Public Key Protocols over Twisted Dihedral Group Rings

Key management is a central problem in information security. The development of quantum computation could make the protocols we currently use unsecure. Because of that, new structures and hard problems are being proposed. In this work, we give a proposal for a key exchange in the context of NIST recommendations. Our protocol has a twisted group ring as setting, jointly with the so-called decomposition problem, and we provide a security and complexity analysis of the protocol. A computationally equivalent cryptosystem is also proposed

Public Key Protocols over Twisted Dihedral Group Rings

Key management is a central problem in information security. The development of quantum computation could make the protocols we currently use unsecure. Because of that, new structures and hard problems are being proposed. In this work, we give a proposal for a key exchange in the context of NIST recommendations. Our protocol has a twisted group ring as setting, jointly with the so-called decomposition problem, and we provide a security and complexity analysis of the protocol. A computationally equivalent cryptosystem is also proposed

SECURE GROUP COMMUNICATIONS USING TWISTED GROUP RINGS

In this paper we introduce a Group Key Management protocol following the idea of the classical protocol that extends the well-known Diffie–Hellman key agreement to a group of users. The protocol is defined in a non-commutative setting, more precisely, in a twisted dihedral group ring. The protocol is defined for an arbitrary cocycle, extending previous key agreements considered for two users. The main objective of this work is to show that there is no lack of security derived from the fact that a larger amount of public information is known by an external observer

55 Intercambio de clave multiusuario en anillos de grupo

La Criptografía que utilizamos actualmente para asegurar nuestras comunicaciones, podría verse comprometida en los próximos años. Se están produciendo cambios en los estándares de los protocolos de clave pública, ante la mejora de los métodos de criptoanálisis, y el posible advenimiento de ordenadores cuánticos suficientemente potentes para implementar el algoritmo de Shor o sus variantes. En este trabajo, que constituye un resumen de [3], proponemos un ambiente alternativo para ofrecer seguridad en un contexto post-cuántico, el álgebra no conmutativa. En particular, proponemos un anillo de grupo torcido mediante un cociclo, y protocolos de acuerdos de clave para dos, y también de varios usuarios; estos últimos se enfrentan a problemas específicos que tenemos en cuenta a la hora de proponer un protocolo post-cuántico para ellos