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
- 1. Cryptographic assumptions, examples, discussions
- 2. The definition of a good pseudorandom generator.
Construction of such a generator from any one-way
- 3. The definition of a good pseudorandom function.
Construction of such a generator from any good pseudorandom
- 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
Senast ändrad 20 mars 2003
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