## Communication Complexity of Group Key Distribution (1998)

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Citations: | 116 - 0 self |

### BibTeX

@MISC{Becker98communicationcomplexity,

author = {Klaus Becker and Uta Wille},

title = {Communication Complexity of Group Key Distribution},

year = {1998}

}

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### Abstract

Communication complexity has always been an important issue when designing group key distribution systems. This paper systematically studies what can be achieved for the most common measures of protocol complexity. Lower bounds for the total number of messages, the total number of exchanges, and the number of necessary rounds are established, whereby models that allow broadcasting have to be distinguished from those that do not. For every measure of protocol complexity, we furthermore show that the corresponding bound is realistic for Diffie--Hellman-based protocols by referring to or introducing protocols that match the bound or exceed it by only one.

### Citations

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(Show Context)
Citation Context ...rp if broadcasting is possible. In order to describe the subsequent Diffie--Hellman-based protocols, let G be a finite cyclic group of order q and let ff be a generator of G (e.g., Diffie and Hellman =-=[DH72]-=- use G = Z p , where p is a prime). Furthermore, we assume that the individual participants choose their random secrets from Z q . A basic idea of the following protocol is to use a Diffie-Hellman key... |

226 | Diffie-Hellman Key Distribution Extended to Group Communication
- Steiner, Tsudik, et al.
- 1996
(Show Context)
Citation Context ... al. [ITW82] and Burmester and Desmedt [BD94]. Beyond the security of the systems, protocol complexity has always been an important issue when designing group key distribution systems. Steiner et al. =-=[STW96], for inst-=-ance, defined a class of "generic n-party DH protocols " for which they showed that security is based on the intractability of the Diffie--Hellman problem. Subsequently, they introduced two ... |

216 |
A secure and efficient conference key distribution system
- Burmester, Desmedt
- 1994
(Show Context)
Citation Context ...posed to extend Diffie--Hellman key exchange to multiparty key distribution. Most notable and best known among those proposals are the protocols by Ingemarson et al. [ITW82] and Burmester and Desmedt =-=[BD94]. Bey-=-ond the security of the systems, protocol complexity has always been an important issue when designing group key distribution systems. Steiner et al. [STW96], for instance, defined a class of "ge... |

135 | Consistent global states of distributed systems: Fundamental concepts and mechanisms
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- 1993
(Show Context)
Citation Context ... protocol, presuming that every party is allowed to send arbitrarily many messages with every time tick and to receive arbitrarily many messages sent by other parties at the beginning of a round (cf. =-=[BM93]-=- p. 133). - simple rounds: minimum number of required synchronous rounds, presuming that every party sends and receives at most one message per round (cf. [ABM87]). Whereas the total number of message... |

128 |
A Conference Key Distribution System
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- 1982
(Show Context)
Citation Context ...6, various solutions have been proposed to extend Diffie--Hellman key exchange to multiparty key distribution. Most notable and best known among those proposals are the protocols by Ingemarson et al. =-=[ITW82]-=- and Burmester and Desmedt [BD94]. Beyond the security of the systems, protocol complexity has always been an important issue when designing group key distribution systems. Steiner et al. [STW96], for... |

34 |
New gossips and telephones
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(Show Context)
Citation Context ...n parties cannot be less than dlog 2 ne, where dxe denotes the smallest integer greater than or equal to x (for the gossip problem it can be shown that the lower bound for odd n is dlog 2 ne + 1; see =-=[Kn75]-=-). From these results and observations we derive the following bounds for contributory key distribution systems without broadcasting. Theorem 1 (without broadcasts) Let P be a contributory group key d... |

32 | Diffie- hellman key distribution extended to groups - Steiner, Tsudik, et al. - 1996 |

28 | Gossips and telephones
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- 1972
(Show Context)
Citation Context ...concerning how many telephone calls are needed to distribute n pieces of information held by n different parties to all the participating parties is known in the literature as the gossip problem, see =-=[BS72]-=- and [Be72]. Baker and Shostak [BS72] have shown that the minimum number of required phone calls is 2 \Delta n \Gamma 4, assuming that ns4. This result immediately provides us with a lower bound for t... |

23 |
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(Show Context)
Citation Context ...rties at the beginning of a round (cf. [BM93] p. 133). - simple rounds: minimum number of required synchronous rounds, presuming that every party sends and receives at most one message per round (cf. =-=[ABM87]-=-). Whereas the total number of messages of a protocol measures the number of packages sent, the number of exchanges can be considered to be the number of connections to be established during a protoco... |

5 |
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(Show Context)
Citation Context ...how many telephone calls are needed to distribute n pieces of information held by n different parties to all the participating parties is known in the literature as the gossip problem, see [BS72] and =-=[Be72]-=-. Baker and Shostak [BS72] have shown that the minimum number of required phone calls is 2 \Delta n \Gamma 4, assuming that ns4. This result immediately provides us with a lower bound for the total nu... |

1 |
Design und Analyse von Konferenzschl usselsystemen
- Becker
- 1996
(Show Context)
Citation Context ...th respect to certain measures of protocol complexity. Following this line of research, we systematically analyze Diffie--Hellman-based key distribution protocols in terms of protocol complexity (see =-=[Be97]-=-). Lower bounds for the total number of messages, the total number of exchanges, and the number of necessary rounds are established, whereby models that allow broadcasting have to be distinguished fro... |

1 |
How to Communicate Efficiently
- Beutelspacher
- 1990
(Show Context)
Citation Context ...s protocol because the vectors ~ b 1 ; : : : ; ~ b d form a basis of the vector space GF (2) d . This cube pattern is also used in [Kn75] to manage the gossip problem with a minimum number of rounds. =-=[Bu90]-=- suggests using parallel classes in more general geometric structures to distribute information between n parties, which might as well serve as a basis for group key distribution protocols. In order t... |