INFORMATION-THEORETIC SECRECY GENERATION Sample Clauses

INFORMATION-THEORETIC SECRECY GENERATION. A. Universal Recovery available at node i such that n P = P . Note that overlap Suppose that k packets P = {p1,. .., pk} are distributed amongst n nodes. Let Pi ⊆ P be the subset of packets initially ∅ ∩ is permitted between these sets (i.e., we do not require Pi Pj = ). The goal of the universal recovery problem is to distribute all k packets to all nodes with a minimum number of transmissions. In [11], it was shown that the minimum number of transmissions required for universal recovery i=1 M (G, {Pi}n ) , i=1 n { } G which is a function of the network topology and initial packet distribution Pi , can be computed in linear time using submodular optimization [16] and network coding [17] if the network is fully connected2. In general, not all k packets need to be transmitted network-wide for universal recovery. As a consequence of [12], the difference between k and packets of common randomness k1 and k2 can be generated. In order for k1 and k2 to be secure from an eavesdropper that observes the transmissions t1,. .., t4 in the information theoretic sense, we require that two conditions hold [12]: • Perfect Secrecy Condition: The mutual information be- tween k1 and k2 and the set of all transmissions is zero.