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Quantum cryptanalysis and cryptography

In recent years, quantum computers and quantum channels were often discussed. It is not clear whether we will ever have scalable quantum computers. But if so much of the known public key cryptography breaks down. This is so since a quantum computer can solve discrete log and factorization problems in polynomial time. Cryptographers are challenged to find new schemes on the one hand potentially unbreakable even if quantum computers were available, to break more nowadays schemes using quantum computers, to use quantum mechanisms to design new schemes.

Most of the known public key cryptosystems rely for their security on the difficulty of number theoretic problems like factoring or a discrete logarithm problem.  It is an important task to find other computational problems whose (assumed) difficulty would lead to secure crypto. A survey and analysis of various proposals is a thesis topic.

In fact, number-theoretic crypto falls down if scalable quantum computers are ever built. The above task is sometimes called "post-quantum crypto". Disregarding the hype of this term, a thesis topic is to present the theory of quantum computing, cryptanalysis, and complexity.

A completely different issue are quantum channels. They seem to be in reach and can be used for key agreement, secure to any computational attack and -within the acknowledged laws of physics- seemingly also secure to any physical attack. It is not clear how to embed this technology in useful protocols.

The aim of these topics is to collect, sort and present the up-to-date literature. It is vital that sources that actually consider the problems are separated from ones just trying to catch the hype. This may give rise to several theses.


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