The Strong Secret Key Rate of Discrete Random Triples

Three parties, Alice, Bob and Eve, know the sequences of random variables X N = [X 1 ; X 2 ; : : : XN ], Y N = [Y 1 ; Y 2 ; : : : Y N ] and Z N = [Z 1 ; Z 2 ; : : : ZN ], respectively, where the triples (X i Y i Z i ), for 1 i N , are generated by a discrete memoryless source according to some probability distribution PXY Z . Motivated by Wyner's and Csisz'ar and Korner's pioneering definition of, and work on, the secrecy capacity of a broadcast channel, the secret key rate of PXY Z was defined by Maurer as the maximal rate M=N at which Alice and Bob can generate secret shared random key bits S 1 ; : : : ; SM by exchanging messages over an insecure public channel accessible to Eve, such that the rate at which Eve obtains information about the key is arbitrarily small, i.e., such that lim N!1 I(S 1 ; : : : ; SM ; Z N ; C t )=N = 0, where C t is the collection of messages exchanged between Alice and Bob over the public channel. However, this definition is n..

The ultimate physical limits of privacy

10.1038/nature13132Nature5077493443-447NATU