**CRYPTOQUANT. CRYPTOGRAPHY AND QUANTUM INFORMATION**
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. 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 first subjects of our group are related to Public Key
Criptography, Criptoanalysis and Quantic Information Theory.
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. 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.
Mathematics helps to design new algorithms and to test their
security by criptoanalysis.
The subjects for our research group are related to Public Key
Cryptography and to the analysis and criptoanalysis of criptographic
primitives. There are many cryptographic primitives based upon
boolean fuctions. For that reason the study of such functions is
crucial. Techniques of spectral analysis are used in cryptography to
study nonlinear propierties of boolean functions. Between public key
criptosystems the cryptographic primitives which may substitute RSA
are very interesting; specially those which use elliptic curves,
lattices or multivalued functions. 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. 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.
In respect to Quantum Information, one of the mayor breakthroughs of
the last years is the possibility to build a quantum computer. 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. One of the most interesting
features of this new discipline is its interdisciplinary nature.
Mathematicians from different subjects (analysis, algebra, topology,
geometry, cryptography...), physicists, computer scientists,
engineers... should share their efforts, knowledgements and points
of view. There is a common concept to all works, independently of
their approach, devoted to quantum information and computation:
entaglement, the characteristic notion that distinguishs quantum
from classical computation. It is a key concept but however poorly
understood. Between the most imteresting questions related to
entaglement we cite the following: decide wheter a density matrix is
entagled or not, topological entaglement and entaglement and quantum
channels. |