An efficient protocol for unconditionally secure secret key exchange

The multiparty secret key exchange problem is to find a k-player protocol for generating an n-bit random key. At the end of the protocol, the key should be known to each player but remain completely secret from a computationally unlimited eavesdropper, Eve, who overhears all communication among the players. The players are initially dealt hands of cards of prespecified sizes from a deck of distinct cards; any remaining cards are given to Eve. Considered here is the case in which each player receives the same fraction p of the cards in the deck, for /3 in the interval (0,1/k]. The efficiency of a secret key exchange protocol is measured by the smallest deck size do for which the protocol is guaranteed of success. A secret key exchange protocol is presented with do = O(n(l//?)2.71). The best previous bound, by Fischer, Paterson, and Rackoff (1991), was super-polynomial in l/p and only handled the special case of k = 2 and n = 1.