Decided topics, 2D1441

Topics in the order in which they will be covered. If lectures are quick we could add more if they are slow late topics might not be treated in official lectures.
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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