- 1. Cryptographic assumptions, examples, discussions and comparisons.
- 2. The definition of a good pseudorandom generator. Construction of such a generator from any one-way permutation.
- 3. The definition of a good pseudorandom function. Construction of such a generator from any good pseudorandom generator.
- 4. Security of encryption. Semantic security (no information is leaked) and non-malleability (cannot produce encryptions of related messages). A system by Cramer and Shoup.
- 5. Zero-knowledge proofs. Proofs for some of the following: graph-isomorphism, graph-colorability or even PSPACE-complete problems. Perfect, statistical and computational flavors. Proofs of knowledge.
- 6. Zero-knowledge arguments. Arguments are proofs whose soundness depends on computational assumptions while the zero-knowledge property usually is perfect.
- 7. Integer lattices. The algorithm of LLL with some application to cryptanalysis, possibly breaking knapsack cryptosystems. Using hardness assumptions on the computation of shortest vector to create cryptosystems.
- 8. Elliptic curve cryptography. The definition of an elliptic curve group. Discussions of which cryptographic constructions that can be used with elliptic curve groups.
- 9. Factorization and discrete logarithms. A study of the best algorithms on classical computers (quadratic sieve, number field sieve). Possibly also a discussion of algorithms for the problems on quantum computers.
- 10. Cryptanalysis of some symmetric crypto scheme. Alternatives at this point: Linear analysis of DES, attack by Biryukov and Shamir on A5/1 or the attack by Fluhrer, Mantin and Shamir on the key scheduling of RC4.

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Senast ändrad 20 mars 2003

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