Mathematicians from different subjects (analysis, algebra, topology, geometry, cryptography.), physicists, computer scientists, engineers. One of the most interesting features of this new discipline is its interdisciplinary nature. The crucial change of the basic rules (Quantum Physics instead of the classical theory) needs a new theory which is still developping: Quantum Information and Computation. In respect to Quantum Information, one of the mayor breakthroughs of the last years is the possibility to build a quantum computer. These systems seem very promising because of their high speed and because they are not limited by Short algorithm and thus will not be affected by the quantum computer. Multivalued cryptography is based upon multivalued maps and the security of such primitives comes from the impossibility of solving in finite time the systems of equations that describe such maps. Between public key criptosystems the cryptographic primitives which may substitute RSA are very interesting specially those which use elliptic curves, lattices or multivalued functions. Techniques of spectral analysis are used in cryptography to study nonlinear propierties of boolean functions. For that reason the study of such functions is crucial. There are many cryptographic primitives based upon boolean fuctions. The subjects for our research group are related to Public Key Cryptography and to the analysis and criptoanalysis of criptographic primitives. Mathematics helps to design new algorithms and to test their security by criptoanalysis.

All these problems are well know and it is also well known the central role played by the Mathematics in all the solutions proposed by modern Cryptography. Information Technologies present big challenges for Mathematics for example, thanks to the development of electronic communications, the uprise of new tools and utilities together with the universal use of computers, there exists a huge traffic and storage of confidential information, that must be protected. The first subjects of our group are related to Public Key Criptography, Criptoanalysis and Quantic Information Theory. Because of the interdisciplinary nature of the topic, we pretend to involve researchers from other centers and instutes in the Madrid area and also to make collaboration with scientist from other places in/outside Spain. The aim of this program is to found a research group dealing with the mathematical challenges of Information Technologies and their interactions with Computer Science, Physics or Engineering.

Crypto quant