search tools on-line.
• The crypto group at ETH Zurich, the leading research group in information theory based cryptography.
• Cryptomathic AS, local software and consulting company, of which I'm a co-founder and -owner. Have a look here to get a feeling for some of the things happening in real life implementations of cryptography.
• Home page of Mihir Bellare, who is one the well known figures in crypto reserach and has one of the most informative personla home pages in the arera. Good source of all kinds of links and publications.