Mathematical Building Blocks Sample Clauses

Mathematical Building Blocks. A. Secrecy via Coded Cooperative Data Exchange Our approach is motivated by recent results on secret key agreement via the coded cooperative data exchange (CCDE) problem. Introduced first by El Rouayeb, et al. in [26], the CCDE problem has received significant attention (e.g., [14, 27]) and is stated as follows. Suppose that k packets are distributed among a network of t clients. What is the minimum number of transmissions M required to recover all k packets at all t clients? In [28], it was shown that if the network5 is fully connected, then the CCDE problem can be solved in polynomial time. At roughly the same time, Chan [19] and Milosavljevic, et al. [32] independently established similar results. In general, less than k transmissions are required by optimal CCDE solutions in fully-connected networks. The 5While the networks considered in this work need not be fully connected at the physical layer (PHY), cryptographic protocols are often implemented at higher layers that see an abstracted, one-hop topology. Moreover, a number of emerging wireless stacks employ cooperative flooding protocols at the PHY and present a fully-connected topology to higher layers [29–31].

Mathematical Building Blocks