The Strong Secret Key Rate ofDiscrete Random

Three parties, Alice, Bob and Eve, know the sequences of ran-generated by a discrete memoryless source according to some probability distribution P XY Z. Motivated by Wyner's and Csiszz ar and KK orner's pioneering definition of, and work on, the secrecy capacity of a broadcast channel, the secret key rate of P XY Z was deened by Maurer as the maximal rate M=N at which Alice and Bob can generate secret shared random key bits S 1 ; : : : ; S M 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,)=N = 0, where C t is the collection of messages exchanged between Alice and Bob over the public channel. However , this deenition is not completely satisfactory because only the rate, but not the total amount of information about the key obtained by Eve is bounded. This paper introduces and investigates the strong secret key rate: it is required that the total amount of information about the key obtained by Eve be negligible, i. Using novel results on privacy ampliication by Bennett, Brassard, Cr epeau and Maurer we demonstrate that the known results for the secret key rate also hold for the stronger deenition.