Many problems in information security can be resolved using combinatorial structures, primarily geometries. In fact, often the most efficient solutions kn'awn are provided by schemes based on geometries. In this expository article we look at two problems in information security and discuss proposed geometrical solutions. In addition, we generalise two known constructions for Key Distribution Pa...

A (g; b) key distribution scheme allows conferences of g users to generate secret keys, such that disjoint coalitions of b users cannot gain any information on the generated key (in the information theoretic sense). In this work, we study the relationships between communication and space eeciency of key distribution schemes. We prove that communication does not help in the context of unrestrict...

Very recently, Jung, Paeng and Kim [IEEE Communications Letters, Vol 8, No 7, pp 446–448, July 2004] have demonstrated the insecurity of Xu and Tilborg’s ID-based conference key distribution scheme, and in addition, have revised the scheme to fix the security flaws discovered by them. However, in this paper, we show that Jung-Paeng-Kim’s revised scheme is still insecure since it is vulnerable t...

In 1997, H. Sakazaki, E. Okamato and M. Mambo [4] proposed an ID-based key distribution system on an elliptic curve over Zn. We will cryptanalyze the scheme and demonstrate that when the hashed ID length is about 160 bits, the scheme is insecure. To be specific, after requesting a small number of keys from the Center, our attack allows a new valid key to be constructed without any further inter...

Decentralized group key management schemes for supporting secure group communication systems have been studied in the two flavors of contributory key agreement and decentralized key distribution. However, the primary focus has been on the former because the latter have been criticized for additional overheads of establishing secure channels and for the possibility of weak keys produced by the g...

Institute of Computer Science, The Hebrew University, Jerusalem, Israel Institute of Theoretical Physics and Astrophysics, University of Gdańsk, Poland Institute for Quantum Information, California Institute of Technology, Pasadena, USA Mathematical Science Research Institute, Berkeley, USA Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK Isaac N...