Authenticated key exchange protocols have an important role for building secure communications amongst two or more entities over the networks. Two party authenticated key exchange protocols where each pair of parties must share a secret with each other; a three-party protocol does not cause any key management problem for the parties. In this paper, an extension of two-party key exchange protocol, which is based on Diffie-Hellman key exchange. is proposed. In this protocol each user exchanges secret key with server then each user uses this secret key to exchange session key with each other. The efficiency and the security analysis of this new key exchange protocol are proven in this paper.
We present a general model for communication among a of players, $P\sb{1}$ through $P\sb{k}$, overheard by a passive eavesdropper, Eve, in which all players including Eve are given private inputs that may be correlated. We define and explore secret key exchange in this model. A protocol specifies how the team players behave. A source specifies a distribution on the team players' inputs. Together, a protocol and a source are a system. An adequate notion of secrecy must depend not only on the protocol, but on any relevant Eve may have about the source. We provide precise mathematical definitions of the multiparty secret key exchange problem that take Eve's into account, and allow us to determine whether a given system achieves secret key exchange with respect to any particular type of knowledge for Eve. Our secrecy requirements are information-theoretic and hold even if Eve is computationally unlimited.
We explore the properties of secret key exchange systems and show formally the intuitive result that the team players' inputs must be correlated in order for secret key exchange to be achieved. We show that any source has a finite capacity for secret key exchange even if the team players are allowed unlimited independent randomization. Specifically, the capacity of a source is the largest number of output values of any secret key exchange system using that source. We present an upper bound on the capacity of arbitrary sources.
In the second half of the dissertation, we focus our attention on sources yielding inputs consisting of hands of prespecified sizes from a randomly shuffled deck of cards. We exhibit several secret key exchange protocols designed to work even if Eve is allowed to see the remaining cards in the deck. Let each team player $P\sb{i}$ hold $s\sb{i}$ cards, let Eve hold $s\sb{e}$ cards, and let k be the number of team players. We present a family of key set protocols, a simple family of protocols that achieve one-bit secret key exchange provided that max $s\sb{i}$ + min $s\sb{i} \ge k$ + $s\sb{e}$. We use a game-theoretic argument to exhibit an optimal key set protocol.
Of particular interest is the symmetric case in which each player receives the same fraction
β of the cards in the deck. The efficiency of a secret key exchange protocol is measured by the smallest deck size $d\sb{0}$ for which the protocol is guaranteed of success. The best previous bound (Fischer, Paterson, and Rackoff, 1991) was super-polynomial in 1/
β and only handled the special case of k = 2 and n = 1. We present the transformation protocol, which achieves n-bit secret key exchange in the symmetric case for any deck size $d > d\sb{0}$ = O(n(1/$\beta)\sp{2.71}$). Using the transformation protocol, we show that if
d≥ (42.8)
⋅ (1/$\beta)\sp{2.71}$(n + 0.07), then the capacity of a source in which each team player receives
βd cards is at least 2$\sp{n}$. (Abstract shortened by UMI.)
Multiple parties observing correlated data seek to recover each other's data and attain omniscience. To that end, they communicate interactively over a noiseless broadcast channel - each bit transmitted over this channel is received by all the parties. We give a universal interactive communication protocol, termed the recursive data exchange protocol (RDE), which attains omniscience for any sequence of data observed by the parties and provide an individual sequence guarantee of performance. As a by-product, for observations of length n, we show the universal rate optimality of RDE up to an O(n-1/2√log n) term in a generative setting where the data sequence is independent and identically distributed (in time). Furthermore, drawing on the duality between omniscience and secret key agreement due to Csiszár and Narayan, we obtain a universal protocol for generating a multiparty secret key of rate at most O(n-1/2√log n) less than the maximum rate possible. A key feature of RDE is its recursive structure whereby when a subset A of parties recover each-other's data, the rates appear as if the parties have been executing the protocol in an alternative model where the parties in A are collocated.