Cryptology deals with mathematical techniques for design and analysis of algorithms and protocols for digital security in the presence of malicious adversaries. For example, encryption and digital signatures are used to construct private and authentic communication channels. Another example is secure computation, which in principle enables an arbitrary computation to be distributed among the processors in a network so that computations remain secret and are performed correctly, even if a certain quorum of the network is under full control by an adversary.
The security of cryptographic methods in use today, such as RSA-encryption, -signatures, and Diffie-Hellman key-exchange, relies on limits to the computational power of potential adversaries. This motivates the following question: which tasks can still be performed securely even in the presence of a computationally unrestricted adversary or, perhaps more realistically, one who has access to a quantum computer?
We discuss several important cryptographic primitives that even withstand such strong (hypothetical) adversaries. As a corollary, these examples will also exhibit interesting connections with algebra, number theory, combinatorics and probability theory.
A (tentative) list of topics is as follows: basics of the mathematical theory of communication and coding theory, secure message transmission, authentication codes, entropic security, secret sharing, secure computation, entropy smoothing (extractors), secret-key agreement by public discussion, bounded storage model.
Voorkennis
Basic undergraduate algebra and probability theory. Prior knowledge of cryptology (e.g. the Mastermath Course on Cryptology) is helpful, but certainly not necessary.
Literatuur
Hand-outs
Toetsing
Graded home work exercises