The purpose of cryptography is to protect the confidentiality and integrity of data, services and transactions. Due to the pervasive digitalization of our society, it has become quite important during the last decades. Usually, one divides it in two domains: Asymmetric cryptography is versatile and mathematically sophisticated but slow, and symmetry cryptography is rather limited and rather ad-hoc, but fast. Most systems require the combination of the two. In his lecture, Joan will speak about interesting developments in both domains.

In asymmetric cryptography, so-called elliptic curves have taken the place of RSA, a cryptographic scheme with security based on the infeasibility of factoring large integers into primes. Both systems are currently under stress as they would be broken by a large-scale quantum computer. Such computers operate by evolving wave functions and the principle of superposition has immense potential for solving certain mathematical problems. While it is far from certain that quantum computers could actually be built, Google, IBM and the European Union are massively investing in related research. This has led to frantic activity in developing asymmetric cryptography that would be immune to attacks that would be possible with quantum computers. This is what is currently hot in asymmetric crypto: so-called post-quantum cryptography.

Symmetric cryptography, the specialization of the speaker, is based on two pillars: basic building blocks, called primitives, and the methods how to use them, called modes. Ever since th 70s the primitive par excellence has been the block cipher. This is a kind of mini cryptographic scheme for the encryption of messages of short fixed length. The first block cipher that was used on a wide scale was the so-called Data Encryption Standard (DES) and it operates on 8-byte messages. Nowadays it has been almost fully replaced by the so-called Advanced Encryption Standard (AES) that supports 16-byte messages. Encryption and authentication of arbitrary-length messages of requires the interventions of modes and during the last decades we have witnessed a proliferation of ever more complicated block cipher modes. Fortunately, since 2006, there is also a counter-movement that has set as its goal to clean up symmetric cryptography. This is called symmetric crypto 2.0. It replaces the block cipher primitive by the much simpler cryptographic permutation and has as its modes constructions that are called sponge, duplex and farfalle.