# Cryptography

### 1999 version, Ivan Damgård

[last update: November 18, 1999]

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

Tuesday 13-14, Aud. D4
Thursday 9-11 Aud. D4

### Documentation

Will consist of hand-in exercises during the course, and a take-home exam at the end of
the course.

### 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.
More material will be added here as we move along, in case I have it available electronically.

### Course Plan

We will be covering the following main points in roughly the order listed.

• 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